Research ArticleA Model of High-Dimensional Feature Reduction Based onVariable Precision Rough Set and Genetic Algorithm inMedical Image

Zhou Tao 12 Lu Huiling 2 Fuyuan Hu 3 Shi Qiu 4 and Wu Cuiying5

1School of Computer Science and Engineering North Minzu University Yinchuan 750021 China2School of Science Ningxia Medical University Yinchuan 750004 China3School of Electronic amp Information Engineering Suzhou University of Science and Technology Suzhou 215009 China4Key Laboratory of Spectral Imaging Technology CAS Xirsquoan Institute of Optics and Precision MechanicsChinese Academy of Sciences Xirsquoan 710119 China5Human Resources Department 4e Second Affiliated Hospital of Xiamen Medical College Xiamen 361021 China

Correspondence should be addressed to Lu Huiling lu_huiling163com

Received 29 March 2020 Accepted 20 April 2020 Published 30 May 2020

Guest Editor Zaoli Yang

Copyright copy 2020 Zhou Tao et al +is is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Aiming at the shortcomings of high feature reduction using traditional rough sets such as insensitivity with noise data and easyloss of potentially useful information combining with genetic algorithm in this paper a VPRS-GA (Variable Precision RoughSet--Genetic Algorithm)model for high-dimensional feature reduction of medical image is proposed Firstly rigid inclusion of thelower approximation is extended to partial inclusion by classification error rate β in the traditional rough set model and the abilitydealing with noise data is improved Secondly some factors of feature reduction are considered such as attribute dependencyattributes reduction length and gene coding weight A general framework of fitness function is put forward and different fitnessfunctions are constructed by using different factors such as weight and classification error rate β Finally 98 dimensional featuresof PETCT lung tumor ROI are extracted to build decision information table of lung tumor patients+ree kinds of experiments inhigh-dimensional feature reduction are carried out using support vector machine to verify the influence of recognition accuracyin different fitness function parameters and classification error rate Experimental results show that classification accuracy isaffected deeply by different weight values under the invariable classification error rate condition and by increasing classificationerror rate under the invariable weigh value condition Hence in order to achieve better recognition accuracy different problemsuse suitable parameter combination

1 Introduction

Rough set theory was developed by Pawlak in 1982 [1] and itis a mathematical tool to deal with vagueness and uncer-tainty +e classification ability unchanged in its main ideadecision or classification rules of problem are derived byknowledge reduction [2] +e Variable Precision Rough Set(VPRS) theory proposed by Ziarko and is an extension oforiginal rough set model For inconsistent informationsystem the VPRS model allows a flexible approximationboundary region by a precision variable β [3] When β 0Pawlak rough set model is a special case of variable precision

rough set model +e main task of variable precision roughset model is to solve the problem of data classification withno function or uncertainty +e hierarchical model of at-tribute reduction for variable precision rough set is studiedby Xiaowei [4] +ere is abnormal phenomenon in existingattribute reduction models therefore a variable precisionrough set attribute reduction algorithm with the propertyof interval is proposed and the reduction abnormalproblem is transformed into a hierarchical model repre-sentation and the reduction anomaly is gradually elimi-nated by the layer-by-layer reduction model Jie andJiayang [5] puts forward that there may be a reduction

HindawiMathematical Problems in EngineeringVolume 2020 Article ID 7653946 18 pageshttpsdoiorg10115520207653946

jump phenomenon in variable precision rough set featurereduction which affects the quality of reduction and bringsthe problem of attribute reduction of variable precisionrough set Pei and Qinghua [6] proposes an FCM clusteringalgorithm based on variable precision rough set accordingto the threshold characteristics of the variable precisionrough set model the algorithm divides the objects in theedge of the cluster into the positive negative and boundaryregions to improve the accuracy of clustering Two dif-ferent solutions of variable precision rough set attributereduction algorithm are proposed by Hao and Junan [7]based on tolerance matrix and minimal reduction of at-tribute core the attribute kernel idea of variable precisionrough set is proposed +e experimental results show thatthe two algorithms can reduce the search space and im-prove the efficiency of the algorithm

Feature reduction is one of the core contents of rough settheory in the condition of keeping the classification abilityfor knowledge base unchanged we delete irrelevant orunimportant knowledge which can reduce the dimension ofthe decision system reduce the time complexity and im-prove the efficiency of the algorithm [8] People want to findthe minimum reduction but it has been proved to be an NP-Hard problem [9] the main research is how to find thesecond optimal solution Genetic algorithm is a computa-tional model which is based on the natural selection andevolution mechanism its core idea is inspired by the naturalselection rule of the survival of the fittest can achieve ahighly parallel random and adaptive search is not easy tofall into local optimal [10] can find the global optimal so-lution with high probability and has great advantage insolving the NP-Hard problem

In this paper a new algorithm of PETCT high-di-mensional feature selection is proposed based on geneticalgorithm and variable precision rough set model On onehand the algorithm considers the value of chromosomecoding the minimum number of attributes and the de-pendency of attributes to construct a general fitness functionframework and adjusting weight coefficient of each factor toachieve different fitness function on the other hand aimingat the limitation of Pawlak rough set model introducing theclassification error rate of β it extends rigid inclusion of thelower approximation for traditional rough set to partialinclusion not only improving the concept of approximatespace but also enhancing the ability to deal with noise dataand changing the range of β to achieve different fitnessfunction Finally through extracting PETCT lung cancerROI 98-dimensional feature to construct the informationdecision table of lung cancer patients 8 group experimentsof high-dimensional features selection are done by usingsupport vector machine to classify and recognize reductionsubsets to verify the degree of influence on the differentweights and different classification error rate and find a setof parameters suitable for this problem (ϖ1 1ω2

1ω3 0 β 06) +e experimental results show that dif-ferent parameters can be used to get different experimentalresults so we should choose the appropriate parametercombination according to different problems so as to getbetter recognition accuracy

2 Materials and Methods

21PETCT PETCTis a kind of advancedmedical imagingtechnology which is a combination of the good performanceof PET and CT on the same device and provides the ana-tomical and functional metabolism of the subjects under thesame conditions [11] PET is a functional image it canprovide metabolic information of tissue and organ andreflect functional changes of the human body from themolecular level such as the physiological pathologicalbiochemical and metabolic but has poor spatial resolutioncannot be accurately located and cannot display the ana-tomical information of the lesions [12] CT belongs to theanatomical structure of images with high spatial resolutionand density resolution it has unique advantages in dis-playing the anatomical structure and density of the body[13] it also can provide detailed anatomical information ofhuman organs and tissues but can not reflect the functionalinformation of tissues and organs [14] (Figure 1)

22 Genetic Algorithm Genetic algorithm is a computa-tional model which is based on the natural selection andevolution mechanism its core idea is inspired by the naturalselection rule of the survival for the fitness so the searchalgorithm is an iterative process of survival and detection isa very effective search and optimization technique canachieve a highly parallel random and adaptive searchcannot easily fall into local optimum and can find the globaloptimal solution with high probability and its robustness isgood [15] General use of genetic algorithm for reduction isachieved by a binary coding 1 indicates that the positionselects the corresponding attribute while 0 indicates that thecorresponding attribute is not selected Genetic algorithmconsists of four parts encoding and decoding fitnessfunction genetic operator and control parameters geneticoperators include selection operator crossover operatorand mutation operator +e selection operator is generallyselected by roulette wheel selection method according to theselection probability pi (fi1113936

Mi1 fi) crossover operator is

a single point crossover with a certain probability p to selectindividuals to participate in crossover mutation operatorselects the individual with the probability p and randomlyselects the corresponding gene of the variant individuals tooperate [16] +e general steps are as follows determiningthe initial population and calculating the target value of eachindividual in the population and the corresponding value ofthe fitness function choosing the chromosomes with highfitness value and forming a matching set (selection)according to certain rules of reproduction (crossover andmutation) to meet the conditions to stop the genetic iter-ation or return to step 3 (Figure 2)

23 Variable Precision Rough Set Ziarko proposed thevariable precision rough set model in 1993 he first proposedthe concept of classification error rate in the case of a givenclassification error rate the objects with the same attributescan be classified into classes as many as possible [17]

2 Mathematical Problems in Engineering

Definition 1 (equivalence class) Assuming that R is anequivalence relation on K a collection of all elementsequivalent to an element k in K is called an equivalence classof k denoted as [k]

Definition 2 (indiscernibility relation) If PsubeR and Pne ϕthen capP is also an equivalence relation it is called theindiscernibility relation on P denoted as ind [P]

Definition 3 (upper approximation and lowerapproximation) +e knowledge base ofK (U R) XsubeU Ris equivalent to the relationship between U +e lower ap-proximation of X can be understood as all of the classifi-cation errors that are not greater than β are included in the Requivalence class in X +e upper approximation of X can beunderstood as the intersection of all those with classificationerror not greater than β and equivalence classes with X is notempty [18] Expressions are as follows

RX β cup Y isinU

R

1113868111386811138681113868111386811138681113868YsubeX1113882 1113883

RXβ cup Y isinU

R

1113868111386811138681113868111386811138681113868YcapXneφ1113882 1113883

(1)

Assume that the decision information table S (U AV f ) where U is a sample of the universe and a nonemptyfinite sample set U x1 X2 x3 Xn and Xi representseach sample A PcupQ P represents a collection of condi-tional attributes Q represents a set of decision attributes V

represents the range of attribute f U times A⟶ V is an in-formation function that gives an attribute value for eachattribute of each xi that is foralla isin A x isin U f(x a) isin Va X

and Y represent nonempty set in finite field U P QsubeA

represents the condition attribute set and decision attributeset ind (P) ind (Q) is an indiscernibility relation determinedby P Q ind (P) is a collection of equivalence classes calledcondition class expressed in UP ie Uind(P) P1 P2P3 Pn ind (P) is a collection of equivalence classes calleddecision class expressed in UQ that is Uind(Q) Q1 Q2Q3 Qn

Definition 4 (majority inclusion relation) If there is a e isin Y

for each e isin X then Y contains X denoted as Y X then

c(X Y) 1 minus |XcapY||X| |X|gt 0

0 |X| 01113896 (2)

where |X| represents the cardinality of the set X and c(X Y)

is the relative classification error rate of set X on set YMake (0le βlt 05) the majority inclusion relation is

defined as YsupeβX⟺ c(X Y)le β the ldquomajorityrdquo requirement

implies that the number of common elements in X and Y isgreater than 50 of the number of elements in X

Definition 5 (β-reduction) Conditional attribute set P is asubset of P for β-reduction or approximate reduction ofdecision attribute set Q and the subset is red(P Q β) andmeets the following two conditions [19]

(1) c(P Q β) c(red(P Q β) Q β)

(2) To remove any attribute from red(P Q β) condition(1) is not valid

+

(a) (b) (c)

=

Figure 1 +e source image of CT PET PETCT

Produceinitial

population

Inputoriginalfeature

Calculatingindividual

fitness

Whethermeets thecondition

Outputattribute sets

SelectionCrossoverMutation

Figure 2 Flow chart of knowledge reduction method based on genetic algorithm

Mathematical Problems in Engineering 3

231 Attribute Dependency

Definition 6 +e dependency of the decision attribute set Qand the conditional attribute set P is defined as

c(P Q β) |pos(P Q β)|

|U| (3)

pos(P Q β) cup YisinUQind(P) βQ |U| is the number of

objects contained in the domain |pos(P Q β)| is thenumber of objects contained in the positive domain of allequivalence classes that are not greater than the β classifi-cation error which indicates that the conditional attributescan correctly divide the object to U|Q c(0le cle 1) is the βdependency of the decision attribute Q to the conditionalattribute P and is an evaluation of the ability to classifyobjects with the classification error βc 0 means that Pcannot be used to divide objects into equivalence classes inQ c 1 means that P can be used to divide objects intoequivalence classes in Q completely 0lt clt 1 means that Pcan be used to divide objects into equivalence classes in Qpartly

232 Attribute Importance

Definition 7 Assume that the decision information table isS (U A V f ) A PcupQ s isin h the relative importance ofattribute s is

Z(s) c(P Q β) minus c(P minus s Q β)

c(P Q β) 1 minus

c(P minus s Q β)

c(P Q β)

(4)

An attribute is able to distinguish an object the greaterthe value the stronger the ability

+e selection of threshold β for variable precision roughset needs to meet the following requirements

+e choice of β to make the classification accuracy ashigh as possible

(1) 0le βlt 05(2) β makes the attributes contained in the reduction

results as little as possible

24 SVM Support vector machine (SVM) is a supervisedlearning model for data analysis pattern recognition andregression analysis in the field of machine learning +e bestcompromise between model complexity (the learning ac-curacy of a particular training sample) and learning ability(ability to identify an arbitrary sample without error) shouldbe found based on limited sample information In order toobtain the best generalization ability the basic idea is to usethe structural risk minimization principle to construct theoptimal classification hyperplane in the attribute space SVMhas some advantages such as good generalization abilitysimple data structure low computational complexity shorttraining time few parameters selection high fitting preci-sion strong robustness and so on [20 21] It has greatadvantages in dealing with small sample nonlinear and

high-dimensional pattern recognition It is often used inpattern recognition [12 22] regression estimation and soon

(1) After the introduction of kernel function and penaltyparameter by SVM the optimal discriminant func-tion model is

f(x) sgn 1113944n

i1aiyjk xi x( 1113857 + b⎛⎝ ⎞⎠ (5)

Among it 0lt altC yi isin 1 minus 1(2) +e optimization function of SVM is

Q(a) 1113944n

i1ai minus

12

1113944

n

ij1aiajyiyjk xi xj1113872 1113873 (6)

(3) +e radial basis kernel function is a widely usedkernel function the kernel function is used in thispaper

k(x y) exp minus gx minus y2

1113872 1113873 (7)

Among them ggt 0 g is an important parameter in thekernel function which affects the complexity of SVMclassification algorithm

+e kernel function parameter g and penalty coefficientC of support vector machine (SVM) is an important pa-rameter which affects the performance of SVM classificationso (C g) is used as the optimization variable In the processof learning SVM 5-fold cross validation is used to calculatethe optimal classification performance of kernel functionparameter and penalty coefficient and then the diagnosisresult of optimization is applied to the SVM classifier forlung cancer the final selection of the sensitivity specificityaccuracy and computation time as the evaluation indexes ofrelated experiments

3 Results and Discussion

31 Main Idea +e main idea of the model is as follows

311 Parameters Population sizeM chromosome lengthN(the number of condition attributes) crossover probabilityPc mutation probability Pm fitness function F(x) and themaximum number of iterations K are the parameters

312 Coding +e binary coding method is used which isrepresented by a binary string whose length is equal to thenumber of condition attributes each bit corresponds to acondition attribute a bit of 1 indicates that the corre-sponding condition attribute is selected 0 indicates that thecondition attribute is not selected eg 00110101 repre-sents a chromosome with a length of 8 and it is known thatthe corresponding 1 2 5 7 of 0 indicates that the corre-sponding condition attribute is not selected thenc3 C4 C6c8 is the last individual to choose the attributes set

4 Mathematical Problems in Engineering

313 4e Initial Population Assuming the population sizeM (the number of chromosomes in the population isM) Mlength of Lr chromosome (0 1) is the randomly generated asthe initial population

314 Genetic Operators Genetic operators include selectionoperator crossover operator and mutation operator +e se-lection operator generally uses the roulette wheel selectionmethod according to the selection probability pi

(fi1113936Mi1 fi) to select Crossover operator uses a single-point

crossover with a certain probability Pc to select the individualuniform crossover +e mutation operator selects the indi-viduals with the probability Pm to carry on the variation andrandomly selects the corresponding bit of the nonnuclearattribute

315 Fitness Function +e fitness function is the core of thegenetic algorithm the fitness value is the only index to evaluatethe fitness function this paper from the gene encoding valuethe minimum number of attributes reduction attribute de-pendency and other aspects constructs a fitness functionframework by adjusting the weights of various factors andchanging the classification error rate to achieve different fitnessfunction +e fitness function is set as follows

target1 Attribute dependency c(P Q β)

(|posβP(Q)||U|) it represents the β dependency ofdecision attribute Q for conditional attribute Ptarget2 Attributes reduction Length |C reduct| ((|P

| minus |Lr|)|P|) |P| is the number of condition attributesrepresented by 0 1 |Lr| represents the number of 1 inattribute P the shorter the better resultstarget3 Gene coding weight function ie Penaltyfunction target3 1113936 abs(r times (r minus 1))|r| Gene valuescan only take 0 and 1 but the chromosome will shownot 1 and not 0 such that the value is less than 0 orgreater than 1 +e value must be punished thereforethe gene coding weight function is constructed If thegene is 0 r times (r minus 1) 0 but the gene is 1r times (r minus 1) 0 So do not punish the genes of 0 or 1 butif there is a chromosome with a length of 6 r [0 0 minus 2minus 1 2 1] (r minus 1) [minus 1 minus 1 minus 3 minus 21 0] r times (r minus 1) [0 0 6 22 0] then 1113936 abs(r times (r minus 1)) 10 length is 6 sotarget3106167

+erefore the fitness function constructed in this paper isF(x) minus ω1 times target 1 minus ω2 times target 2 + ω3 times target 3 (8)

whereω is the weight coefficient of fitness functionω (0 1 23) because the genetic algorithm can only find the minimumvalue and the bigger the fitness value the better it is so theobjective function is minus and the penalty function is plus

Flow chart about this model is given in Figure 3

32 Model Concrete Steps

Input A decision information table S (U A V f )Output red(P Q β)

generate (M) Lr 98Initial population M 01 se-quence of Chromosome length 98Setting β ω crossover probability Pc mutationprobability Pm iteration number KBegin

for i 1 Ktarget1 (|posβP(Q)||U|)

target2 ((|P| minus |Lr|)|P|)

target3 (1113936 abs(r times (r minus 1))|r|)

Fitnessfunction minus ω1 times target1 minus ω2 times target2 + ω3 times target3Fitness functionP Select (M 2 Pc)Crossover probability PcQCrossover (P 2 Pc)Crossover algorithmQprimeMutation (Q Pm)Mutation algorithmEnd

33 Experimental Environment and Data

331 Hardware Environment Intel Core i5 4670-34GHzwith 80GB memory and 500GB hard disk were used

332 Software Environment Matlab R2012b LibSVM andWindows 7 operating system were used

333 Experimental Data +e PETCT images of 2000 lungcancer patients were collected as the study samples (1000cases of benign lung tumor 1000 cases of malignant lungtumor) Firstly ROI was extracted from the lung tumorand pretreated then 8-dimensional shape features 7-di-mensional gray features 3-dimensional Tamura features56-dimensional GLCM features and the 24-dimensionalfrequency domain features were extracted from the lungtumor ROI and 98-dimensional feature vectors are dis-creted and normalized In the decision attribute 1 rep-resents the lung malignant tumor and minus 1 represents thelung benign tumor Figure 4(a) shows four PETCT im-ages ROI of Lung malignant tumor and Figure 4(b) showsfour PETCT images ROI of lung benign tumor Table 1gives the feature values of two patients with lung cancer(one patient was a malignant tumor and the other was abenign tumor)

34Analysis ofExperimentalResults In this paper 3 kinds ofexperiments are designed according to the weight value ω

(0 1 2 3) of the fitness function and the classification errorrate β 04 02 0 (namely the inclusion degree1 minus β 06 08 1 ) For first type of experiments1 minus β 06 according to the different values of ω to do thethree groups of experiments totally For second type ofexperiments ϖ1 1ω2 1 ω3 0 according to the dif-ferent values of β to do three groups of experiments Forthird type of experiments 1 minus β 06 by increasing the ω

Mathematical Problems in Engineering 5

value to achieve the best fitness function to achieve the bestresults

341 Experiment 1mdashResearch on Different Weight Coeffi-cients under the Condition in the Same Classification ErrorRate ϖ values and β values of experiment 1 are shown inTable 2 and 1 minus β 06

(1) 1st Group Experiment ϖ1ω2ω3 1 0 0 +e al-gorithm is run 5 times according to this group weights theresults of the 5 groups are given in Table 3 including thereduction of the conditional attributes the length of re-duction the optimal fitness value the attribute dependencydegree and the time +e convergence of VPRS-GA under

the variation for fitness function value in one time is shownin Figure 5

Each reduction is classified by SVM classifier using themethod of 5-fold cross validation through changing thetraining samples and test samples the results of the fivegroups were obtained including accuracy sensitivityspecificity and time (training samples are constructed by800 malignant samples and 800 benign samples testingsamples are constructed by 200 malignant samples and 200benign samples the experiment is repeated 5 times bychanging training samples and testing samples) Finally theaverage values of these five groups are obtained as the finalresult of the reduction and shown in Table 4

+e weight value in this group experiment isϖ1ω2ω3 1 0 0 attribute dependency degree are

Output attributeset C_reduct1 C_re

duct2middotmiddotmiddotC_reductn

Indiscernibility relationfunction

Lower approximation

Relative positive domainposD

c function

Recognitionresult

SVMmodel

TrainingSVM

Reducedtraining set

Reducedtesting set

Target

Satisfycondition

Yes

No

Mutation Pm

Crossover Pc

Select Ps

F (x) = ndashω1 times target1 ndash ω2 times target2 + ω3 times target3β = 06 08 1

Initial population

Fitness value

Figure 3 Flow chart of high-dimensional feature selection based on genetic algorithm and variable precision rough set

(a) (b)

Figure 4 Part of lung tumor PETCT image ROI (a) Part of the lung malignant tumor PETCT-ROI (b) Part of the lung benign tumorPETCT-ROI

6 Mathematical Problems in Engineering

Table 1 ROI feature values of lung tumor PETCT image

Types of disease Shapefeature

Grayfeature

Tamuratexture

Texture features of GLCM Texture feature of wavelet

0 degree 45degrees

90degrees

135degrees Norm Standard

deviation Energy

Lung malignanttumor

60000 1222810 147000 00808 00779 00790 00611 6492580 371752 1000000012 14911500 309650 28937 29067 28989 31284 269473 38486 0001700000 386154 02326 02576 02820 02653 04490 93520 13355 0000200000 minus 05056 01668 01676 01659 01649 168200 24025 0000700000 24166 00792 00759 00772 00566 271143 38693 0001700000 140453 02576 02820 02653 04490 203163 29020 0001000000 70524 164110 164469 163584 164431 131755 18818 0000400000 27089 27072 27100 28066 183441 26199 00008

05755 06007 05810 073452109390 2117900 2095780 208825003064 03351 03135 03950

minus 06779 minus 06708 minus 06775 minus 0569600000 00000 00000 0000007625 07802 07658 08001

Lung benigntumor

40000 503912 101616 08087 07915 08077 07864 3799170 26741 1000000033 60006 18835 04324 04732 04370 04840 57551 08211 0000200000 24496 26329 00433 00621 00469 00679 11745 01677 0000000000 05649 94899 78127 92429 92429 34684 04955 0000100000 28589 08082 07905 08072 07853 20823 02972 0000000000 3283 00433 00621 00469 00679 21821 03117 0000000000 32559 78367 78363 78396 78363 08937 01276 0000000000 04024 04301 04045 04370 22387 03197 00000

01782 02326 01894 02481555257 550899 555291 54983100596 00873 00650 00958

minus 04707 minus 03295 minus 04351 minus 0291100000 00000 00000 0000020429 21172 20651 21394

Table 3 Results of VPRS-GA running 5 times when 1-β 06 ω1 1ω2 0ω3 0

Experimenttimes C_ reduction Reduction

lengthOptimal

fitness valueAttribute

dependency degree Time (s)

1 4 5 8 9 11 12 13 17 20 22 23 24 27 30 32 33 35 38 42 48 4952 57 59 61 62 63 64 65 68 70 72 73 75 77 78 80 87 88 91 92 41 minus 09705 09705 9719144

21 2 3 4 5 8 11 12 13 14 16 17 19 23 24 25 26 27 28 30 32 3638 39 40 42 43 44 46 47 52 53 55 61 63 66 67 69 71 72 73 77

79 80 82 84 85 87 9249 minus 09685 09685 10076907

3 4 611 12 1517 18 24 25 26 28 29 31 36 38 39 42 43 45 47 4953 56 65 68 69 72 76 77 79 80 81 83 85 88 91 92 37 minus 09695 09695 10432000

4 4 8 9 11 12 13 14 15 17 23 29 34 35 39 40 43 47 48 50 53 5556 60 61 64 68 70 75 80 81 82 83 84 86 34 minus 09790 09790 9473111

5 3 4 6 81011 12 13151719 20 21 24 26 29 31 39 42 44 45 4850 53 54 56 59 64 68 77 83 84 87 89 92 35 minus 09775 09775 9645092

Average value 392 minus 09730 09730 9869251

Table 2 Fitness function weight proportion and β value

Experiment times1 minus β 06

ω1 ω2 ω3First group experiment 1 0 0Second group experiment 1 1 0+ird group experiment 1 1 1

Mathematical Problems in Engineering 7

regarded as fitness function +e average attribute de-pendency degree is 0973 the average length of reductionis 392 and the average optimal fitness value is minus 0973+e average recognition accuracy of the experiment is9692 +e premature phenomena are shown in Fig-ure 5 and evolution progress is terminated early

(2) 2nd Group Experiment ϖ1ω2ω3 1 1 0 +isexperiment introduces an objective function to control thelength of reduction (the shorter the length of reduction thebetter it is) the influence degree of the objective functionwhich controls the reduction on the fitness function and the

final recognition accuracy is verified +e algorithm is run 5times according to this group weights and the results of the 5groups are given in Table 5 including the reduction of theconditional attributes the length of reduction the optimalfitness value the attribute dependency and the time +econvergence of VPRS-GA under the variation for fitnessfunction value in one time is shown in Figure 6

Each reduction is classified by SVM classifier using themethod of 5-fold cross validation through changing thetraining samples and test samples the results of the fivegroups were obtained including accuracy sensitivityspecificity and time (training samples are constructed by

ndash06

ndash07

ndash08

ndash09

ndash10 50 100 150

Generation stopping criteria

Best ndash09695 Mean ndash0944425

Fitn

ess v

alue

Best fitnessMean fitness

Figure 5 +e variation of fitness function value in a running process for Experiment 1-first group

Table 4 +e statistical results of the first group for experiment 1 with the SVM classifier

Experiment times Accuracy () Sensitivity () Specificity () Time (s)

Reduction 1

1 9250 8600 9900 3326072 9725 9750 9700 3450513 9900 9900 9900 3586774 9800 9950 9650 3510755 9925 10000 9850 355948

Average value 9720 9640 9800 348672

Reduction 2

1 9325 8700 9950 4365332 9725 9800 9650 4459003 9875 9850 9900 4395064 9750 9900 9600 4450645 9925 10000 9850 448513

Average value 9720 9650 9790 443103

Reduction 3

1 9275 8750 9800 3269162 9575 9750 9400 3372093 9800 9800 9800 3407014 9700 9850 9550 3331745 9850 9950 9750 333257

Average value 9640 9620 9660 334251

Reduction 4

1 9375 8850 9900 3064852 9650 9750 9550 3192403 9750 9700 9800 3240824 9775 9900 9650 3254195 9900 10000 9800 361516

Average value 9690 9640 9740 318806

Reduction 5

1 9400 8900 9900 3195572 9650 9750 9550 3369093 9725 9700 9750 3301594 9775 9900 9650 3999805 9900 10000 9800 325692

Average value 9690 9650 9730 342459

8 Mathematical Problems in Engineering

800 malignant samples and 800 benign samples testingsamples are constructed by 200 malignant samples and 200benign samples the experiment is repeated 5 times bychanging training samples and testing samples) Finally theaverage values of these five groups are obtained as the finalresult of the reduction and shown in Table 6

+e experimental weight of this group is ϖ1

ω2ω3 1 1 0 attribute dependency degree and thelength of reduction are regarded as fitness function As canbe seen from Table 5 the reduction length is 13 17 and soon +e average length of reduction was 17 which wassignificantly reduced compared with the average length ofthe reduction in Table 3 in the experiment of the first groupswhich reduced the time improved the efficiency of the al-gorithm and increased the attribute dependency of thealgorithm even up to 1 +e average recognition accuracy ofthe experimental group was 9698 which was increased by006 compared with that in the first groups

(3) 3rd Group Experiment ϖ1ω2ω3 1 1 1 On thebasis of attribute dependency degree and attribute reductionlength this experiment introduces gene coding weightfunction in order to verify the effect of gene coding weightfunction on fitness function and the final recognition ac-curacy +e algorithm are run 5 times according to thisgroup weights the results of the 5 groups are given inTable 7 including the reduction of the conditional attributesthe length of reduction the optimal fitness value the at-tribute dependency and the time +e convergence ofVPRS-GA under the variation for fitness function value inone time is shown in Figure 7

Each reduction is classified by SVM classifier using themethod of 5-fold cross validation through changing thetraining samples and test samples the results of the fivegroups were obtained including accuracy sensitivityspecificity and time (training samples are constructed by800 malignant samples and 800 benign samples testingsamples are constructed by 200 malignant samples and 200benign samples the experiment is repeated 5 times bychanging training samples and testing samples) Finally theaverage values of these five groups are obtained as the finalresult of the reduction and shown in Table 8

+e experimental weight of this group is ϖ1 ω2ω3=1 1 1 attribute dependency degree the length of re-duction and gene coding weight value are regarded as fitnessfunction However the premature phenomena are shown inFigure 7 and evolution progress is terminated early FromTable 7 we can see that the attribute dependency decreasesgradually and even the attribute dependency of Reduction 1is reduced to 0759 +e average recognition accuracy of theexperimental group was 9685+e accuracy of recognitionwas decreased compared with the second groups and henceusing gene encoding weight function in the fitness functionto improve recognition accuracy is useless only for thesamples with different results to analyze specific issues +e3 experiment runs of experiment 1 verified the necessity ofthe fitness function by continuously introducing fitnessobjective function such as target1 target2 and target3 theconclusion is that the fitness function is better when it is notbigger but after the introduction of target3 the accuracydeclines therefore the introduction of target1 and target2 inthis algorithm can get better results

Table 5 Results of VPRS-GA running 5 times when 1 minus β 06 ω1 1ω2 1ω3 0

Experiment times C_ reduction Reductionlength

Optimalfitness value

Attributedependency

degreeTime (s)

1 5 9 14 20 26 41 43 46 48 54 55 57 64 66 74 79 86 90 18 minus 46487 09965 107240722 1 4 11 12 14 24 34 40 42 43 56 60 61 65 67 68 71 72 85 19 minus 40109 1 63281223 2 13 27 29 39 42 45 56 59 63 68 70 75 13 minus 46512 09990 110239674 1 3 4 7 9 11 12 15 30 34 38 42 46 48 55 62 65 77 79 19 minus 49674 1 87946705 3 9 11 13 29 39 41 42 43 46 50 55 65 c77 85 86 16 minus 44114 09815 15075539

Average value 17 minus 45379 09954 10389274

ndash1

ndash2

ndash3

ndash4

ndash5

Fitn

ess v

alue

Best ndash496739 Mean ndash492312

0 50 100 150Generation stopping criteria

Best fitnessMean fitness

Figure 6 +e variation of fitness function value in a running process for experiment 1-second group

Mathematical Problems in Engineering 9

342 Experiment 2mdashResearch on Different ClassificationError Rates under the Condition in the Same WeightCoefficient According to experiment 1 we can see thatwhen ω1 1 ω2 1 ω3 0 the experimental results arethe best so in experiment 2 the case of the weight value ofwas unchanged ω1 1 ω2 1 ω3 0 and the β value waschanged and they are shown in Table 9

(1) 1st Group Experiment 1 minus β 06 +e algorithm is run 5times according to this group weights the results of the 5groups are shown in Table 5 including the reduction of the

conditional attributes the length of reduction the optimalfitness value the attribute dependency and the time +econvergence of VPRS-GA under the variation for fitnessfunction value for one time is shown in Figure 6 (ie notrepeated in the second group of experiment 1)

(2) 2nd Group Experiment 1 minus β 08 +e algorithm are is 5times according to this group weights the results of the 5groups are given in Table 10 including the reduction of theconditional attributes the length of reduction the optimalfitness value the attribute dependency and the time +e

Table 6 +e statistical results of the second group for experiment 1 with the SVM classifier

Experiment times Accuracy () Sensitivity () Specificity () Time (s)

Reduction 1

1 9300 8600 10000 1164882 9625 9600 9650 1255113 9850 9900 9800 1315094 9725 9850 9600 1344685 9925 10000 9850 144839

Average value 9685 9590 9780 130563

Reduction 2

1 9425 8900 9950 1210962 9725 9700 9750 1286363 9800 9800 9800 1356774 9750 9800 9700 1381965 9875 9900 9850 136691

Average value 9715 9620 9810 132059

Reduction 3

1 9300 8750 9850 877572 9725 9750 9700 1034243 9775 9800 9750 1074114 9775 9850 9700 1123445 9900 10000 9800 113006

Average value 9695 9630 9760 104788

Reduction 4

1 9375 8750 10000 1464172 9650 9750 9550 1547363 9750 9700 9800 1576214 9800 9900 9700 1613555 9925 10000 9850 163381

Average value 9700 9620 9780 156702

Reduction 5

1 9250 8650 9850 1249332 9675 9800 9550 1400573 9800 9800 9800 1451944 9800 9900 9700 1457925 9950 9950 9950 150400

Average value 9695 9620 9770 141275

Table 7 Results of VPRS-GA running 5 times when 1 minus β 06 ω1 1ω2 1ω3 1

Experimenttimes C_ reduction Reduction

lengthOptimal

fitness valueAttribute

dependency degree Time (s)

1 4 5 7 26 27 34 35 41 47 54 55 71 74 75 78 80 83 90 18 minus 14192 07590 6888635

2 4 15 16 19 22 27 28 29 30 35 38 42 45 50 52 53 59 61 6264 65 70 71 72 77 87 88 27 minus 15232 08640 8124857

3 6 17 19 24 28 31 33 34 38 39 43 45 47 48 49 51 55 56 6667 69 70 71 72 76 77 78 80 81 84 87 89 91 92 34 minus 13545 07950 9521511

4 3 6 8 91617 19 20 24 25 28 35 37 39 41 42 46 49 51 52 5459 63 65 66 74 83 86 28 minus 14703 08365 8714839

5 1 7 8 15 17 19 20 23 29 37 45 48 54 60 62 70 73 75 77 7879 86 22 minus 14990 07995 7797617

Average value 258 minus 14532 08108 8209492

10 Mathematical Problems in Engineering

convergence of VPRS-GA under the variation for fitnessfunction value for one time is shown in Figure 8

Each reduction is classified by SVM classifier using themethod of 5-fold cross validation through changing thetraining samples and test samples the results of the five

groups were obtained including accuracy sensitivityspecificity and time (training samples are constructed by800 malignant samples and 800 benign samples testingsamples are constructed by 200 malignant samples and 200benign samples the experiment is repeated 5 times by

ndash08

ndash1

ndash12

ndash14

ndash16

Fitn

ess v

alue

Best ndash141919 Mean ndash128476

0 50 100 150Generation stopping criteria

Best fitnessMean fitness

Figure 7 +e variation of fitness function value in a running process for experiment 1-third group

Table 8 +e statistical results of the third group for experiment 1 with the SVM classifier

Experiment times Accuracy () Sensitivity () Specificity () Time (s)

Reduction 1

1 9275 8600 9950 924922 9725 9750 9700 1074613 9850 9850 9850 1138114 9775 9900 9650 1155605 9875 10000 9750 117022

Average value 9700 9620 9780 109269

Reduction 2

1 9350 8750 9950 1482452 9700 9650 9750 1615353 9775 9850 9700 1664524 9800 9850 9750 1754505 9875 9950 9800 172348

Average value 9700 9610 9790 164806

Reduction 3

1 9125 8300 9950 2019042 9650 9700 9600 2185353 9800 9800 9800 2196054 9625 9900 9350 2230915 9825 10000 9650 236896

Average value 9605 9540 9670 220006

Reduction 4

1 9300 8700 9900 1654542 9675 9600 9750 1724323 9875 9850 9900 1793014 9800 9900 9700 1895605 9900 9950 9850 185249

Average value 9710 9600 9820 178399

Reduction 5

1 9275 8600 9950 1411732 9725 9800 9650 1612953 9900 9950 9850 1589924 9775 9950 9600 1648765 9875 10000 9750 166070

Average value 9710 9660 9760 158481

Table 9 Fitness function weight proportion and β value

Experiment timesω1 1 ω2 1 ω3 0

1 minus β 06 1 minus β 08 1 minus β 1First group experiment Second group experiment +ird group experiment

Mathematical Problems in Engineering 11

changing training samples and testing samples) Finally theaverage values of these five groups are obtained as the finalresult of the reduction and shown in Table 11

In the case of constant weight ϖ and classification errorrate of β 02 (which contains 1 minus β 08) the classificationerror rate is changed on the basis of the attribute dependencyand the length of control reduction +e premature phe-nomena are shown in Figure 8 and evolution progress isterminated early such that the attribute dependency ofreduction 5 was 08405 appeared in attribute dependency onless than 09 compared with first groups of experiment 2attribute dependency declined +e average recognitionaccuracy of the experimental group was 9674 Comparedwith the classification error rate of 04 and inclusion degreeof 06 the accuracy was decreased by 024

(3) 3rd Group Experiment 1 minus β1 +e algorithm is run 5times according to the group weights and the results of the 5groups are shown in Table 12 including the reduction of theconditional attributes the length of reduction the optimalfitness value the attribute dependency and the time +econvergence of VPRS-GA under the variation for fitnessfunction value for one time is shown in Figure 9

Each reduction is classified by SVM classifier using themethod of 5-fold cross validation through changing thetraining samples and test samples the results of the fivegroups were obtained including accuracy sensitivityspecificity and time (training samples are constructed by800 malignant samples and 800 benign samples testingsamples are constructed by 200 malignant samples and 200

benign samples the experiment is repeated 5 times bychanging training samples and testing samples) Finally theaverage values of these five groups are obtained as the finalresult of the reduction and shown in Table 13

In the case of constant weight ϖ and classification errorrate of β= 0 (which contains 1 minus β= 1) the classificationerror rate is reduced and the inclusion degree is improved onthe basis of the attribute dependency and the length ofcontrol reduction +e premature phenomena are shown inFigure 9 and evolution progress is terminated early +eaverage recognition accuracy of the experimental group was9573 which was decreased by 006 compared with thatin the second group In experiment 2 the effect of changingthe classification error rate on the recognition accuracy wasverified by the 3 groups of experiments By continuallyreducing the classification error rate the final recognitionaccuracy has been declining when inclusion degree is 1β= 0 variable precision rough set becomes Pawlak rough setthe recognition accuracy of the recognition accuracy of isminimum which was verified the advantages of variableprecision rough set

343 Experiment 3mdashResearch on Increasing the WeightCoefficient under the Condition in the Same ClassificationError Rate According to experiment 1 and experiment 2we can know that when β 06 ω1 1 ω2 1 ω3 0 therecognition accuracy is the best therefore in the thirdexperiment by increasing the weight of ω 3 groups ofexperiments are performed fitness goals target 1 (attribute

Table 10 Results of VPRS-GA running 5 times when 1 minus β 08 ω1 1ω2 1ω3 0

Experimenttimes C_ reduction Reduction

lengthOptimal fitness

valueAttribute

dependency degree Time (s)

1 8 9 11 12 15 16 17 18 25 26 29 31 35 39 40 41 42 48 5865 67 68 70 83 84 91 26 minus 67816 09490 10002827

2 1 6 8 9 11 12 15 17 21 23 26 28 30 31 34 44 50 56 58 5962 63 64 68 71 75 77 82 89 92 30 minus 67797 09615 9477387

3 6 8 12 14 15 16 17 21 28 35 38 39 45 49 55 58 61 62 6465 77 82 85 23 minus 68694 09070 12866181

4 4 6 7 8 11 12 13 16 17 20 25 26 31 32 34 35 41 42 44 4950 55 58 68 72 74 76 78 79 85 89 92 32 minus 67225 09540 10510220

5 3 6 8 9 10 16 17 26 27 34 36 37 38 40 42 44 46 51 52 6266 67 84 86 87 25 minus 65892 08405 8469324

Average value 272 minus 67484 09224 10265188

ndash55

ndash6

ndash65

ndash7

Fitn

ess v

alue

Best ndash686942 Mean ndash653584

0 50 100 150Generation stopping criteria

Best fitnessMean fitness

Figure 8 +e variation of fitness function value in a running process for experiment 2-second group

12 Mathematical Problems in Engineering

Table 11 +e statistical results of the second group for experiment 2 with the SVM classifier

Experiment times Accuracy () Sensitivity () Specificity () Time (s)

Reduction 1

1 9300 8650 9950 2280072 9575 9700 9450 2376463 9700 9600 9800 2332504 9750 9850 9650 2444915 9925 10000 9850 244816

Average value 9650 9560 9740 237642

Reduction 2

1 9375 8800 9950 2524032 9625 9750 9500 2652893 9800 9700 9900 2655234 9800 9900 9700 2682125 9950 10000 9900 275880

Average value 9710 9630 9790 265461

Reduction 3

1 9275 8750 9800 1807802 9675 9750 9600 1929923 9700 9600 9800 1872434 9775 9950 9600 2084825 9875 10000 9750 203507

Average value 9660 9610 9710 194601

Reduction 4

1 9200 8650 9750 2572602 9700 9750 9650 2730243 9775 9650 9900 2723164 9750 9900 9600 2815545 9900 10000 9800 291471

Average value 9665 9590 9740 275125

Reduction 5

1 9275 8750 9800 1437152 9675 9600 9750 1526373 9750 9800 9700 1589294 9775 9900 9650 1629975 9950 10000 9900 166792

Average value 9685 9610 9760 157014

Table 12 Results of VPRS-GA running 5 times when 1 minus β 1 ω1 1ω2 1ω3 0

Experimenttimes C_ reduction Reduction

lengthOptimal fitness

valueAttribute dependency

degree Time (s)

1 15 44 68 73 79 84 6 minus 27313 07965 114499012 34 51 54 75 80 90 6 minus 27047 08460 96993913 2 34 49 70 71 72 76 81 8 minus 34057 07535 112334894 12 25 78 85 4 minus 22872 09285 11668133

5 6 7 12 13 42 44 55 57 65 66 69 77 81 8687 15 minus 33230 08665 13236077

Average value 78 minus 28903 08382 11457398

ndash1

ndash2

ndash3

ndash4

Fitn

ess v

alue

0 50 100 150Generation stopping criteria

Best fitnessMean fitness

Best ndash340567 Mean ndash330598

Figure 9 +e variation of fitness function value in a running process for experiment 2-third group

Mathematical Problems in Engineering 13

dependency) target 2 (the minimum number of attributesreduction) and target 3 (gene encoding weight function)the three objective functions play an important role in theevaluation of fitness function However the importance offitness function is reduced in these three objectives+erefore in this experiment when the other conditions areunchanged the weight coefficient of the target 1 is increasedto verify the influence of the change in the weight coefficienton the experimental results and they are shown in Table 14

(1) 1st Group Experiment ω1 1 ω2 1 ω3 0 +e al-gorithm are run 5 times according to this group weights theresults of the 5 groups are given in Table 5 including thereduction of the conditional attributes the length of reduc-tion the optimal fitness value the attribute dependency andthe time +e convergence of VPRS-GA under the variationfor fitness function value in one time is shown in Figure 6 (ienot repeated for the second group of experiment 1)

(2) 2nd Group Experiment ω1 2 ω2 1 ω3 0 +ealgorithm is run 5 times according to this group weights theresults of the 5 groups are given in Table 15 including thereduction of the conditional attributes the length of re-duction the optimal fitness value the attribute dependencyand the time +e convergence of VPRS-GA under thevariation for fitness function value in one time is shown inFigure 10

Each reduction is classified by SVM classifier using themethod of 5-fold cross validation through changing thetraining samples and test samples the results of the fivegroups were obtained including accuracy sensitivityspecificity and time (training samples are constructed by800 malignant samples and 800 benign samples testingsamples are constructed by 200 malignant samples and 200benign samples the experiment is repeated 5 times bychanging training samples and testing samples) Finally theaverage values of these five groups are obtained as the finalresult of the reduction and shown in Table 16

+e experimental group in the case of 1 minus β= 06 un-changed the weight of ω1 was increased +e attributedependency and the optimal fitness function are relativelyhigh the average precision of reduction 1 reduction 2 andreduction 3 in Table 16 is more than 97 and that of re-duction 2 is even up to 9725 +e average recognitionaccuracy of the experimental group is 9703 which ishigher than that of the first group

Table 13 +e statistical results of the third group for experiment 2 with the SVM classifier

Experiment times Accuracy () Sensitivity () Specificity () Time (s)

Reduction 1

1 9225 8450 10000 812712 9550 9700 9400 945833 9575 9400 9750 881984 9600 9800 9400 937545 9725 9900 9550 98691

Average value 9535 9450 9620 91299

Reduction 2

1 9200 8450 9950 648942 9625 9550 9700 801983 9525 9300 9750 773374 9600 9750 9450 760125 9800 10000 9600 82763

Average value 9550 9410 9690 76241

Reduction 3

1 9200 8450 9950 648942 9625 9550 9700 801983 9525 9300 9750 773374 9600 9750 9450 760125 9800 10000 9600 82763

Average value 9550 9410 9690 76241

Reduction 4

1 9275 8550 10000 672642 9675 9600 9750 784673 9600 9450 9750 730224 9575 9750 9400 794605 9800 10000 9600 84184

Average value 9585 9470 9700 76479

Reduction 5

1 9200 8450 9950 1147192 9625 9750 9500 1287053 9850 9900 9800 1320494 9775 9950 9600 1335135 9850 10000 9700 133144

Average value 9660 9610 9710 128426

Table 14 Fitness function weight proportion and β value

Experiment times1 minus β 06

ω1 ω2 ω3First group experiment 1 1 0Second group experiment 2 1 0+ird group experiment 3 1 0

14 Mathematical Problems in Engineering

ndash2

ndash25

ndash3

Fitn

ess v

alue

0 50 100 150Generation stopping criteria

Best fitnessMean fitness

Best ndash2915 Mean ndash291446

Figure 10 +e variation of fitness function value in a running process for experiment 3-second group

Table 15 Results of VPRS-GA running 5 times when 1 minus β 06 ω1 2ω2 1ω3 0

Experimenttimes C_ reduction Reduction

lengthOptimal fitness

valueAttribute dependency

degree Time (s)

1 2 3 4 5 11 13 16 18 24 30 34 37 39 41 42 51 55 64 7077 78 82 22 minus 34859 09060 21515464

2 8 9 11 12 14 15 23 25 26 29 30 33 37 42 43 45 46 5060 61 69 74 80 87 89 25 minus 30845 09390 42761634

3 8 11 12 13 16 18 19 24 29 36 37 43 64 65 68 71 86 9192 19 minus 35039 09150 26197164

4 2 3 4 8 10 11 12 13 15 16 19 23 25 30 48 55 64 65 6874 77 80 81 83 84 86 89 27 minus 29150 09575 44271631

5 5 8 911 121517 23 25 29 31 36 39 41 48 54 59 63 8083 86 89 22 minus 29920 09525 43161464

Average value 23 minus 31962 09340 35581471

Table 16 +e statistical results of the second group for experiment 3 with the SVM classifier

Experiment times Accuracy () Sensitivity () Specificity () Time (s)

Reduction 1

1 9275 8600 9950 1884972 9725 9800 9650 1571623 9850 9900 9800 1586914 9800 9900 9700 1646035 9950 10000 9900 161914

Average value 9720 9640 9800 166173

Reduction 2

1 9450 8950 9950 1908132 9675 9800 9550 2002513 9775 9800 9750 1970084 9850 9900 9800 2009245 9875 9900 9850 209245

Average value 9725 9670 9780 199648

Reduction 3

1 9400 8800 10000 1313692 9725 9800 9650 1447973 9800 9800 9800 1426624 9725 9850 9600 1471905 9925 10000 9850 148799

Average value 9715 9650 9780 142963

Reduction 4

1 9350 8750 9950 2404562 9700 9750 9650 2520823 9800 9800 9800 2511754 9775 9950 9600 2701885 9825 10000 9650 267471

Average value 9690 9650 9730 256274

Reduction 5

1 9325 8800 9850 1809592 9600 9800 9400 1965633 9750 9750 9750 1967234 9800 9900 9700 2078295 9850 9950 9750 219703

Average value 9665 9640 9690 200355

Mathematical Problems in Engineering 15

Table 17 Results of VPRS-GA running 5 times when 1 minus β 1 ω1 1ω2 1ω3 0

Experimenttimes C_ reduction Reduction

lengthOptimal fitness

valueAttribute

dependency degree Time (s)

1 3 4 5 8 9 11 12 17 19 29 34 35 38 46 52 53 55 59 63 6672 75 77 78 79 87 92 27 minus 38867 09550 28981789

2 4 8 9 11 12 15 17 29 33 37 38 39 42 43 48 55 67 73 7881 83 84 88 89 90 25 minus 38167 09715 55783772

3 2 3 4 8 9 10 11 12 13 15 16 19 24 25 30 36 49 54 55 6064 67 68 70 74 77 83 85 86 91 30 minus 38807 09530 34831096

4 4 5 7 11 12 14 15 17 25 29 33 36 39 41 42 47 48 50 5556 58 62 67 69 72 74 77 84 86 90 91 31 minus 39430 09665 35742822

5 3 4 5 8 9 11 12 17 19 29 34 35 38 46 52 53 55 59 63 6672 75 77 78 79 87 92 27 minus 38867 09550 27919582

Average value 28 minus 38827 09602 36651812

ndash3

ndash35

ndash40 50 100 150

Generation stopping criteria

Fitn

ess v

alue

Best fitnessMean fitness

Best ndash394298 Mean ndash393327

Figure 11 +e variation of fitness function value in a running process for experiment 3-third group

Table 18 +e statistical results of the Second group for experiment 3 with the SVM classifier

Experiment times Accuracy () Sensitivity () Specificity () Time (s)

Reduction 1

1 9200 8700 9700 2187172 9750 9750 9750 2105503 9850 9850 9850 2032064 9800 9900 9700 2211645 9925 10000 9850 272536

Average value 9705 9640 9770 225235

Reduction 2

1 9400 8850 9950 2331232 9575 9750 9400 2433493 9750 9700 9800 2442024 9775 9900 9650 2566075 9900 9950 9850 259071

Average value 9680 9630 9730 247270

Reduction 3

1 9275 8650 9900 2525842 9625 9750 9500 2624123 9775 9800 9750 2601274 9775 9900 9650 2686705 9875 10000 9750 265387

Average value 9665 9620 9710 261836

Reduction 4

1 9150 8550 9750 2532312 9625 9750 9500 2649433 9750 9700 9800 2752834 9800 9950 9650 3229545 9825 9950 9700 277432

Average value 9630 9580 9680 278769

Reduction 5

1 9200 8800 9600 1951962 9700 9700 9700 2148893 9825 9800 9850 2036124 9850 10000 9700 2133615 9900 9900 9900 225526

Average value 9695 9640 9750 210517

16 Mathematical Problems in Engineering

(3) 3rd Group Experiment ω1 3 ω2 1 ω3 0 +e al-gorithm is run 5 times according to the group weights andthe results of the 5 groups are given in Table 17 including thereduction of the conditional attributes the length of re-duction the optimal fitness value the attribute dependencyand the time +e convergence of VPRS-GA under thevariation for fitness function value for one time is shown inFigure 11

Each reduction is classified by SVM classifier using themethod of 5-fold cross validation through changing thetraining samples and test samples the results of the fivegroups were obtained including accuracy sensitivityspecificity and time (training samples are constructed by800 malignant samples and 800 benign samples testingsamples are constructed by 200 malignant samples and 200benign samples the experiment is repeated 5 times bychanging training samples and testing samples) Finally theaverage values of these five groups are obtained as the finalresult of the reduction and shown in Table 18

+e experiment in the case of 1 minus β 06 unchangedincrease the weight of the ω1 ω1 3 ω2 1 ω3 0 InTable 18 the recognition accuracy of reduction 1 is over 97only +e average recognition accuracy of the experimentalgroup is 9675 and the accuracy is decreased by 028compared with that in the other second groups +e threegroups of experiment 3 the purpose is to verify whether theexperimental accuracy is influenced by increasing theweight +e experimental results show that the accuracy ofsecond group for experimental weight 2 1 0 comparedwith first group experiment when 1 1 0 is high but thethird groups of experimental weight was 3 1 0 and theaccuracy declined therefore the weight of 2 1 0 is the bestchoice for this experiment

4 Conclusions

Aiming at the deficiency of the traditional rough set modelthis paper proposes a new feature selection model based ongenetic algorithm and variable precision rough set by in-troducing the β value the rigid inclusion of the approxi-mation for the traditional rough set is relaxed and then wedesign the 3 kinds of experiments by constructing the de-cision information table of the PETCT feature for lungtumor ROI +e first type of experiment is the inclusion of1 minus β 06 and different values of ω made a total of threegroups of experiments the experimental results show thatthe better recognition accuracy can be obtained when theweight is 1 1 0 and the results show that the gene codingweight function has no effect on the fitness function For thesecond type of experiments ϖ1 1ω2 1 ω3 0according to the different values of β to do three groups ofexperiments the results show that the recognition accuracyof 1 minus β 06 is the best which shows that the larger the βvalue is the lower approximate cardinality will be largerthen the relative accuracy will increase For the third type ofexperiments 1 minus β 06 ω value is increased to achieve thebest fitness function in order to achieve the best results +eexperimental results show that the recognition accuracy isbetter than the others when the weight value is 2 1 0 so it

is better to solve the problem by increasing the proportion ofattribute dependency +rough the above experiments it isshown that the high-dimensional feature selection algorithmbased on genetic algorithm and variable precision rough setcan solve the multiobjective optimization problem wellHowever when the fitness function and its parameters areapplied in the specific application it is necessary to analyzethe specific problems

Data Availability

+e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

+e authors declare no conflicts of interest

Acknowledgments

+is work was supported by National Natural ScienceFoundation of China (Grant nos 61561040 and 61876121)First-Class Disciplines Foundation of Ningxia (NoNXYLXK2017B09)

References

[1] S Luo D Miao Z Zhang Y Zhang and S Hu ldquoA neigh-borhood rough set model with nominal metric embeddingrdquoInformation Sciences vol 520 pp 373ndash388 2020

[2] B Barman and S Patra ldquoVariable precision rough set basedunsupervised band selection technique for hyperspectralimage classificationrdquo Knowledge-Based Systems vol 1936Article ID 105414 2020

[3] Y Chenyi and L Jinjin ldquoApproximate attribute reductionunder variable precision rough set βrdquo Journal of ShandongUniversity vol 11 pp 17ndash21 2011

[4] S Xiaowei Research on Hierarchical Model of Attribute Re-duction in Variable Precision Rough Set Central SouthUniversity Changsha China 2013

[5] Z Jie and W Jiayang ldquoAnalysis of reduction feature ofvariable precision rough set modelrdquo Computer ApplicationResearch vol 7 pp 12ndash15 2007

[6] Z Pei and Z Qinghua ldquoFCM clustering algorithm based onvariable precision rough setrdquo Journal of Shanxi Universityvol 3 pp 342ndash348 2016

[7] C Hao and Y Junan ldquoAttribute kernel and minimum at-tribute reduction algorithm of variable precision rough setrdquoActa Sinica Sinica vol 5 pp 1011ndash1017 2012

[8] S Xu X Yang H Yu D-J Yu J Yang and E CC TsangldquoMulti-label learning with label-specific feature reductionrdquoKnowledge-Based Systems vol 104 pp 52ndash61 2016

[9] I Maryam and G Hassan ldquoFeature space discriminantanalysis for hyperspectral data feature reductionrdquo ISPRSJournal of Photogrammetry and Remote Sensing vol 102pp 1ndash13 2015

[10] S Q Wang C Y Gao C Luo G M Zheng and Y N ZhouldquoResearch on feature selectionattribute reduction methodbased on rough set theoryrdquo Procedia Computer Sciencevol 154 pp 194ndash198e 2019

[11] A W Omar M Azzam O Hadi and B Jamal ldquoCEAP SVM-based intelligent detection model for clustered vehicular ad

Mathematical Problems in Engineering 17

hoc networksrdquo Expert Systems with Applications vol 50pp 40ndash54 2016

[12] H Lee and Y-P P Chen ldquoImage based computer aideddiagnosis system for cancer detectionrdquo Expert Systems withApplications vol 42 no 12 pp 5356ndash5365 2015

[13] J A Guy and P L Harold ldquoAfter detection the improvedaccuracy of lung cancer assessment using radiologic com-puter-aided diagnosisrdquo Academic Radiology vol 23 no 2pp 186ndash191 2016

[14] E Kiyonori T Shodayu J Binghu et al ldquoPleural invasion byperipheral lung cancer prediction with three-dimensionalCTrdquo Academic Radiology vol 3 pp 310ndash319 2015

[15] B Koohestani ldquoA crossover operator for improving the ef-ficiency of permutation-based genetic algorithmsrdquo ExpertSystems with Applications vol 1511 Article ID 113381 2020

[16] N K Lee X Li and D Wang ldquoA comprehensive survey ongenetic algorithms for DNA motif predictionrdquo InformationSciences vol 466 pp 25ndash43 2018

[17] S Shibao and Y Leilei ldquoResearch on variable precision roughset model and its applicationrdquo Computer Engineering andApplication vol 07 pp 10ndash13 2009

[18] T Xiaolong Several Problems of Multi Granularity VariablePrecision Rough Set Guangxi University For NationalitiesNanning China 2015

[19] W Xueming Research on Several Rough Set Models andNeural Network University of Electronic Science and Tech-nology of China Chengdu China 2013

[20] T Sun J Wang X Li et al ldquoComparative evaluation ofsupport vector machines for computer aided diagnosis of lungcancer in CT based on a multi-dimensional data setrdquo Com-puter Methods and Programs in Biomedicine vol 111 no 2pp 519ndash524 2013

[21] Z Yang T Ouyang X Fu and X Peng ldquoA decision-makingalgorithm for online shopping using deep-learning-basedopinion pairs mining and q -rung orthopair fuzzy interactionHeronianmean operatorsrdquo International Journal of IntelligentSystems vol 35 no 5 pp 783ndash825 2020

[22] W Chen C Lin C Li et al ldquoTracing the evolution of 3Dprinting technology in China using LDA-based patent ab-stract miningrdquo IEEE Transactions on Engineering Manage-men vol 36 pp 1ndash11 2020

18 Mathematical Problems in Engineering

Definition 1 (equivalence class) Assuming that R is anequivalence relation on K a collection of all elementsequivalent to an element k in K is called an equivalence classof k denoted as [k]

Definition 2 (indiscernibility relation) If PsubeR and Pne ϕthen capP is also an equivalence relation it is called theindiscernibility relation on P denoted as ind [P]

Definition 3 (upper approximation and lowerapproximation) +e knowledge base ofK (U R) XsubeU Ris equivalent to the relationship between U +e lower ap-proximation of X can be understood as all of the classifi-cation errors that are not greater than β are included in the Requivalence class in X +e upper approximation of X can beunderstood as the intersection of all those with classificationerror not greater than β and equivalence classes with X is notempty [18] Expressions are as follows

RX β cup Y isinU

R

1113868111386811138681113868111386811138681113868YsubeX1113882 1113883

RXβ cup Y isinU

R

1113868111386811138681113868111386811138681113868YcapXneφ1113882 1113883

(1)

Assume that the decision information table S (U AV f ) where U is a sample of the universe and a nonemptyfinite sample set U x1 X2 x3 Xn and Xi representseach sample A PcupQ P represents a collection of condi-tional attributes Q represents a set of decision attributes V

represents the range of attribute f U times A⟶ V is an in-formation function that gives an attribute value for eachattribute of each xi that is foralla isin A x isin U f(x a) isin Va X

and Y represent nonempty set in finite field U P QsubeA

represents the condition attribute set and decision attributeset ind (P) ind (Q) is an indiscernibility relation determinedby P Q ind (P) is a collection of equivalence classes calledcondition class expressed in UP ie Uind(P) P1 P2P3 Pn ind (P) is a collection of equivalence classes calleddecision class expressed in UQ that is Uind(Q) Q1 Q2Q3 Qn

Definition 4 (majority inclusion relation) If there is a e isin Y

for each e isin X then Y contains X denoted as Y X then

c(X Y) 1 minus |XcapY||X| |X|gt 0

0 |X| 01113896 (2)

where |X| represents the cardinality of the set X and c(X Y)

is the relative classification error rate of set X on set YMake (0le βlt 05) the majority inclusion relation is

defined as YsupeβX⟺ c(X Y)le β the ldquomajorityrdquo requirement

implies that the number of common elements in X and Y isgreater than 50 of the number of elements in X

Definition 5 (β-reduction) Conditional attribute set P is asubset of P for β-reduction or approximate reduction ofdecision attribute set Q and the subset is red(P Q β) andmeets the following two conditions [19]

(1) c(P Q β) c(red(P Q β) Q β)

(2) To remove any attribute from red(P Q β) condition(1) is not valid

+

(a) (b) (c)

=

Figure 1 +e source image of CT PET PETCT

Produceinitial

population

Inputoriginalfeature

Calculatingindividual

fitness

Whethermeets thecondition

Outputattribute sets

SelectionCrossoverMutation

Figure 2 Flow chart of knowledge reduction method based on genetic algorithm

Mathematical Problems in Engineering 3

231 Attribute Dependency

Definition 6 +e dependency of the decision attribute set Qand the conditional attribute set P is defined as

c(P Q β) |pos(P Q β)|

|U| (3)

pos(P Q β) cup YisinUQind(P) βQ |U| is the number of

objects contained in the domain |pos(P Q β)| is thenumber of objects contained in the positive domain of allequivalence classes that are not greater than the β classifi-cation error which indicates that the conditional attributescan correctly divide the object to U|Q c(0le cle 1) is the βdependency of the decision attribute Q to the conditionalattribute P and is an evaluation of the ability to classifyobjects with the classification error βc 0 means that Pcannot be used to divide objects into equivalence classes inQ c 1 means that P can be used to divide objects intoequivalence classes in Q completely 0lt clt 1 means that Pcan be used to divide objects into equivalence classes in Qpartly

232 Attribute Importance

Definition 7 Assume that the decision information table isS (U A V f ) A PcupQ s isin h the relative importance ofattribute s is

Z(s) c(P Q β) minus c(P minus s Q β)

c(P Q β) 1 minus

c(P minus s Q β)

c(P Q β)

(4)

An attribute is able to distinguish an object the greaterthe value the stronger the ability

+e selection of threshold β for variable precision roughset needs to meet the following requirements

+e choice of β to make the classification accuracy ashigh as possible

(1) 0le βlt 05(2) β makes the attributes contained in the reduction

results as little as possible

24 SVM Support vector machine (SVM) is a supervisedlearning model for data analysis pattern recognition andregression analysis in the field of machine learning +e bestcompromise between model complexity (the learning ac-curacy of a particular training sample) and learning ability(ability to identify an arbitrary sample without error) shouldbe found based on limited sample information In order toobtain the best generalization ability the basic idea is to usethe structural risk minimization principle to construct theoptimal classification hyperplane in the attribute space SVMhas some advantages such as good generalization abilitysimple data structure low computational complexity shorttraining time few parameters selection high fitting preci-sion strong robustness and so on [20 21] It has greatadvantages in dealing with small sample nonlinear and

high-dimensional pattern recognition It is often used inpattern recognition [12 22] regression estimation and soon

(1) After the introduction of kernel function and penaltyparameter by SVM the optimal discriminant func-tion model is

f(x) sgn 1113944n

i1aiyjk xi x( 1113857 + b⎛⎝ ⎞⎠ (5)

Among it 0lt altC yi isin 1 minus 1(2) +e optimization function of SVM is

Q(a) 1113944n

i1ai minus

12

1113944

n

ij1aiajyiyjk xi xj1113872 1113873 (6)

(3) +e radial basis kernel function is a widely usedkernel function the kernel function is used in thispaper

k(x y) exp minus gx minus y2

1113872 1113873 (7)

Among them ggt 0 g is an important parameter in thekernel function which affects the complexity of SVMclassification algorithm

+e kernel function parameter g and penalty coefficientC of support vector machine (SVM) is an important pa-rameter which affects the performance of SVM classificationso (C g) is used as the optimization variable In the processof learning SVM 5-fold cross validation is used to calculatethe optimal classification performance of kernel functionparameter and penalty coefficient and then the diagnosisresult of optimization is applied to the SVM classifier forlung cancer the final selection of the sensitivity specificityaccuracy and computation time as the evaluation indexes ofrelated experiments

3 Results and Discussion

31 Main Idea +e main idea of the model is as follows

311 Parameters Population sizeM chromosome lengthN(the number of condition attributes) crossover probabilityPc mutation probability Pm fitness function F(x) and themaximum number of iterations K are the parameters

312 Coding +e binary coding method is used which isrepresented by a binary string whose length is equal to thenumber of condition attributes each bit corresponds to acondition attribute a bit of 1 indicates that the corre-sponding condition attribute is selected 0 indicates that thecondition attribute is not selected eg 00110101 repre-sents a chromosome with a length of 8 and it is known thatthe corresponding 1 2 5 7 of 0 indicates that the corre-sponding condition attribute is not selected thenc3 C4 C6c8 is the last individual to choose the attributes set

4 Mathematical Problems in Engineering

313 4e Initial Population Assuming the population sizeM (the number of chromosomes in the population isM) Mlength of Lr chromosome (0 1) is the randomly generated asthe initial population

314 Genetic Operators Genetic operators include selectionoperator crossover operator and mutation operator +e se-lection operator generally uses the roulette wheel selectionmethod according to the selection probability pi

(fi1113936Mi1 fi) to select Crossover operator uses a single-point

crossover with a certain probability Pc to select the individualuniform crossover +e mutation operator selects the indi-viduals with the probability Pm to carry on the variation andrandomly selects the corresponding bit of the nonnuclearattribute

315 Fitness Function +e fitness function is the core of thegenetic algorithm the fitness value is the only index to evaluatethe fitness function this paper from the gene encoding valuethe minimum number of attributes reduction attribute de-pendency and other aspects constructs a fitness functionframework by adjusting the weights of various factors andchanging the classification error rate to achieve different fitnessfunction +e fitness function is set as follows

target1 Attribute dependency c(P Q β)

(|posβP(Q)||U|) it represents the β dependency ofdecision attribute Q for conditional attribute Ptarget2 Attributes reduction Length |C reduct| ((|P

| minus |Lr|)|P|) |P| is the number of condition attributesrepresented by 0 1 |Lr| represents the number of 1 inattribute P the shorter the better resultstarget3 Gene coding weight function ie Penaltyfunction target3 1113936 abs(r times (r minus 1))|r| Gene valuescan only take 0 and 1 but the chromosome will shownot 1 and not 0 such that the value is less than 0 orgreater than 1 +e value must be punished thereforethe gene coding weight function is constructed If thegene is 0 r times (r minus 1) 0 but the gene is 1r times (r minus 1) 0 So do not punish the genes of 0 or 1 butif there is a chromosome with a length of 6 r [0 0 minus 2minus 1 2 1] (r minus 1) [minus 1 minus 1 minus 3 minus 21 0] r times (r minus 1) [0 0 6 22 0] then 1113936 abs(r times (r minus 1)) 10 length is 6 sotarget3106167

+erefore the fitness function constructed in this paper isF(x) minus ω1 times target 1 minus ω2 times target 2 + ω3 times target 3 (8)

whereω is the weight coefficient of fitness functionω (0 1 23) because the genetic algorithm can only find the minimumvalue and the bigger the fitness value the better it is so theobjective function is minus and the penalty function is plus

Flow chart about this model is given in Figure 3

32 Model Concrete Steps

Input A decision information table S (U A V f )Output red(P Q β)

generate (M) Lr 98Initial population M 01 se-quence of Chromosome length 98Setting β ω crossover probability Pc mutationprobability Pm iteration number KBegin

for i 1 Ktarget1 (|posβP(Q)||U|)

target2 ((|P| minus |Lr|)|P|)

target3 (1113936 abs(r times (r minus 1))|r|)

Fitnessfunction minus ω1 times target1 minus ω2 times target2 + ω3 times target3Fitness functionP Select (M 2 Pc)Crossover probability PcQCrossover (P 2 Pc)Crossover algorithmQprimeMutation (Q Pm)Mutation algorithmEnd

33 Experimental Environment and Data

331 Hardware Environment Intel Core i5 4670-34GHzwith 80GB memory and 500GB hard disk were used

332 Software Environment Matlab R2012b LibSVM andWindows 7 operating system were used

333 Experimental Data +e PETCT images of 2000 lungcancer patients were collected as the study samples (1000cases of benign lung tumor 1000 cases of malignant lungtumor) Firstly ROI was extracted from the lung tumorand pretreated then 8-dimensional shape features 7-di-mensional gray features 3-dimensional Tamura features56-dimensional GLCM features and the 24-dimensionalfrequency domain features were extracted from the lungtumor ROI and 98-dimensional feature vectors are dis-creted and normalized In the decision attribute 1 rep-resents the lung malignant tumor and minus 1 represents thelung benign tumor Figure 4(a) shows four PETCT im-ages ROI of Lung malignant tumor and Figure 4(b) showsfour PETCT images ROI of lung benign tumor Table 1gives the feature values of two patients with lung cancer(one patient was a malignant tumor and the other was abenign tumor)

34Analysis ofExperimentalResults In this paper 3 kinds ofexperiments are designed according to the weight value ω

(0 1 2 3) of the fitness function and the classification errorrate β 04 02 0 (namely the inclusion degree1 minus β 06 08 1 ) For first type of experiments1 minus β 06 according to the different values of ω to do thethree groups of experiments totally For second type ofexperiments ϖ1 1ω2 1 ω3 0 according to the dif-ferent values of β to do three groups of experiments Forthird type of experiments 1 minus β 06 by increasing the ω

Mathematical Problems in Engineering 5

value to achieve the best fitness function to achieve the bestresults

341 Experiment 1mdashResearch on Different Weight Coeffi-cients under the Condition in the Same Classification ErrorRate ϖ values and β values of experiment 1 are shown inTable 2 and 1 minus β 06

(1) 1st Group Experiment ϖ1ω2ω3 1 0 0 +e al-gorithm is run 5 times according to this group weights theresults of the 5 groups are given in Table 3 including thereduction of the conditional attributes the length of re-duction the optimal fitness value the attribute dependencydegree and the time +e convergence of VPRS-GA under

the variation for fitness function value in one time is shownin Figure 5

Each reduction is classified by SVM classifier using themethod of 5-fold cross validation through changing thetraining samples and test samples the results of the fivegroups were obtained including accuracy sensitivityspecificity and time (training samples are constructed by800 malignant samples and 800 benign samples testingsamples are constructed by 200 malignant samples and 200benign samples the experiment is repeated 5 times bychanging training samples and testing samples) Finally theaverage values of these five groups are obtained as the finalresult of the reduction and shown in Table 4

+e weight value in this group experiment isϖ1ω2ω3 1 0 0 attribute dependency degree are

Output attributeset C_reduct1 C_re

duct2middotmiddotmiddotC_reductn

Indiscernibility relationfunction

Lower approximation

Relative positive domainposD

c function

Recognitionresult

SVMmodel

TrainingSVM

Reducedtraining set

Reducedtesting set

Target

Satisfycondition

Yes

No

Mutation Pm

Crossover Pc

Select Ps

F (x) = ndashω1 times target1 ndash ω2 times target2 + ω3 times target3β = 06 08 1

Initial population

Fitness value

Figure 3 Flow chart of high-dimensional feature selection based on genetic algorithm and variable precision rough set

(a) (b)

Figure 4 Part of lung tumor PETCT image ROI (a) Part of the lung malignant tumor PETCT-ROI (b) Part of the lung benign tumorPETCT-ROI

6 Mathematical Problems in Engineering

Table 1 ROI feature values of lung tumor PETCT image

Types of disease Shapefeature

Grayfeature

Tamuratexture

Texture features of GLCM Texture feature of wavelet

0 degree 45degrees

90degrees

135degrees Norm Standard

deviation Energy

Lung malignanttumor

60000 1222810 147000 00808 00779 00790 00611 6492580 371752 1000000012 14911500 309650 28937 29067 28989 31284 269473 38486 0001700000 386154 02326 02576 02820 02653 04490 93520 13355 0000200000 minus 05056 01668 01676 01659 01649 168200 24025 0000700000 24166 00792 00759 00772 00566 271143 38693 0001700000 140453 02576 02820 02653 04490 203163 29020 0001000000 70524 164110 164469 163584 164431 131755 18818 0000400000 27089 27072 27100 28066 183441 26199 00008

05755 06007 05810 073452109390 2117900 2095780 208825003064 03351 03135 03950

minus 06779 minus 06708 minus 06775 minus 0569600000 00000 00000 0000007625 07802 07658 08001

Lung benigntumor

40000 503912 101616 08087 07915 08077 07864 3799170 26741 1000000033 60006 18835 04324 04732 04370 04840 57551 08211 0000200000 24496 26329 00433 00621 00469 00679 11745 01677 0000000000 05649 94899 78127 92429 92429 34684 04955 0000100000 28589 08082 07905 08072 07853 20823 02972 0000000000 3283 00433 00621 00469 00679 21821 03117 0000000000 32559 78367 78363 78396 78363 08937 01276 0000000000 04024 04301 04045 04370 22387 03197 00000

01782 02326 01894 02481555257 550899 555291 54983100596 00873 00650 00958

minus 04707 minus 03295 minus 04351 minus 0291100000 00000 00000 0000020429 21172 20651 21394

Table 3 Results of VPRS-GA running 5 times when 1-β 06 ω1 1ω2 0ω3 0

Experimenttimes C_ reduction Reduction

lengthOptimal

fitness valueAttribute

dependency degree Time (s)

1 4 5 8 9 11 12 13 17 20 22 23 24 27 30 32 33 35 38 42 48 4952 57 59 61 62 63 64 65 68 70 72 73 75 77 78 80 87 88 91 92 41 minus 09705 09705 9719144

21 2 3 4 5 8 11 12 13 14 16 17 19 23 24 25 26 27 28 30 32 3638 39 40 42 43 44 46 47 52 53 55 61 63 66 67 69 71 72 73 77

79 80 82 84 85 87 9249 minus 09685 09685 10076907

3 4 611 12 1517 18 24 25 26 28 29 31 36 38 39 42 43 45 47 4953 56 65 68 69 72 76 77 79 80 81 83 85 88 91 92 37 minus 09695 09695 10432000

4 4 8 9 11 12 13 14 15 17 23 29 34 35 39 40 43 47 48 50 53 5556 60 61 64 68 70 75 80 81 82 83 84 86 34 minus 09790 09790 9473111

5 3 4 6 81011 12 13151719 20 21 24 26 29 31 39 42 44 45 4850 53 54 56 59 64 68 77 83 84 87 89 92 35 minus 09775 09775 9645092

Average value 392 minus 09730 09730 9869251

Table 2 Fitness function weight proportion and β value

Experiment times1 minus β 06

ω1 ω2 ω3First group experiment 1 0 0Second group experiment 1 1 0+ird group experiment 1 1 1

Mathematical Problems in Engineering 7

regarded as fitness function +e average attribute de-pendency degree is 0973 the average length of reductionis 392 and the average optimal fitness value is minus 0973+e average recognition accuracy of the experiment is9692 +e premature phenomena are shown in Fig-ure 5 and evolution progress is terminated early

(2) 2nd Group Experiment ϖ1ω2ω3 1 1 0 +isexperiment introduces an objective function to control thelength of reduction (the shorter the length of reduction thebetter it is) the influence degree of the objective functionwhich controls the reduction on the fitness function and the

final recognition accuracy is verified +e algorithm is run 5times according to this group weights and the results of the 5groups are given in Table 5 including the reduction of theconditional attributes the length of reduction the optimalfitness value the attribute dependency and the time +econvergence of VPRS-GA under the variation for fitnessfunction value in one time is shown in Figure 6

Each reduction is classified by SVM classifier using themethod of 5-fold cross validation through changing thetraining samples and test samples the results of the fivegroups were obtained including accuracy sensitivityspecificity and time (training samples are constructed by

ndash06

ndash07

ndash08

ndash09

ndash10 50 100 150

Generation stopping criteria

Best ndash09695 Mean ndash0944425

Fitn

ess v

alue

Best fitnessMean fitness

Figure 5 +e variation of fitness function value in a running process for Experiment 1-first group

Table 4 +e statistical results of the first group for experiment 1 with the SVM classifier

Experiment times Accuracy () Sensitivity () Specificity () Time (s)

Reduction 1

1 9250 8600 9900 3326072 9725 9750 9700 3450513 9900 9900 9900 3586774 9800 9950 9650 3510755 9925 10000 9850 355948

Average value 9720 9640 9800 348672

Reduction 2

1 9325 8700 9950 4365332 9725 9800 9650 4459003 9875 9850 9900 4395064 9750 9900 9600 4450645 9925 10000 9850 448513

Average value 9720 9650 9790 443103

Reduction 3

1 9275 8750 9800 3269162 9575 9750 9400 3372093 9800 9800 9800 3407014 9700 9850 9550 3331745 9850 9950 9750 333257

Average value 9640 9620 9660 334251

Reduction 4

1 9375 8850 9900 3064852 9650 9750 9550 3192403 9750 9700 9800 3240824 9775 9900 9650 3254195 9900 10000 9800 361516

Average value 9690 9640 9740 318806

Reduction 5

1 9400 8900 9900 3195572 9650 9750 9550 3369093 9725 9700 9750 3301594 9775 9900 9650 3999805 9900 10000 9800 325692

Average value 9690 9650 9730 342459

8 Mathematical Problems in Engineering

800 malignant samples and 800 benign samples testingsamples are constructed by 200 malignant samples and 200benign samples the experiment is repeated 5 times bychanging training samples and testing samples) Finally theaverage values of these five groups are obtained as the finalresult of the reduction and shown in Table 6

+e experimental weight of this group is ϖ1

ω2ω3 1 1 0 attribute dependency degree and thelength of reduction are regarded as fitness function As canbe seen from Table 5 the reduction length is 13 17 and soon +e average length of reduction was 17 which wassignificantly reduced compared with the average length ofthe reduction in Table 3 in the experiment of the first groupswhich reduced the time improved the efficiency of the al-gorithm and increased the attribute dependency of thealgorithm even up to 1 +e average recognition accuracy ofthe experimental group was 9698 which was increased by006 compared with that in the first groups

(3) 3rd Group Experiment ϖ1ω2ω3 1 1 1 On thebasis of attribute dependency degree and attribute reductionlength this experiment introduces gene coding weightfunction in order to verify the effect of gene coding weightfunction on fitness function and the final recognition ac-curacy +e algorithm are run 5 times according to thisgroup weights the results of the 5 groups are given inTable 7 including the reduction of the conditional attributesthe length of reduction the optimal fitness value the at-tribute dependency and the time +e convergence ofVPRS-GA under the variation for fitness function value inone time is shown in Figure 7

Each reduction is classified by SVM classifier using themethod of 5-fold cross validation through changing thetraining samples and test samples the results of the fivegroups were obtained including accuracy sensitivityspecificity and time (training samples are constructed by800 malignant samples and 800 benign samples testingsamples are constructed by 200 malignant samples and 200benign samples the experiment is repeated 5 times bychanging training samples and testing samples) Finally theaverage values of these five groups are obtained as the finalresult of the reduction and shown in Table 8

+e experimental weight of this group is ϖ1 ω2ω3=1 1 1 attribute dependency degree the length of re-duction and gene coding weight value are regarded as fitnessfunction However the premature phenomena are shown inFigure 7 and evolution progress is terminated early FromTable 7 we can see that the attribute dependency decreasesgradually and even the attribute dependency of Reduction 1is reduced to 0759 +e average recognition accuracy of theexperimental group was 9685+e accuracy of recognitionwas decreased compared with the second groups and henceusing gene encoding weight function in the fitness functionto improve recognition accuracy is useless only for thesamples with different results to analyze specific issues +e3 experiment runs of experiment 1 verified the necessity ofthe fitness function by continuously introducing fitnessobjective function such as target1 target2 and target3 theconclusion is that the fitness function is better when it is notbigger but after the introduction of target3 the accuracydeclines therefore the introduction of target1 and target2 inthis algorithm can get better results

Table 5 Results of VPRS-GA running 5 times when 1 minus β 06 ω1 1ω2 1ω3 0

Experiment times C_ reduction Reductionlength

Optimalfitness value

Attributedependency

degreeTime (s)

1 5 9 14 20 26 41 43 46 48 54 55 57 64 66 74 79 86 90 18 minus 46487 09965 107240722 1 4 11 12 14 24 34 40 42 43 56 60 61 65 67 68 71 72 85 19 minus 40109 1 63281223 2 13 27 29 39 42 45 56 59 63 68 70 75 13 minus 46512 09990 110239674 1 3 4 7 9 11 12 15 30 34 38 42 46 48 55 62 65 77 79 19 minus 49674 1 87946705 3 9 11 13 29 39 41 42 43 46 50 55 65 c77 85 86 16 minus 44114 09815 15075539

Average value 17 minus 45379 09954 10389274

ndash1

ndash2

ndash3

ndash4

ndash5

Fitn

ess v

alue

Best ndash496739 Mean ndash492312

0 50 100 150Generation stopping criteria

Best fitnessMean fitness

Figure 6 +e variation of fitness function value in a running process for experiment 1-second group

Mathematical Problems in Engineering 9

342 Experiment 2mdashResearch on Different ClassificationError Rates under the Condition in the Same WeightCoefficient According to experiment 1 we can see thatwhen ω1 1 ω2 1 ω3 0 the experimental results arethe best so in experiment 2 the case of the weight value ofwas unchanged ω1 1 ω2 1 ω3 0 and the β value waschanged and they are shown in Table 9

(1) 1st Group Experiment 1 minus β 06 +e algorithm is run 5times according to this group weights the results of the 5groups are shown in Table 5 including the reduction of the

conditional attributes the length of reduction the optimalfitness value the attribute dependency and the time +econvergence of VPRS-GA under the variation for fitnessfunction value for one time is shown in Figure 6 (ie notrepeated in the second group of experiment 1)

(2) 2nd Group Experiment 1 minus β 08 +e algorithm are is 5times according to this group weights the results of the 5groups are given in Table 10 including the reduction of theconditional attributes the length of reduction the optimalfitness value the attribute dependency and the time +e

Table 6 +e statistical results of the second group for experiment 1 with the SVM classifier

Experiment times Accuracy () Sensitivity () Specificity () Time (s)

Reduction 1

1 9300 8600 10000 1164882 9625 9600 9650 1255113 9850 9900 9800 1315094 9725 9850 9600 1344685 9925 10000 9850 144839

Average value 9685 9590 9780 130563

Reduction 2

1 9425 8900 9950 1210962 9725 9700 9750 1286363 9800 9800 9800 1356774 9750 9800 9700 1381965 9875 9900 9850 136691

Average value 9715 9620 9810 132059

Reduction 3

1 9300 8750 9850 877572 9725 9750 9700 1034243 9775 9800 9750 1074114 9775 9850 9700 1123445 9900 10000 9800 113006

Average value 9695 9630 9760 104788

Reduction 4

1 9375 8750 10000 1464172 9650 9750 9550 1547363 9750 9700 9800 1576214 9800 9900 9700 1613555 9925 10000 9850 163381

Average value 9700 9620 9780 156702

Reduction 5

1 9250 8650 9850 1249332 9675 9800 9550 1400573 9800 9800 9800 1451944 9800 9900 9700 1457925 9950 9950 9950 150400

Average value 9695 9620 9770 141275

Table 7 Results of VPRS-GA running 5 times when 1 minus β 06 ω1 1ω2 1ω3 1

Experimenttimes C_ reduction Reduction

lengthOptimal

fitness valueAttribute

dependency degree Time (s)

1 4 5 7 26 27 34 35 41 47 54 55 71 74 75 78 80 83 90 18 minus 14192 07590 6888635

2 4 15 16 19 22 27 28 29 30 35 38 42 45 50 52 53 59 61 6264 65 70 71 72 77 87 88 27 minus 15232 08640 8124857

3 6 17 19 24 28 31 33 34 38 39 43 45 47 48 49 51 55 56 6667 69 70 71 72 76 77 78 80 81 84 87 89 91 92 34 minus 13545 07950 9521511

4 3 6 8 91617 19 20 24 25 28 35 37 39 41 42 46 49 51 52 5459 63 65 66 74 83 86 28 minus 14703 08365 8714839

5 1 7 8 15 17 19 20 23 29 37 45 48 54 60 62 70 73 75 77 7879 86 22 minus 14990 07995 7797617

Average value 258 minus 14532 08108 8209492

10 Mathematical Problems in Engineering

convergence of VPRS-GA under the variation for fitnessfunction value for one time is shown in Figure 8

Each reduction is classified by SVM classifier using themethod of 5-fold cross validation through changing thetraining samples and test samples the results of the five

groups were obtained including accuracy sensitivityspecificity and time (training samples are constructed by800 malignant samples and 800 benign samples testingsamples are constructed by 200 malignant samples and 200benign samples the experiment is repeated 5 times by

ndash08

ndash1

ndash12

ndash14

ndash16

Fitn

ess v

alue

Best ndash141919 Mean ndash128476

0 50 100 150Generation stopping criteria

Best fitnessMean fitness

Figure 7 +e variation of fitness function value in a running process for experiment 1-third group

Table 8 +e statistical results of the third group for experiment 1 with the SVM classifier

Experiment times Accuracy () Sensitivity () Specificity () Time (s)

Reduction 1

1 9275 8600 9950 924922 9725 9750 9700 1074613 9850 9850 9850 1138114 9775 9900 9650 1155605 9875 10000 9750 117022

Average value 9700 9620 9780 109269

Reduction 2

1 9350 8750 9950 1482452 9700 9650 9750 1615353 9775 9850 9700 1664524 9800 9850 9750 1754505 9875 9950 9800 172348

Average value 9700 9610 9790 164806

Reduction 3

1 9125 8300 9950 2019042 9650 9700 9600 2185353 9800 9800 9800 2196054 9625 9900 9350 2230915 9825 10000 9650 236896

Average value 9605 9540 9670 220006

Reduction 4

1 9300 8700 9900 1654542 9675 9600 9750 1724323 9875 9850 9900 1793014 9800 9900 9700 1895605 9900 9950 9850 185249

Average value 9710 9600 9820 178399

Reduction 5

1 9275 8600 9950 1411732 9725 9800 9650 1612953 9900 9950 9850 1589924 9775 9950 9600 1648765 9875 10000 9750 166070

Average value 9710 9660 9760 158481

Table 9 Fitness function weight proportion and β value

Experiment timesω1 1 ω2 1 ω3 0

1 minus β 06 1 minus β 08 1 minus β 1First group experiment Second group experiment +ird group experiment

Mathematical Problems in Engineering 11

changing training samples and testing samples) Finally theaverage values of these five groups are obtained as the finalresult of the reduction and shown in Table 11

In the case of constant weight ϖ and classification errorrate of β 02 (which contains 1 minus β 08) the classificationerror rate is changed on the basis of the attribute dependencyand the length of control reduction +e premature phe-nomena are shown in Figure 8 and evolution progress isterminated early such that the attribute dependency ofreduction 5 was 08405 appeared in attribute dependency onless than 09 compared with first groups of experiment 2attribute dependency declined +e average recognitionaccuracy of the experimental group was 9674 Comparedwith the classification error rate of 04 and inclusion degreeof 06 the accuracy was decreased by 024

(3) 3rd Group Experiment 1 minus β1 +e algorithm is run 5times according to the group weights and the results of the 5groups are shown in Table 12 including the reduction of theconditional attributes the length of reduction the optimalfitness value the attribute dependency and the time +econvergence of VPRS-GA under the variation for fitnessfunction value for one time is shown in Figure 9

Each reduction is classified by SVM classifier using themethod of 5-fold cross validation through changing thetraining samples and test samples the results of the fivegroups were obtained including accuracy sensitivityspecificity and time (training samples are constructed by800 malignant samples and 800 benign samples testingsamples are constructed by 200 malignant samples and 200

benign samples the experiment is repeated 5 times bychanging training samples and testing samples) Finally theaverage values of these five groups are obtained as the finalresult of the reduction and shown in Table 13

In the case of constant weight ϖ and classification errorrate of β= 0 (which contains 1 minus β= 1) the classificationerror rate is reduced and the inclusion degree is improved onthe basis of the attribute dependency and the length ofcontrol reduction +e premature phenomena are shown inFigure 9 and evolution progress is terminated early +eaverage recognition accuracy of the experimental group was9573 which was decreased by 006 compared with thatin the second group In experiment 2 the effect of changingthe classification error rate on the recognition accuracy wasverified by the 3 groups of experiments By continuallyreducing the classification error rate the final recognitionaccuracy has been declining when inclusion degree is 1β= 0 variable precision rough set becomes Pawlak rough setthe recognition accuracy of the recognition accuracy of isminimum which was verified the advantages of variableprecision rough set

343 Experiment 3mdashResearch on Increasing the WeightCoefficient under the Condition in the Same ClassificationError Rate According to experiment 1 and experiment 2we can know that when β 06 ω1 1 ω2 1 ω3 0 therecognition accuracy is the best therefore in the thirdexperiment by increasing the weight of ω 3 groups ofexperiments are performed fitness goals target 1 (attribute

Table 10 Results of VPRS-GA running 5 times when 1 minus β 08 ω1 1ω2 1ω3 0

Experimenttimes C_ reduction Reduction

lengthOptimal fitness

valueAttribute

dependency degree Time (s)

1 8 9 11 12 15 16 17 18 25 26 29 31 35 39 40 41 42 48 5865 67 68 70 83 84 91 26 minus 67816 09490 10002827

2 1 6 8 9 11 12 15 17 21 23 26 28 30 31 34 44 50 56 58 5962 63 64 68 71 75 77 82 89 92 30 minus 67797 09615 9477387

3 6 8 12 14 15 16 17 21 28 35 38 39 45 49 55 58 61 62 6465 77 82 85 23 minus 68694 09070 12866181

4 4 6 7 8 11 12 13 16 17 20 25 26 31 32 34 35 41 42 44 4950 55 58 68 72 74 76 78 79 85 89 92 32 minus 67225 09540 10510220

5 3 6 8 9 10 16 17 26 27 34 36 37 38 40 42 44 46 51 52 6266 67 84 86 87 25 minus 65892 08405 8469324

Average value 272 minus 67484 09224 10265188

ndash55

ndash6

ndash65

ndash7

Fitn

ess v

alue

Best ndash686942 Mean ndash653584

0 50 100 150Generation stopping criteria

Best fitnessMean fitness

Figure 8 +e variation of fitness function value in a running process for experiment 2-second group

12 Mathematical Problems in Engineering

Table 11 +e statistical results of the second group for experiment 2 with the SVM classifier

Experiment times Accuracy () Sensitivity () Specificity () Time (s)

Reduction 1

1 9300 8650 9950 2280072 9575 9700 9450 2376463 9700 9600 9800 2332504 9750 9850 9650 2444915 9925 10000 9850 244816

Average value 9650 9560 9740 237642

Reduction 2

1 9375 8800 9950 2524032 9625 9750 9500 2652893 9800 9700 9900 2655234 9800 9900 9700 2682125 9950 10000 9900 275880

Average value 9710 9630 9790 265461

Reduction 3

1 9275 8750 9800 1807802 9675 9750 9600 1929923 9700 9600 9800 1872434 9775 9950 9600 2084825 9875 10000 9750 203507

Average value 9660 9610 9710 194601

Reduction 4

1 9200 8650 9750 2572602 9700 9750 9650 2730243 9775 9650 9900 2723164 9750 9900 9600 2815545 9900 10000 9800 291471

Average value 9665 9590 9740 275125

Reduction 5

1 9275 8750 9800 1437152 9675 9600 9750 1526373 9750 9800 9700 1589294 9775 9900 9650 1629975 9950 10000 9900 166792

Average value 9685 9610 9760 157014

Table 12 Results of VPRS-GA running 5 times when 1 minus β 1 ω1 1ω2 1ω3 0

Experimenttimes C_ reduction Reduction

lengthOptimal fitness

valueAttribute dependency

degree Time (s)

1 15 44 68 73 79 84 6 minus 27313 07965 114499012 34 51 54 75 80 90 6 minus 27047 08460 96993913 2 34 49 70 71 72 76 81 8 minus 34057 07535 112334894 12 25 78 85 4 minus 22872 09285 11668133

5 6 7 12 13 42 44 55 57 65 66 69 77 81 8687 15 minus 33230 08665 13236077

Average value 78 minus 28903 08382 11457398

ndash1

ndash2

ndash3

ndash4

Fitn

ess v

alue

0 50 100 150Generation stopping criteria

Best fitnessMean fitness

Best ndash340567 Mean ndash330598

Figure 9 +e variation of fitness function value in a running process for experiment 2-third group

Mathematical Problems in Engineering 13

dependency) target 2 (the minimum number of attributesreduction) and target 3 (gene encoding weight function)the three objective functions play an important role in theevaluation of fitness function However the importance offitness function is reduced in these three objectives+erefore in this experiment when the other conditions areunchanged the weight coefficient of the target 1 is increasedto verify the influence of the change in the weight coefficienton the experimental results and they are shown in Table 14

(1) 1st Group Experiment ω1 1 ω2 1 ω3 0 +e al-gorithm are run 5 times according to this group weights theresults of the 5 groups are given in Table 5 including thereduction of the conditional attributes the length of reduc-tion the optimal fitness value the attribute dependency andthe time +e convergence of VPRS-GA under the variationfor fitness function value in one time is shown in Figure 6 (ienot repeated for the second group of experiment 1)

(2) 2nd Group Experiment ω1 2 ω2 1 ω3 0 +ealgorithm is run 5 times according to this group weights theresults of the 5 groups are given in Table 15 including thereduction of the conditional attributes the length of re-duction the optimal fitness value the attribute dependencyand the time +e convergence of VPRS-GA under thevariation for fitness function value in one time is shown inFigure 10

Each reduction is classified by SVM classifier using themethod of 5-fold cross validation through changing thetraining samples and test samples the results of the fivegroups were obtained including accuracy sensitivityspecificity and time (training samples are constructed by800 malignant samples and 800 benign samples testingsamples are constructed by 200 malignant samples and 200benign samples the experiment is repeated 5 times bychanging training samples and testing samples) Finally theaverage values of these five groups are obtained as the finalresult of the reduction and shown in Table 16

+e experimental group in the case of 1 minus β= 06 un-changed the weight of ω1 was increased +e attributedependency and the optimal fitness function are relativelyhigh the average precision of reduction 1 reduction 2 andreduction 3 in Table 16 is more than 97 and that of re-duction 2 is even up to 9725 +e average recognitionaccuracy of the experimental group is 9703 which ishigher than that of the first group

Table 13 +e statistical results of the third group for experiment 2 with the SVM classifier

Experiment times Accuracy () Sensitivity () Specificity () Time (s)

Reduction 1

1 9225 8450 10000 812712 9550 9700 9400 945833 9575 9400 9750 881984 9600 9800 9400 937545 9725 9900 9550 98691

Average value 9535 9450 9620 91299

Reduction 2

1 9200 8450 9950 648942 9625 9550 9700 801983 9525 9300 9750 773374 9600 9750 9450 760125 9800 10000 9600 82763

Average value 9550 9410 9690 76241

Reduction 3

1 9200 8450 9950 648942 9625 9550 9700 801983 9525 9300 9750 773374 9600 9750 9450 760125 9800 10000 9600 82763

Average value 9550 9410 9690 76241

Reduction 4

1 9275 8550 10000 672642 9675 9600 9750 784673 9600 9450 9750 730224 9575 9750 9400 794605 9800 10000 9600 84184

Average value 9585 9470 9700 76479

Reduction 5

1 9200 8450 9950 1147192 9625 9750 9500 1287053 9850 9900 9800 1320494 9775 9950 9600 1335135 9850 10000 9700 133144

Average value 9660 9610 9710 128426

Table 14 Fitness function weight proportion and β value

Experiment times1 minus β 06

ω1 ω2 ω3First group experiment 1 1 0Second group experiment 2 1 0+ird group experiment 3 1 0

14 Mathematical Problems in Engineering

ndash2

ndash25

ndash3

Fitn

ess v

alue

0 50 100 150Generation stopping criteria

Best fitnessMean fitness

Best ndash2915 Mean ndash291446

Figure 10 +e variation of fitness function value in a running process for experiment 3-second group

Table 15 Results of VPRS-GA running 5 times when 1 minus β 06 ω1 2ω2 1ω3 0

Experimenttimes C_ reduction Reduction

lengthOptimal fitness

valueAttribute dependency

degree Time (s)

1 2 3 4 5 11 13 16 18 24 30 34 37 39 41 42 51 55 64 7077 78 82 22 minus 34859 09060 21515464

2 8 9 11 12 14 15 23 25 26 29 30 33 37 42 43 45 46 5060 61 69 74 80 87 89 25 minus 30845 09390 42761634

3 8 11 12 13 16 18 19 24 29 36 37 43 64 65 68 71 86 9192 19 minus 35039 09150 26197164

4 2 3 4 8 10 11 12 13 15 16 19 23 25 30 48 55 64 65 6874 77 80 81 83 84 86 89 27 minus 29150 09575 44271631

5 5 8 911 121517 23 25 29 31 36 39 41 48 54 59 63 8083 86 89 22 minus 29920 09525 43161464

Average value 23 minus 31962 09340 35581471

Table 16 +e statistical results of the second group for experiment 3 with the SVM classifier

Experiment times Accuracy () Sensitivity () Specificity () Time (s)

Reduction 1

1 9275 8600 9950 1884972 9725 9800 9650 1571623 9850 9900 9800 1586914 9800 9900 9700 1646035 9950 10000 9900 161914

Average value 9720 9640 9800 166173

Reduction 2

1 9450 8950 9950 1908132 9675 9800 9550 2002513 9775 9800 9750 1970084 9850 9900 9800 2009245 9875 9900 9850 209245

Average value 9725 9670 9780 199648

Reduction 3

1 9400 8800 10000 1313692 9725 9800 9650 1447973 9800 9800 9800 1426624 9725 9850 9600 1471905 9925 10000 9850 148799

Average value 9715 9650 9780 142963

Reduction 4

1 9350 8750 9950 2404562 9700 9750 9650 2520823 9800 9800 9800 2511754 9775 9950 9600 2701885 9825 10000 9650 267471

Average value 9690 9650 9730 256274

Reduction 5

1 9325 8800 9850 1809592 9600 9800 9400 1965633 9750 9750 9750 1967234 9800 9900 9700 2078295 9850 9950 9750 219703

Average value 9665 9640 9690 200355

Mathematical Problems in Engineering 15

Table 17 Results of VPRS-GA running 5 times when 1 minus β 1 ω1 1ω2 1ω3 0

Experimenttimes C_ reduction Reduction

lengthOptimal fitness

valueAttribute

dependency degree Time (s)

1 3 4 5 8 9 11 12 17 19 29 34 35 38 46 52 53 55 59 63 6672 75 77 78 79 87 92 27 minus 38867 09550 28981789

2 4 8 9 11 12 15 17 29 33 37 38 39 42 43 48 55 67 73 7881 83 84 88 89 90 25 minus 38167 09715 55783772

3 2 3 4 8 9 10 11 12 13 15 16 19 24 25 30 36 49 54 55 6064 67 68 70 74 77 83 85 86 91 30 minus 38807 09530 34831096

4 4 5 7 11 12 14 15 17 25 29 33 36 39 41 42 47 48 50 5556 58 62 67 69 72 74 77 84 86 90 91 31 minus 39430 09665 35742822

5 3 4 5 8 9 11 12 17 19 29 34 35 38 46 52 53 55 59 63 6672 75 77 78 79 87 92 27 minus 38867 09550 27919582

Average value 28 minus 38827 09602 36651812

ndash3

ndash35

ndash40 50 100 150

Generation stopping criteria

Fitn

ess v

alue

Best fitnessMean fitness

Best ndash394298 Mean ndash393327

Figure 11 +e variation of fitness function value in a running process for experiment 3-third group

Table 18 +e statistical results of the Second group for experiment 3 with the SVM classifier

Experiment times Accuracy () Sensitivity () Specificity () Time (s)

Reduction 1

1 9200 8700 9700 2187172 9750 9750 9750 2105503 9850 9850 9850 2032064 9800 9900 9700 2211645 9925 10000 9850 272536

Average value 9705 9640 9770 225235

Reduction 2

1 9400 8850 9950 2331232 9575 9750 9400 2433493 9750 9700 9800 2442024 9775 9900 9650 2566075 9900 9950 9850 259071

Average value 9680 9630 9730 247270

Reduction 3

1 9275 8650 9900 2525842 9625 9750 9500 2624123 9775 9800 9750 2601274 9775 9900 9650 2686705 9875 10000 9750 265387

Average value 9665 9620 9710 261836

Reduction 4

1 9150 8550 9750 2532312 9625 9750 9500 2649433 9750 9700 9800 2752834 9800 9950 9650 3229545 9825 9950 9700 277432

Average value 9630 9580 9680 278769

Reduction 5

1 9200 8800 9600 1951962 9700 9700 9700 2148893 9825 9800 9850 2036124 9850 10000 9700 2133615 9900 9900 9900 225526

Average value 9695 9640 9750 210517

16 Mathematical Problems in Engineering

(3) 3rd Group Experiment ω1 3 ω2 1 ω3 0 +e al-gorithm is run 5 times according to the group weights andthe results of the 5 groups are given in Table 17 including thereduction of the conditional attributes the length of re-duction the optimal fitness value the attribute dependencyand the time +e convergence of VPRS-GA under thevariation for fitness function value for one time is shown inFigure 11

Each reduction is classified by SVM classifier using themethod of 5-fold cross validation through changing thetraining samples and test samples the results of the fivegroups were obtained including accuracy sensitivityspecificity and time (training samples are constructed by800 malignant samples and 800 benign samples testingsamples are constructed by 200 malignant samples and 200benign samples the experiment is repeated 5 times bychanging training samples and testing samples) Finally theaverage values of these five groups are obtained as the finalresult of the reduction and shown in Table 18

+e experiment in the case of 1 minus β 06 unchangedincrease the weight of the ω1 ω1 3 ω2 1 ω3 0 InTable 18 the recognition accuracy of reduction 1 is over 97only +e average recognition accuracy of the experimentalgroup is 9675 and the accuracy is decreased by 028compared with that in the other second groups +e threegroups of experiment 3 the purpose is to verify whether theexperimental accuracy is influenced by increasing theweight +e experimental results show that the accuracy ofsecond group for experimental weight 2 1 0 comparedwith first group experiment when 1 1 0 is high but thethird groups of experimental weight was 3 1 0 and theaccuracy declined therefore the weight of 2 1 0 is the bestchoice for this experiment

4 Conclusions

Aiming at the deficiency of the traditional rough set modelthis paper proposes a new feature selection model based ongenetic algorithm and variable precision rough set by in-troducing the β value the rigid inclusion of the approxi-mation for the traditional rough set is relaxed and then wedesign the 3 kinds of experiments by constructing the de-cision information table of the PETCT feature for lungtumor ROI +e first type of experiment is the inclusion of1 minus β 06 and different values of ω made a total of threegroups of experiments the experimental results show thatthe better recognition accuracy can be obtained when theweight is 1 1 0 and the results show that the gene codingweight function has no effect on the fitness function For thesecond type of experiments ϖ1 1ω2 1 ω3 0according to the different values of β to do three groups ofexperiments the results show that the recognition accuracyof 1 minus β 06 is the best which shows that the larger the βvalue is the lower approximate cardinality will be largerthen the relative accuracy will increase For the third type ofexperiments 1 minus β 06 ω value is increased to achieve thebest fitness function in order to achieve the best results +eexperimental results show that the recognition accuracy isbetter than the others when the weight value is 2 1 0 so it

is better to solve the problem by increasing the proportion ofattribute dependency +rough the above experiments it isshown that the high-dimensional feature selection algorithmbased on genetic algorithm and variable precision rough setcan solve the multiobjective optimization problem wellHowever when the fitness function and its parameters areapplied in the specific application it is necessary to analyzethe specific problems

Data Availability

+e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

+e authors declare no conflicts of interest

Acknowledgments

+is work was supported by National Natural ScienceFoundation of China (Grant nos 61561040 and 61876121)First-Class Disciplines Foundation of Ningxia (NoNXYLXK2017B09)

References

[1] S Luo D Miao Z Zhang Y Zhang and S Hu ldquoA neigh-borhood rough set model with nominal metric embeddingrdquoInformation Sciences vol 520 pp 373ndash388 2020

[2] B Barman and S Patra ldquoVariable precision rough set basedunsupervised band selection technique for hyperspectralimage classificationrdquo Knowledge-Based Systems vol 1936Article ID 105414 2020

[3] Y Chenyi and L Jinjin ldquoApproximate attribute reductionunder variable precision rough set βrdquo Journal of ShandongUniversity vol 11 pp 17ndash21 2011

[4] S Xiaowei Research on Hierarchical Model of Attribute Re-duction in Variable Precision Rough Set Central SouthUniversity Changsha China 2013

[5] Z Jie and W Jiayang ldquoAnalysis of reduction feature ofvariable precision rough set modelrdquo Computer ApplicationResearch vol 7 pp 12ndash15 2007

[6] Z Pei and Z Qinghua ldquoFCM clustering algorithm based onvariable precision rough setrdquo Journal of Shanxi Universityvol 3 pp 342ndash348 2016

[7] C Hao and Y Junan ldquoAttribute kernel and minimum at-tribute reduction algorithm of variable precision rough setrdquoActa Sinica Sinica vol 5 pp 1011ndash1017 2012

[8] S Xu X Yang H Yu D-J Yu J Yang and E CC TsangldquoMulti-label learning with label-specific feature reductionrdquoKnowledge-Based Systems vol 104 pp 52ndash61 2016

[9] I Maryam and G Hassan ldquoFeature space discriminantanalysis for hyperspectral data feature reductionrdquo ISPRSJournal of Photogrammetry and Remote Sensing vol 102pp 1ndash13 2015

[10] S Q Wang C Y Gao C Luo G M Zheng and Y N ZhouldquoResearch on feature selectionattribute reduction methodbased on rough set theoryrdquo Procedia Computer Sciencevol 154 pp 194ndash198e 2019

[11] A W Omar M Azzam O Hadi and B Jamal ldquoCEAP SVM-based intelligent detection model for clustered vehicular ad

Mathematical Problems in Engineering 17

hoc networksrdquo Expert Systems with Applications vol 50pp 40ndash54 2016

[12] H Lee and Y-P P Chen ldquoImage based computer aideddiagnosis system for cancer detectionrdquo Expert Systems withApplications vol 42 no 12 pp 5356ndash5365 2015

[13] J A Guy and P L Harold ldquoAfter detection the improvedaccuracy of lung cancer assessment using radiologic com-puter-aided diagnosisrdquo Academic Radiology vol 23 no 2pp 186ndash191 2016

[14] E Kiyonori T Shodayu J Binghu et al ldquoPleural invasion byperipheral lung cancer prediction with three-dimensionalCTrdquo Academic Radiology vol 3 pp 310ndash319 2015

[15] B Koohestani ldquoA crossover operator for improving the ef-ficiency of permutation-based genetic algorithmsrdquo ExpertSystems with Applications vol 1511 Article ID 113381 2020

[16] N K Lee X Li and D Wang ldquoA comprehensive survey ongenetic algorithms for DNA motif predictionrdquo InformationSciences vol 466 pp 25ndash43 2018

[17] S Shibao and Y Leilei ldquoResearch on variable precision roughset model and its applicationrdquo Computer Engineering andApplication vol 07 pp 10ndash13 2009

[18] T Xiaolong Several Problems of Multi Granularity VariablePrecision Rough Set Guangxi University For NationalitiesNanning China 2015

[19] W Xueming Research on Several Rough Set Models andNeural Network University of Electronic Science and Tech-nology of China Chengdu China 2013

[20] T Sun J Wang X Li et al ldquoComparative evaluation ofsupport vector machines for computer aided diagnosis of lungcancer in CT based on a multi-dimensional data setrdquo Com-puter Methods and Programs in Biomedicine vol 111 no 2pp 519ndash524 2013

[21] Z Yang T Ouyang X Fu and X Peng ldquoA decision-makingalgorithm for online shopping using deep-learning-basedopinion pairs mining and q -rung orthopair fuzzy interactionHeronianmean operatorsrdquo International Journal of IntelligentSystems vol 35 no 5 pp 783ndash825 2020

[22] W Chen C Lin C Li et al ldquoTracing the evolution of 3Dprinting technology in China using LDA-based patent ab-stract miningrdquo IEEE Transactions on Engineering Manage-men vol 36 pp 1ndash11 2020

18 Mathematical Problems in Engineering

231 Attribute Dependency

Definition 6 +e dependency of the decision attribute set Qand the conditional attribute set P is defined as

c(P Q β) |pos(P Q β)|

|U| (3)

pos(P Q β) cup YisinUQind(P) βQ |U| is the number of

objects contained in the domain |pos(P Q β)| is thenumber of objects contained in the positive domain of allequivalence classes that are not greater than the β classifi-cation error which indicates that the conditional attributescan correctly divide the object to U|Q c(0le cle 1) is the βdependency of the decision attribute Q to the conditionalattribute P and is an evaluation of the ability to classifyobjects with the classification error βc 0 means that Pcannot be used to divide objects into equivalence classes inQ c 1 means that P can be used to divide objects intoequivalence classes in Q completely 0lt clt 1 means that Pcan be used to divide objects into equivalence classes in Qpartly

232 Attribute Importance

Definition 7 Assume that the decision information table isS (U A V f ) A PcupQ s isin h the relative importance ofattribute s is

Z(s) c(P Q β) minus c(P minus s Q β)

c(P Q β) 1 minus

c(P minus s Q β)

c(P Q β)

(4)

An attribute is able to distinguish an object the greaterthe value the stronger the ability

+e selection of threshold β for variable precision roughset needs to meet the following requirements

+e choice of β to make the classification accuracy ashigh as possible

(1) 0le βlt 05(2) β makes the attributes contained in the reduction

results as little as possible

24 SVM Support vector machine (SVM) is a supervisedlearning model for data analysis pattern recognition andregression analysis in the field of machine learning +e bestcompromise between model complexity (the learning ac-curacy of a particular training sample) and learning ability(ability to identify an arbitrary sample without error) shouldbe found based on limited sample information In order toobtain the best generalization ability the basic idea is to usethe structural risk minimization principle to construct theoptimal classification hyperplane in the attribute space SVMhas some advantages such as good generalization abilitysimple data structure low computational complexity shorttraining time few parameters selection high fitting preci-sion strong robustness and so on [20 21] It has greatadvantages in dealing with small sample nonlinear and

high-dimensional pattern recognition It is often used inpattern recognition [12 22] regression estimation and soon

(1) After the introduction of kernel function and penaltyparameter by SVM the optimal discriminant func-tion model is

f(x) sgn 1113944n

i1aiyjk xi x( 1113857 + b⎛⎝ ⎞⎠ (5)

Among it 0lt altC yi isin 1 minus 1(2) +e optimization function of SVM is

Q(a) 1113944n

i1ai minus

12

1113944

n

ij1aiajyiyjk xi xj1113872 1113873 (6)

(3) +e radial basis kernel function is a widely usedkernel function the kernel function is used in thispaper

k(x y) exp minus gx minus y2

1113872 1113873 (7)

Among them ggt 0 g is an important parameter in thekernel function which affects the complexity of SVMclassification algorithm

+e kernel function parameter g and penalty coefficientC of support vector machine (SVM) is an important pa-rameter which affects the performance of SVM classificationso (C g) is used as the optimization variable In the processof learning SVM 5-fold cross validation is used to calculatethe optimal classification performance of kernel functionparameter and penalty coefficient and then the diagnosisresult of optimization is applied to the SVM classifier forlung cancer the final selection of the sensitivity specificityaccuracy and computation time as the evaluation indexes ofrelated experiments

3 Results and Discussion

31 Main Idea +e main idea of the model is as follows

311 Parameters Population sizeM chromosome lengthN(the number of condition attributes) crossover probabilityPc mutation probability Pm fitness function F(x) and themaximum number of iterations K are the parameters

312 Coding +e binary coding method is used which isrepresented by a binary string whose length is equal to thenumber of condition attributes each bit corresponds to acondition attribute a bit of 1 indicates that the corre-sponding condition attribute is selected 0 indicates that thecondition attribute is not selected eg 00110101 repre-sents a chromosome with a length of 8 and it is known thatthe corresponding 1 2 5 7 of 0 indicates that the corre-sponding condition attribute is not selected thenc3 C4 C6c8 is the last individual to choose the attributes set

4 Mathematical Problems in Engineering

313 4e Initial Population Assuming the population sizeM (the number of chromosomes in the population isM) Mlength of Lr chromosome (0 1) is the randomly generated asthe initial population

314 Genetic Operators Genetic operators include selectionoperator crossover operator and mutation operator +e se-lection operator generally uses the roulette wheel selectionmethod according to the selection probability pi

(fi1113936Mi1 fi) to select Crossover operator uses a single-point

crossover with a certain probability Pc to select the individualuniform crossover +e mutation operator selects the indi-viduals with the probability Pm to carry on the variation andrandomly selects the corresponding bit of the nonnuclearattribute

315 Fitness Function +e fitness function is the core of thegenetic algorithm the fitness value is the only index to evaluatethe fitness function this paper from the gene encoding valuethe minimum number of attributes reduction attribute de-pendency and other aspects constructs a fitness functionframework by adjusting the weights of various factors andchanging the classification error rate to achieve different fitnessfunction +e fitness function is set as follows

target1 Attribute dependency c(P Q β)

(|posβP(Q)||U|) it represents the β dependency ofdecision attribute Q for conditional attribute Ptarget2 Attributes reduction Length |C reduct| ((|P

| minus |Lr|)|P|) |P| is the number of condition attributesrepresented by 0 1 |Lr| represents the number of 1 inattribute P the shorter the better resultstarget3 Gene coding weight function ie Penaltyfunction target3 1113936 abs(r times (r minus 1))|r| Gene valuescan only take 0 and 1 but the chromosome will shownot 1 and not 0 such that the value is less than 0 orgreater than 1 +e value must be punished thereforethe gene coding weight function is constructed If thegene is 0 r times (r minus 1) 0 but the gene is 1r times (r minus 1) 0 So do not punish the genes of 0 or 1 butif there is a chromosome with a length of 6 r [0 0 minus 2minus 1 2 1] (r minus 1) [minus 1 minus 1 minus 3 minus 21 0] r times (r minus 1) [0 0 6 22 0] then 1113936 abs(r times (r minus 1)) 10 length is 6 sotarget3106167

+erefore the fitness function constructed in this paper isF(x) minus ω1 times target 1 minus ω2 times target 2 + ω3 times target 3 (8)

whereω is the weight coefficient of fitness functionω (0 1 23) because the genetic algorithm can only find the minimumvalue and the bigger the fitness value the better it is so theobjective function is minus and the penalty function is plus

Flow chart about this model is given in Figure 3

32 Model Concrete Steps

Input A decision information table S (U A V f )Output red(P Q β)

generate (M) Lr 98Initial population M 01 se-quence of Chromosome length 98Setting β ω crossover probability Pc mutationprobability Pm iteration number KBegin

for i 1 Ktarget1 (|posβP(Q)||U|)

target2 ((|P| minus |Lr|)|P|)

target3 (1113936 abs(r times (r minus 1))|r|)

Fitnessfunction minus ω1 times target1 minus ω2 times target2 + ω3 times target3Fitness functionP Select (M 2 Pc)Crossover probability PcQCrossover (P 2 Pc)Crossover algorithmQprimeMutation (Q Pm)Mutation algorithmEnd

33 Experimental Environment and Data

331 Hardware Environment Intel Core i5 4670-34GHzwith 80GB memory and 500GB hard disk were used

332 Software Environment Matlab R2012b LibSVM andWindows 7 operating system were used

333 Experimental Data +e PETCT images of 2000 lungcancer patients were collected as the study samples (1000cases of benign lung tumor 1000 cases of malignant lungtumor) Firstly ROI was extracted from the lung tumorand pretreated then 8-dimensional shape features 7-di-mensional gray features 3-dimensional Tamura features56-dimensional GLCM features and the 24-dimensionalfrequency domain features were extracted from the lungtumor ROI and 98-dimensional feature vectors are dis-creted and normalized In the decision attribute 1 rep-resents the lung malignant tumor and minus 1 represents thelung benign tumor Figure 4(a) shows four PETCT im-ages ROI of Lung malignant tumor and Figure 4(b) showsfour PETCT images ROI of lung benign tumor Table 1gives the feature values of two patients with lung cancer(one patient was a malignant tumor and the other was abenign tumor)

34Analysis ofExperimentalResults In this paper 3 kinds ofexperiments are designed according to the weight value ω

(0 1 2 3) of the fitness function and the classification errorrate β 04 02 0 (namely the inclusion degree1 minus β 06 08 1 ) For first type of experiments1 minus β 06 according to the different values of ω to do thethree groups of experiments totally For second type ofexperiments ϖ1 1ω2 1 ω3 0 according to the dif-ferent values of β to do three groups of experiments Forthird type of experiments 1 minus β 06 by increasing the ω

Mathematical Problems in Engineering 5

value to achieve the best fitness function to achieve the bestresults

341 Experiment 1mdashResearch on Different Weight Coeffi-cients under the Condition in the Same Classification ErrorRate ϖ values and β values of experiment 1 are shown inTable 2 and 1 minus β 06

(1) 1st Group Experiment ϖ1ω2ω3 1 0 0 +e al-gorithm is run 5 times according to this group weights theresults of the 5 groups are given in Table 3 including thereduction of the conditional attributes the length of re-duction the optimal fitness value the attribute dependencydegree and the time +e convergence of VPRS-GA under

the variation for fitness function value in one time is shownin Figure 5

Each reduction is classified by SVM classifier using themethod of 5-fold cross validation through changing thetraining samples and test samples the results of the fivegroups were obtained including accuracy sensitivityspecificity and time (training samples are constructed by800 malignant samples and 800 benign samples testingsamples are constructed by 200 malignant samples and 200benign samples the experiment is repeated 5 times bychanging training samples and testing samples) Finally theaverage values of these five groups are obtained as the finalresult of the reduction and shown in Table 4

+e weight value in this group experiment isϖ1ω2ω3 1 0 0 attribute dependency degree are

Output attributeset C_reduct1 C_re

duct2middotmiddotmiddotC_reductn

Indiscernibility relationfunction

Lower approximation

Relative positive domainposD

c function

Recognitionresult

SVMmodel

TrainingSVM

Reducedtraining set

Reducedtesting set

Target

Satisfycondition

Yes

No

Mutation Pm

Crossover Pc

Select Ps

F (x) = ndashω1 times target1 ndash ω2 times target2 + ω3 times target3β = 06 08 1

Initial population

Fitness value

Figure 3 Flow chart of high-dimensional feature selection based on genetic algorithm and variable precision rough set

(a) (b)

Figure 4 Part of lung tumor PETCT image ROI (a) Part of the lung malignant tumor PETCT-ROI (b) Part of the lung benign tumorPETCT-ROI

6 Mathematical Problems in Engineering

Table 1 ROI feature values of lung tumor PETCT image

Types of disease Shapefeature

Grayfeature

Tamuratexture

Texture features of GLCM Texture feature of wavelet

0 degree 45degrees

90degrees

135degrees Norm Standard

deviation Energy

Lung malignanttumor

60000 1222810 147000 00808 00779 00790 00611 6492580 371752 1000000012 14911500 309650 28937 29067 28989 31284 269473 38486 0001700000 386154 02326 02576 02820 02653 04490 93520 13355 0000200000 minus 05056 01668 01676 01659 01649 168200 24025 0000700000 24166 00792 00759 00772 00566 271143 38693 0001700000 140453 02576 02820 02653 04490 203163 29020 0001000000 70524 164110 164469 163584 164431 131755 18818 0000400000 27089 27072 27100 28066 183441 26199 00008

05755 06007 05810 073452109390 2117900 2095780 208825003064 03351 03135 03950

minus 06779 minus 06708 minus 06775 minus 0569600000 00000 00000 0000007625 07802 07658 08001

Lung benigntumor

40000 503912 101616 08087 07915 08077 07864 3799170 26741 1000000033 60006 18835 04324 04732 04370 04840 57551 08211 0000200000 24496 26329 00433 00621 00469 00679 11745 01677 0000000000 05649 94899 78127 92429 92429 34684 04955 0000100000 28589 08082 07905 08072 07853 20823 02972 0000000000 3283 00433 00621 00469 00679 21821 03117 0000000000 32559 78367 78363 78396 78363 08937 01276 0000000000 04024 04301 04045 04370 22387 03197 00000

01782 02326 01894 02481555257 550899 555291 54983100596 00873 00650 00958

minus 04707 minus 03295 minus 04351 minus 0291100000 00000 00000 0000020429 21172 20651 21394

Table 3 Results of VPRS-GA running 5 times when 1-β 06 ω1 1ω2 0ω3 0

Experimenttimes C_ reduction Reduction

lengthOptimal

fitness valueAttribute

dependency degree Time (s)

1 4 5 8 9 11 12 13 17 20 22 23 24 27 30 32 33 35 38 42 48 4952 57 59 61 62 63 64 65 68 70 72 73 75 77 78 80 87 88 91 92 41 minus 09705 09705 9719144

21 2 3 4 5 8 11 12 13 14 16 17 19 23 24 25 26 27 28 30 32 3638 39 40 42 43 44 46 47 52 53 55 61 63 66 67 69 71 72 73 77

79 80 82 84 85 87 9249 minus 09685 09685 10076907

3 4 611 12 1517 18 24 25 26 28 29 31 36 38 39 42 43 45 47 4953 56 65 68 69 72 76 77 79 80 81 83 85 88 91 92 37 minus 09695 09695 10432000

4 4 8 9 11 12 13 14 15 17 23 29 34 35 39 40 43 47 48 50 53 5556 60 61 64 68 70 75 80 81 82 83 84 86 34 minus 09790 09790 9473111

5 3 4 6 81011 12 13151719 20 21 24 26 29 31 39 42 44 45 4850 53 54 56 59 64 68 77 83 84 87 89 92 35 minus 09775 09775 9645092

Average value 392 minus 09730 09730 9869251

Table 2 Fitness function weight proportion and β value

Experiment times1 minus β 06

ω1 ω2 ω3First group experiment 1 0 0Second group experiment 1 1 0+ird group experiment 1 1 1

Mathematical Problems in Engineering 7

regarded as fitness function +e average attribute de-pendency degree is 0973 the average length of reductionis 392 and the average optimal fitness value is minus 0973+e average recognition accuracy of the experiment is9692 +e premature phenomena are shown in Fig-ure 5 and evolution progress is terminated early

(2) 2nd Group Experiment ϖ1ω2ω3 1 1 0 +isexperiment introduces an objective function to control thelength of reduction (the shorter the length of reduction thebetter it is) the influence degree of the objective functionwhich controls the reduction on the fitness function and the

final recognition accuracy is verified +e algorithm is run 5times according to this group weights and the results of the 5groups are given in Table 5 including the reduction of theconditional attributes the length of reduction the optimalfitness value the attribute dependency and the time +econvergence of VPRS-GA under the variation for fitnessfunction value in one time is shown in Figure 6

Each reduction is classified by SVM classifier using themethod of 5-fold cross validation through changing thetraining samples and test samples the results of the fivegroups were obtained including accuracy sensitivityspecificity and time (training samples are constructed by

ndash06

ndash07

ndash08

ndash09

ndash10 50 100 150

Generation stopping criteria

Best ndash09695 Mean ndash0944425

Fitn

ess v

alue

Best fitnessMean fitness

Figure 5 +e variation of fitness function value in a running process for Experiment 1-first group

Table 4 +e statistical results of the first group for experiment 1 with the SVM classifier

Experiment times Accuracy () Sensitivity () Specificity () Time (s)

Reduction 1

1 9250 8600 9900 3326072 9725 9750 9700 3450513 9900 9900 9900 3586774 9800 9950 9650 3510755 9925 10000 9850 355948

Average value 9720 9640 9800 348672

Reduction 2

1 9325 8700 9950 4365332 9725 9800 9650 4459003 9875 9850 9900 4395064 9750 9900 9600 4450645 9925 10000 9850 448513

Average value 9720 9650 9790 443103

Reduction 3

1 9275 8750 9800 3269162 9575 9750 9400 3372093 9800 9800 9800 3407014 9700 9850 9550 3331745 9850 9950 9750 333257

Average value 9640 9620 9660 334251

Reduction 4

1 9375 8850 9900 3064852 9650 9750 9550 3192403 9750 9700 9800 3240824 9775 9900 9650 3254195 9900 10000 9800 361516

Average value 9690 9640 9740 318806

Reduction 5

1 9400 8900 9900 3195572 9650 9750 9550 3369093 9725 9700 9750 3301594 9775 9900 9650 3999805 9900 10000 9800 325692

Average value 9690 9650 9730 342459

8 Mathematical Problems in Engineering

800 malignant samples and 800 benign samples testingsamples are constructed by 200 malignant samples and 200benign samples the experiment is repeated 5 times bychanging training samples and testing samples) Finally theaverage values of these five groups are obtained as the finalresult of the reduction and shown in Table 6

+e experimental weight of this group is ϖ1

ω2ω3 1 1 0 attribute dependency degree and thelength of reduction are regarded as fitness function As canbe seen from Table 5 the reduction length is 13 17 and soon +e average length of reduction was 17 which wassignificantly reduced compared with the average length ofthe reduction in Table 3 in the experiment of the first groupswhich reduced the time improved the efficiency of the al-gorithm and increased the attribute dependency of thealgorithm even up to 1 +e average recognition accuracy ofthe experimental group was 9698 which was increased by006 compared with that in the first groups

(3) 3rd Group Experiment ϖ1ω2ω3 1 1 1 On thebasis of attribute dependency degree and attribute reductionlength this experiment introduces gene coding weightfunction in order to verify the effect of gene coding weightfunction on fitness function and the final recognition ac-curacy +e algorithm are run 5 times according to thisgroup weights the results of the 5 groups are given inTable 7 including the reduction of the conditional attributesthe length of reduction the optimal fitness value the at-tribute dependency and the time +e convergence ofVPRS-GA under the variation for fitness function value inone time is shown in Figure 7

Each reduction is classified by SVM classifier using themethod of 5-fold cross validation through changing thetraining samples and test samples the results of the fivegroups were obtained including accuracy sensitivityspecificity and time (training samples are constructed by800 malignant samples and 800 benign samples testingsamples are constructed by 200 malignant samples and 200benign samples the experiment is repeated 5 times bychanging training samples and testing samples) Finally theaverage values of these five groups are obtained as the finalresult of the reduction and shown in Table 8

+e experimental weight of this group is ϖ1 ω2ω3=1 1 1 attribute dependency degree the length of re-duction and gene coding weight value are regarded as fitnessfunction However the premature phenomena are shown inFigure 7 and evolution progress is terminated early FromTable 7 we can see that the attribute dependency decreasesgradually and even the attribute dependency of Reduction 1is reduced to 0759 +e average recognition accuracy of theexperimental group was 9685+e accuracy of recognitionwas decreased compared with the second groups and henceusing gene encoding weight function in the fitness functionto improve recognition accuracy is useless only for thesamples with different results to analyze specific issues +e3 experiment runs of experiment 1 verified the necessity ofthe fitness function by continuously introducing fitnessobjective function such as target1 target2 and target3 theconclusion is that the fitness function is better when it is notbigger but after the introduction of target3 the accuracydeclines therefore the introduction of target1 and target2 inthis algorithm can get better results

Table 5 Results of VPRS-GA running 5 times when 1 minus β 06 ω1 1ω2 1ω3 0

Experiment times C_ reduction Reductionlength

Optimalfitness value

Attributedependency

degreeTime (s)

1 5 9 14 20 26 41 43 46 48 54 55 57 64 66 74 79 86 90 18 minus 46487 09965 107240722 1 4 11 12 14 24 34 40 42 43 56 60 61 65 67 68 71 72 85 19 minus 40109 1 63281223 2 13 27 29 39 42 45 56 59 63 68 70 75 13 minus 46512 09990 110239674 1 3 4 7 9 11 12 15 30 34 38 42 46 48 55 62 65 77 79 19 minus 49674 1 87946705 3 9 11 13 29 39 41 42 43 46 50 55 65 c77 85 86 16 minus 44114 09815 15075539

Average value 17 minus 45379 09954 10389274

ndash1

ndash2

ndash3

ndash4

ndash5

Fitn

ess v

alue

Best ndash496739 Mean ndash492312

0 50 100 150Generation stopping criteria

Best fitnessMean fitness

Figure 6 +e variation of fitness function value in a running process for experiment 1-second group

Mathematical Problems in Engineering 9

342 Experiment 2mdashResearch on Different ClassificationError Rates under the Condition in the Same WeightCoefficient According to experiment 1 we can see thatwhen ω1 1 ω2 1 ω3 0 the experimental results arethe best so in experiment 2 the case of the weight value ofwas unchanged ω1 1 ω2 1 ω3 0 and the β value waschanged and they are shown in Table 9

(1) 1st Group Experiment 1 minus β 06 +e algorithm is run 5times according to this group weights the results of the 5groups are shown in Table 5 including the reduction of the

conditional attributes the length of reduction the optimalfitness value the attribute dependency and the time +econvergence of VPRS-GA under the variation for fitnessfunction value for one time is shown in Figure 6 (ie notrepeated in the second group of experiment 1)

(2) 2nd Group Experiment 1 minus β 08 +e algorithm are is 5times according to this group weights the results of the 5groups are given in Table 10 including the reduction of theconditional attributes the length of reduction the optimalfitness value the attribute dependency and the time +e

Table 6 +e statistical results of the second group for experiment 1 with the SVM classifier

Experiment times Accuracy () Sensitivity () Specificity () Time (s)

Reduction 1

1 9300 8600 10000 1164882 9625 9600 9650 1255113 9850 9900 9800 1315094 9725 9850 9600 1344685 9925 10000 9850 144839

Average value 9685 9590 9780 130563

Reduction 2

1 9425 8900 9950 1210962 9725 9700 9750 1286363 9800 9800 9800 1356774 9750 9800 9700 1381965 9875 9900 9850 136691

Average value 9715 9620 9810 132059

Reduction 3

1 9300 8750 9850 877572 9725 9750 9700 1034243 9775 9800 9750 1074114 9775 9850 9700 1123445 9900 10000 9800 113006

Average value 9695 9630 9760 104788

Reduction 4

1 9375 8750 10000 1464172 9650 9750 9550 1547363 9750 9700 9800 1576214 9800 9900 9700 1613555 9925 10000 9850 163381

Average value 9700 9620 9780 156702

Reduction 5

1 9250 8650 9850 1249332 9675 9800 9550 1400573 9800 9800 9800 1451944 9800 9900 9700 1457925 9950 9950 9950 150400

Average value 9695 9620 9770 141275

Table 7 Results of VPRS-GA running 5 times when 1 minus β 06 ω1 1ω2 1ω3 1

Experimenttimes C_ reduction Reduction

lengthOptimal

fitness valueAttribute

dependency degree Time (s)

1 4 5 7 26 27 34 35 41 47 54 55 71 74 75 78 80 83 90 18 minus 14192 07590 6888635

2 4 15 16 19 22 27 28 29 30 35 38 42 45 50 52 53 59 61 6264 65 70 71 72 77 87 88 27 minus 15232 08640 8124857

3 6 17 19 24 28 31 33 34 38 39 43 45 47 48 49 51 55 56 6667 69 70 71 72 76 77 78 80 81 84 87 89 91 92 34 minus 13545 07950 9521511

4 3 6 8 91617 19 20 24 25 28 35 37 39 41 42 46 49 51 52 5459 63 65 66 74 83 86 28 minus 14703 08365 8714839

5 1 7 8 15 17 19 20 23 29 37 45 48 54 60 62 70 73 75 77 7879 86 22 minus 14990 07995 7797617

Average value 258 minus 14532 08108 8209492

10 Mathematical Problems in Engineering

convergence of VPRS-GA under the variation for fitnessfunction value for one time is shown in Figure 8

Each reduction is classified by SVM classifier using themethod of 5-fold cross validation through changing thetraining samples and test samples the results of the five

groups were obtained including accuracy sensitivityspecificity and time (training samples are constructed by800 malignant samples and 800 benign samples testingsamples are constructed by 200 malignant samples and 200benign samples the experiment is repeated 5 times by

ndash08

ndash1

ndash12

ndash14

ndash16

Fitn

ess v

alue

Best ndash141919 Mean ndash128476

0 50 100 150Generation stopping criteria

Best fitnessMean fitness

Figure 7 +e variation of fitness function value in a running process for experiment 1-third group

Table 8 +e statistical results of the third group for experiment 1 with the SVM classifier

Experiment times Accuracy () Sensitivity () Specificity () Time (s)

Reduction 1

1 9275 8600 9950 924922 9725 9750 9700 1074613 9850 9850 9850 1138114 9775 9900 9650 1155605 9875 10000 9750 117022

Average value 9700 9620 9780 109269

Reduction 2

1 9350 8750 9950 1482452 9700 9650 9750 1615353 9775 9850 9700 1664524 9800 9850 9750 1754505 9875 9950 9800 172348

Average value 9700 9610 9790 164806

Reduction 3

1 9125 8300 9950 2019042 9650 9700 9600 2185353 9800 9800 9800 2196054 9625 9900 9350 2230915 9825 10000 9650 236896

Average value 9605 9540 9670 220006

Reduction 4

1 9300 8700 9900 1654542 9675 9600 9750 1724323 9875 9850 9900 1793014 9800 9900 9700 1895605 9900 9950 9850 185249

Average value 9710 9600 9820 178399

Reduction 5

1 9275 8600 9950 1411732 9725 9800 9650 1612953 9900 9950 9850 1589924 9775 9950 9600 1648765 9875 10000 9750 166070

Average value 9710 9660 9760 158481

Table 9 Fitness function weight proportion and β value

Experiment timesω1 1 ω2 1 ω3 0

1 minus β 06 1 minus β 08 1 minus β 1First group experiment Second group experiment +ird group experiment

Mathematical Problems in Engineering 11

changing training samples and testing samples) Finally theaverage values of these five groups are obtained as the finalresult of the reduction and shown in Table 11

In the case of constant weight ϖ and classification errorrate of β 02 (which contains 1 minus β 08) the classificationerror rate is changed on the basis of the attribute dependencyand the length of control reduction +e premature phe-nomena are shown in Figure 8 and evolution progress isterminated early such that the attribute dependency ofreduction 5 was 08405 appeared in attribute dependency onless than 09 compared with first groups of experiment 2attribute dependency declined +e average recognitionaccuracy of the experimental group was 9674 Comparedwith the classification error rate of 04 and inclusion degreeof 06 the accuracy was decreased by 024

(3) 3rd Group Experiment 1 minus β1 +e algorithm is run 5times according to the group weights and the results of the 5groups are shown in Table 12 including the reduction of theconditional attributes the length of reduction the optimalfitness value the attribute dependency and the time +econvergence of VPRS-GA under the variation for fitnessfunction value for one time is shown in Figure 9

Each reduction is classified by SVM classifier using themethod of 5-fold cross validation through changing thetraining samples and test samples the results of the fivegroups were obtained including accuracy sensitivityspecificity and time (training samples are constructed by800 malignant samples and 800 benign samples testingsamples are constructed by 200 malignant samples and 200

benign samples the experiment is repeated 5 times bychanging training samples and testing samples) Finally theaverage values of these five groups are obtained as the finalresult of the reduction and shown in Table 13

In the case of constant weight ϖ and classification errorrate of β= 0 (which contains 1 minus β= 1) the classificationerror rate is reduced and the inclusion degree is improved onthe basis of the attribute dependency and the length ofcontrol reduction +e premature phenomena are shown inFigure 9 and evolution progress is terminated early +eaverage recognition accuracy of the experimental group was9573 which was decreased by 006 compared with thatin the second group In experiment 2 the effect of changingthe classification error rate on the recognition accuracy wasverified by the 3 groups of experiments By continuallyreducing the classification error rate the final recognitionaccuracy has been declining when inclusion degree is 1β= 0 variable precision rough set becomes Pawlak rough setthe recognition accuracy of the recognition accuracy of isminimum which was verified the advantages of variableprecision rough set

343 Experiment 3mdashResearch on Increasing the WeightCoefficient under the Condition in the Same ClassificationError Rate According to experiment 1 and experiment 2we can know that when β 06 ω1 1 ω2 1 ω3 0 therecognition accuracy is the best therefore in the thirdexperiment by increasing the weight of ω 3 groups ofexperiments are performed fitness goals target 1 (attribute

Table 10 Results of VPRS-GA running 5 times when 1 minus β 08 ω1 1ω2 1ω3 0

Experimenttimes C_ reduction Reduction

lengthOptimal fitness

valueAttribute

dependency degree Time (s)

1 8 9 11 12 15 16 17 18 25 26 29 31 35 39 40 41 42 48 5865 67 68 70 83 84 91 26 minus 67816 09490 10002827

2 1 6 8 9 11 12 15 17 21 23 26 28 30 31 34 44 50 56 58 5962 63 64 68 71 75 77 82 89 92 30 minus 67797 09615 9477387

3 6 8 12 14 15 16 17 21 28 35 38 39 45 49 55 58 61 62 6465 77 82 85 23 minus 68694 09070 12866181

4 4 6 7 8 11 12 13 16 17 20 25 26 31 32 34 35 41 42 44 4950 55 58 68 72 74 76 78 79 85 89 92 32 minus 67225 09540 10510220

5 3 6 8 9 10 16 17 26 27 34 36 37 38 40 42 44 46 51 52 6266 67 84 86 87 25 minus 65892 08405 8469324

Average value 272 minus 67484 09224 10265188

ndash55

ndash6

ndash65

ndash7

Fitn

ess v

alue

Best ndash686942 Mean ndash653584

0 50 100 150Generation stopping criteria

Best fitnessMean fitness

Figure 8 +e variation of fitness function value in a running process for experiment 2-second group

12 Mathematical Problems in Engineering

Table 11 +e statistical results of the second group for experiment 2 with the SVM classifier

Experiment times Accuracy () Sensitivity () Specificity () Time (s)

Reduction 1

1 9300 8650 9950 2280072 9575 9700 9450 2376463 9700 9600 9800 2332504 9750 9850 9650 2444915 9925 10000 9850 244816

Average value 9650 9560 9740 237642

Reduction 2

1 9375 8800 9950 2524032 9625 9750 9500 2652893 9800 9700 9900 2655234 9800 9900 9700 2682125 9950 10000 9900 275880

Average value 9710 9630 9790 265461

Reduction 3

1 9275 8750 9800 1807802 9675 9750 9600 1929923 9700 9600 9800 1872434 9775 9950 9600 2084825 9875 10000 9750 203507

Average value 9660 9610 9710 194601

Reduction 4

1 9200 8650 9750 2572602 9700 9750 9650 2730243 9775 9650 9900 2723164 9750 9900 9600 2815545 9900 10000 9800 291471

Average value 9665 9590 9740 275125

Reduction 5

1 9275 8750 9800 1437152 9675 9600 9750 1526373 9750 9800 9700 1589294 9775 9900 9650 1629975 9950 10000 9900 166792

Average value 9685 9610 9760 157014

Table 12 Results of VPRS-GA running 5 times when 1 minus β 1 ω1 1ω2 1ω3 0

Experimenttimes C_ reduction Reduction

lengthOptimal fitness

valueAttribute dependency

degree Time (s)

1 15 44 68 73 79 84 6 minus 27313 07965 114499012 34 51 54 75 80 90 6 minus 27047 08460 96993913 2 34 49 70 71 72 76 81 8 minus 34057 07535 112334894 12 25 78 85 4 minus 22872 09285 11668133

5 6 7 12 13 42 44 55 57 65 66 69 77 81 8687 15 minus 33230 08665 13236077

Average value 78 minus 28903 08382 11457398

ndash1

ndash2

ndash3

ndash4

Fitn

ess v

alue

0 50 100 150Generation stopping criteria

Best fitnessMean fitness

Best ndash340567 Mean ndash330598

Figure 9 +e variation of fitness function value in a running process for experiment 2-third group

Mathematical Problems in Engineering 13

dependency) target 2 (the minimum number of attributesreduction) and target 3 (gene encoding weight function)the three objective functions play an important role in theevaluation of fitness function However the importance offitness function is reduced in these three objectives+erefore in this experiment when the other conditions areunchanged the weight coefficient of the target 1 is increasedto verify the influence of the change in the weight coefficienton the experimental results and they are shown in Table 14

(1) 1st Group Experiment ω1 1 ω2 1 ω3 0 +e al-gorithm are run 5 times according to this group weights theresults of the 5 groups are given in Table 5 including thereduction of the conditional attributes the length of reduc-tion the optimal fitness value the attribute dependency andthe time +e convergence of VPRS-GA under the variationfor fitness function value in one time is shown in Figure 6 (ienot repeated for the second group of experiment 1)

(2) 2nd Group Experiment ω1 2 ω2 1 ω3 0 +ealgorithm is run 5 times according to this group weights theresults of the 5 groups are given in Table 15 including thereduction of the conditional attributes the length of re-duction the optimal fitness value the attribute dependencyand the time +e convergence of VPRS-GA under thevariation for fitness function value in one time is shown inFigure 10

Each reduction is classified by SVM classifier using themethod of 5-fold cross validation through changing thetraining samples and test samples the results of the fivegroups were obtained including accuracy sensitivityspecificity and time (training samples are constructed by800 malignant samples and 800 benign samples testingsamples are constructed by 200 malignant samples and 200benign samples the experiment is repeated 5 times bychanging training samples and testing samples) Finally theaverage values of these five groups are obtained as the finalresult of the reduction and shown in Table 16

+e experimental group in the case of 1 minus β= 06 un-changed the weight of ω1 was increased +e attributedependency and the optimal fitness function are relativelyhigh the average precision of reduction 1 reduction 2 andreduction 3 in Table 16 is more than 97 and that of re-duction 2 is even up to 9725 +e average recognitionaccuracy of the experimental group is 9703 which ishigher than that of the first group

Table 13 +e statistical results of the third group for experiment 2 with the SVM classifier

Experiment times Accuracy () Sensitivity () Specificity () Time (s)

Reduction 1

1 9225 8450 10000 812712 9550 9700 9400 945833 9575 9400 9750 881984 9600 9800 9400 937545 9725 9900 9550 98691

Average value 9535 9450 9620 91299

Reduction 2

1 9200 8450 9950 648942 9625 9550 9700 801983 9525 9300 9750 773374 9600 9750 9450 760125 9800 10000 9600 82763

Average value 9550 9410 9690 76241

Reduction 3

1 9200 8450 9950 648942 9625 9550 9700 801983 9525 9300 9750 773374 9600 9750 9450 760125 9800 10000 9600 82763

Average value 9550 9410 9690 76241

Reduction 4

1 9275 8550 10000 672642 9675 9600 9750 784673 9600 9450 9750 730224 9575 9750 9400 794605 9800 10000 9600 84184

Average value 9585 9470 9700 76479

Reduction 5

1 9200 8450 9950 1147192 9625 9750 9500 1287053 9850 9900 9800 1320494 9775 9950 9600 1335135 9850 10000 9700 133144

Average value 9660 9610 9710 128426

Table 14 Fitness function weight proportion and β value

Experiment times1 minus β 06

ω1 ω2 ω3First group experiment 1 1 0Second group experiment 2 1 0+ird group experiment 3 1 0

14 Mathematical Problems in Engineering

ndash2

ndash25

ndash3

Fitn

ess v

alue

0 50 100 150Generation stopping criteria

Best fitnessMean fitness

Best ndash2915 Mean ndash291446

Figure 10 +e variation of fitness function value in a running process for experiment 3-second group

Table 15 Results of VPRS-GA running 5 times when 1 minus β 06 ω1 2ω2 1ω3 0

Experimenttimes C_ reduction Reduction

lengthOptimal fitness

valueAttribute dependency

degree Time (s)

1 2 3 4 5 11 13 16 18 24 30 34 37 39 41 42 51 55 64 7077 78 82 22 minus 34859 09060 21515464

2 8 9 11 12 14 15 23 25 26 29 30 33 37 42 43 45 46 5060 61 69 74 80 87 89 25 minus 30845 09390 42761634

3 8 11 12 13 16 18 19 24 29 36 37 43 64 65 68 71 86 9192 19 minus 35039 09150 26197164

4 2 3 4 8 10 11 12 13 15 16 19 23 25 30 48 55 64 65 6874 77 80 81 83 84 86 89 27 minus 29150 09575 44271631

5 5 8 911 121517 23 25 29 31 36 39 41 48 54 59 63 8083 86 89 22 minus 29920 09525 43161464

Average value 23 minus 31962 09340 35581471

Table 16 +e statistical results of the second group for experiment 3 with the SVM classifier

Experiment times Accuracy () Sensitivity () Specificity () Time (s)

Reduction 1

1 9275 8600 9950 1884972 9725 9800 9650 1571623 9850 9900 9800 1586914 9800 9900 9700 1646035 9950 10000 9900 161914

Average value 9720 9640 9800 166173

Reduction 2

1 9450 8950 9950 1908132 9675 9800 9550 2002513 9775 9800 9750 1970084 9850 9900 9800 2009245 9875 9900 9850 209245

Average value 9725 9670 9780 199648

Reduction 3

1 9400 8800 10000 1313692 9725 9800 9650 1447973 9800 9800 9800 1426624 9725 9850 9600 1471905 9925 10000 9850 148799

Average value 9715 9650 9780 142963

Reduction 4

1 9350 8750 9950 2404562 9700 9750 9650 2520823 9800 9800 9800 2511754 9775 9950 9600 2701885 9825 10000 9650 267471

Average value 9690 9650 9730 256274

Reduction 5

1 9325 8800 9850 1809592 9600 9800 9400 1965633 9750 9750 9750 1967234 9800 9900 9700 2078295 9850 9950 9750 219703

Average value 9665 9640 9690 200355

Mathematical Problems in Engineering 15

Table 17 Results of VPRS-GA running 5 times when 1 minus β 1 ω1 1ω2 1ω3 0

Experimenttimes C_ reduction Reduction

lengthOptimal fitness

valueAttribute

dependency degree Time (s)

1 3 4 5 8 9 11 12 17 19 29 34 35 38 46 52 53 55 59 63 6672 75 77 78 79 87 92 27 minus 38867 09550 28981789

2 4 8 9 11 12 15 17 29 33 37 38 39 42 43 48 55 67 73 7881 83 84 88 89 90 25 minus 38167 09715 55783772

3 2 3 4 8 9 10 11 12 13 15 16 19 24 25 30 36 49 54 55 6064 67 68 70 74 77 83 85 86 91 30 minus 38807 09530 34831096

4 4 5 7 11 12 14 15 17 25 29 33 36 39 41 42 47 48 50 5556 58 62 67 69 72 74 77 84 86 90 91 31 minus 39430 09665 35742822

5 3 4 5 8 9 11 12 17 19 29 34 35 38 46 52 53 55 59 63 6672 75 77 78 79 87 92 27 minus 38867 09550 27919582

Average value 28 minus 38827 09602 36651812

ndash3

ndash35

ndash40 50 100 150

Generation stopping criteria

Fitn

ess v

alue

Best fitnessMean fitness

Best ndash394298 Mean ndash393327

Figure 11 +e variation of fitness function value in a running process for experiment 3-third group

Table 18 +e statistical results of the Second group for experiment 3 with the SVM classifier

Experiment times Accuracy () Sensitivity () Specificity () Time (s)

Reduction 1

1 9200 8700 9700 2187172 9750 9750 9750 2105503 9850 9850 9850 2032064 9800 9900 9700 2211645 9925 10000 9850 272536

Average value 9705 9640 9770 225235

Reduction 2

1 9400 8850 9950 2331232 9575 9750 9400 2433493 9750 9700 9800 2442024 9775 9900 9650 2566075 9900 9950 9850 259071

Average value 9680 9630 9730 247270

Reduction 3

1 9275 8650 9900 2525842 9625 9750 9500 2624123 9775 9800 9750 2601274 9775 9900 9650 2686705 9875 10000 9750 265387

Average value 9665 9620 9710 261836

Reduction 4

1 9150 8550 9750 2532312 9625 9750 9500 2649433 9750 9700 9800 2752834 9800 9950 9650 3229545 9825 9950 9700 277432

Average value 9630 9580 9680 278769

Reduction 5

1 9200 8800 9600 1951962 9700 9700 9700 2148893 9825 9800 9850 2036124 9850 10000 9700 2133615 9900 9900 9900 225526

Average value 9695 9640 9750 210517

16 Mathematical Problems in Engineering

(3) 3rd Group Experiment ω1 3 ω2 1 ω3 0 +e al-gorithm is run 5 times according to the group weights andthe results of the 5 groups are given in Table 17 including thereduction of the conditional attributes the length of re-duction the optimal fitness value the attribute dependencyand the time +e convergence of VPRS-GA under thevariation for fitness function value for one time is shown inFigure 11

Each reduction is classified by SVM classifier using themethod of 5-fold cross validation through changing thetraining samples and test samples the results of the fivegroups were obtained including accuracy sensitivityspecificity and time (training samples are constructed by800 malignant samples and 800 benign samples testingsamples are constructed by 200 malignant samples and 200benign samples the experiment is repeated 5 times bychanging training samples and testing samples) Finally theaverage values of these five groups are obtained as the finalresult of the reduction and shown in Table 18

+e experiment in the case of 1 minus β 06 unchangedincrease the weight of the ω1 ω1 3 ω2 1 ω3 0 InTable 18 the recognition accuracy of reduction 1 is over 97only +e average recognition accuracy of the experimentalgroup is 9675 and the accuracy is decreased by 028compared with that in the other second groups +e threegroups of experiment 3 the purpose is to verify whether theexperimental accuracy is influenced by increasing theweight +e experimental results show that the accuracy ofsecond group for experimental weight 2 1 0 comparedwith first group experiment when 1 1 0 is high but thethird groups of experimental weight was 3 1 0 and theaccuracy declined therefore the weight of 2 1 0 is the bestchoice for this experiment

4 Conclusions

Aiming at the deficiency of the traditional rough set modelthis paper proposes a new feature selection model based ongenetic algorithm and variable precision rough set by in-troducing the β value the rigid inclusion of the approxi-mation for the traditional rough set is relaxed and then wedesign the 3 kinds of experiments by constructing the de-cision information table of the PETCT feature for lungtumor ROI +e first type of experiment is the inclusion of1 minus β 06 and different values of ω made a total of threegroups of experiments the experimental results show thatthe better recognition accuracy can be obtained when theweight is 1 1 0 and the results show that the gene codingweight function has no effect on the fitness function For thesecond type of experiments ϖ1 1ω2 1 ω3 0according to the different values of β to do three groups ofexperiments the results show that the recognition accuracyof 1 minus β 06 is the best which shows that the larger the βvalue is the lower approximate cardinality will be largerthen the relative accuracy will increase For the third type ofexperiments 1 minus β 06 ω value is increased to achieve thebest fitness function in order to achieve the best results +eexperimental results show that the recognition accuracy isbetter than the others when the weight value is 2 1 0 so it

is better to solve the problem by increasing the proportion ofattribute dependency +rough the above experiments it isshown that the high-dimensional feature selection algorithmbased on genetic algorithm and variable precision rough setcan solve the multiobjective optimization problem wellHowever when the fitness function and its parameters areapplied in the specific application it is necessary to analyzethe specific problems

Data Availability

+e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

+e authors declare no conflicts of interest

Acknowledgments

+is work was supported by National Natural ScienceFoundation of China (Grant nos 61561040 and 61876121)First-Class Disciplines Foundation of Ningxia (NoNXYLXK2017B09)

References

[1] S Luo D Miao Z Zhang Y Zhang and S Hu ldquoA neigh-borhood rough set model with nominal metric embeddingrdquoInformation Sciences vol 520 pp 373ndash388 2020

[2] B Barman and S Patra ldquoVariable precision rough set basedunsupervised band selection technique for hyperspectralimage classificationrdquo Knowledge-Based Systems vol 1936Article ID 105414 2020

[3] Y Chenyi and L Jinjin ldquoApproximate attribute reductionunder variable precision rough set βrdquo Journal of ShandongUniversity vol 11 pp 17ndash21 2011

[4] S Xiaowei Research on Hierarchical Model of Attribute Re-duction in Variable Precision Rough Set Central SouthUniversity Changsha China 2013

[5] Z Jie and W Jiayang ldquoAnalysis of reduction feature ofvariable precision rough set modelrdquo Computer ApplicationResearch vol 7 pp 12ndash15 2007

[6] Z Pei and Z Qinghua ldquoFCM clustering algorithm based onvariable precision rough setrdquo Journal of Shanxi Universityvol 3 pp 342ndash348 2016

[7] C Hao and Y Junan ldquoAttribute kernel and minimum at-tribute reduction algorithm of variable precision rough setrdquoActa Sinica Sinica vol 5 pp 1011ndash1017 2012

[8] S Xu X Yang H Yu D-J Yu J Yang and E CC TsangldquoMulti-label learning with label-specific feature reductionrdquoKnowledge-Based Systems vol 104 pp 52ndash61 2016

[9] I Maryam and G Hassan ldquoFeature space discriminantanalysis for hyperspectral data feature reductionrdquo ISPRSJournal of Photogrammetry and Remote Sensing vol 102pp 1ndash13 2015

[10] S Q Wang C Y Gao C Luo G M Zheng and Y N ZhouldquoResearch on feature selectionattribute reduction methodbased on rough set theoryrdquo Procedia Computer Sciencevol 154 pp 194ndash198e 2019

[11] A W Omar M Azzam O Hadi and B Jamal ldquoCEAP SVM-based intelligent detection model for clustered vehicular ad

Mathematical Problems in Engineering 17

hoc networksrdquo Expert Systems with Applications vol 50pp 40ndash54 2016

[12] H Lee and Y-P P Chen ldquoImage based computer aideddiagnosis system for cancer detectionrdquo Expert Systems withApplications vol 42 no 12 pp 5356ndash5365 2015

[13] J A Guy and P L Harold ldquoAfter detection the improvedaccuracy of lung cancer assessment using radiologic com-puter-aided diagnosisrdquo Academic Radiology vol 23 no 2pp 186ndash191 2016

[14] E Kiyonori T Shodayu J Binghu et al ldquoPleural invasion byperipheral lung cancer prediction with three-dimensionalCTrdquo Academic Radiology vol 3 pp 310ndash319 2015

[15] B Koohestani ldquoA crossover operator for improving the ef-ficiency of permutation-based genetic algorithmsrdquo ExpertSystems with Applications vol 1511 Article ID 113381 2020

[16] N K Lee X Li and D Wang ldquoA comprehensive survey ongenetic algorithms for DNA motif predictionrdquo InformationSciences vol 466 pp 25ndash43 2018

[17] S Shibao and Y Leilei ldquoResearch on variable precision roughset model and its applicationrdquo Computer Engineering andApplication vol 07 pp 10ndash13 2009

[18] T Xiaolong Several Problems of Multi Granularity VariablePrecision Rough Set Guangxi University For NationalitiesNanning China 2015

[19] W Xueming Research on Several Rough Set Models andNeural Network University of Electronic Science and Tech-nology of China Chengdu China 2013

[20] T Sun J Wang X Li et al ldquoComparative evaluation ofsupport vector machines for computer aided diagnosis of lungcancer in CT based on a multi-dimensional data setrdquo Com-puter Methods and Programs in Biomedicine vol 111 no 2pp 519ndash524 2013

[21] Z Yang T Ouyang X Fu and X Peng ldquoA decision-makingalgorithm for online shopping using deep-learning-basedopinion pairs mining and q -rung orthopair fuzzy interactionHeronianmean operatorsrdquo International Journal of IntelligentSystems vol 35 no 5 pp 783ndash825 2020

[22] W Chen C Lin C Li et al ldquoTracing the evolution of 3Dprinting technology in China using LDA-based patent ab-stract miningrdquo IEEE Transactions on Engineering Manage-men vol 36 pp 1ndash11 2020

18 Mathematical Problems in Engineering

313 4e Initial Population Assuming the population sizeM (the number of chromosomes in the population isM) Mlength of Lr chromosome (0 1) is the randomly generated asthe initial population

314 Genetic Operators Genetic operators include selectionoperator crossover operator and mutation operator +e se-lection operator generally uses the roulette wheel selectionmethod according to the selection probability pi

(fi1113936Mi1 fi) to select Crossover operator uses a single-point

crossover with a certain probability Pc to select the individualuniform crossover +e mutation operator selects the indi-viduals with the probability Pm to carry on the variation andrandomly selects the corresponding bit of the nonnuclearattribute

315 Fitness Function +e fitness function is the core of thegenetic algorithm the fitness value is the only index to evaluatethe fitness function this paper from the gene encoding valuethe minimum number of attributes reduction attribute de-pendency and other aspects constructs a fitness functionframework by adjusting the weights of various factors andchanging the classification error rate to achieve different fitnessfunction +e fitness function is set as follows

target1 Attribute dependency c(P Q β)

(|posβP(Q)||U|) it represents the β dependency ofdecision attribute Q for conditional attribute Ptarget2 Attributes reduction Length |C reduct| ((|P

| minus |Lr|)|P|) |P| is the number of condition attributesrepresented by 0 1 |Lr| represents the number of 1 inattribute P the shorter the better resultstarget3 Gene coding weight function ie Penaltyfunction target3 1113936 abs(r times (r minus 1))|r| Gene valuescan only take 0 and 1 but the chromosome will shownot 1 and not 0 such that the value is less than 0 orgreater than 1 +e value must be punished thereforethe gene coding weight function is constructed If thegene is 0 r times (r minus 1) 0 but the gene is 1r times (r minus 1) 0 So do not punish the genes of 0 or 1 butif there is a chromosome with a length of 6 r [0 0 minus 2minus 1 2 1] (r minus 1) [minus 1 minus 1 minus 3 minus 21 0] r times (r minus 1) [0 0 6 22 0] then 1113936 abs(r times (r minus 1)) 10 length is 6 sotarget3106167

+erefore the fitness function constructed in this paper isF(x) minus ω1 times target 1 minus ω2 times target 2 + ω3 times target 3 (8)

whereω is the weight coefficient of fitness functionω (0 1 23) because the genetic algorithm can only find the minimumvalue and the bigger the fitness value the better it is so theobjective function is minus and the penalty function is plus

Flow chart about this model is given in Figure 3

32 Model Concrete Steps

Input A decision information table S (U A V f )Output red(P Q β)

generate (M) Lr 98Initial population M 01 se-quence of Chromosome length 98Setting β ω crossover probability Pc mutationprobability Pm iteration number KBegin

for i 1 Ktarget1 (|posβP(Q)||U|)

target2 ((|P| minus |Lr|)|P|)

target3 (1113936 abs(r times (r minus 1))|r|)

Fitnessfunction minus ω1 times target1 minus ω2 times target2 + ω3 times target3Fitness functionP Select (M 2 Pc)Crossover probability PcQCrossover (P 2 Pc)Crossover algorithmQprimeMutation (Q Pm)Mutation algorithmEnd

33 Experimental Environment and Data

331 Hardware Environment Intel Core i5 4670-34GHzwith 80GB memory and 500GB hard disk were used

332 Software Environment Matlab R2012b LibSVM andWindows 7 operating system were used

333 Experimental Data +e PETCT images of 2000 lungcancer patients were collected as the study samples (1000cases of benign lung tumor 1000 cases of malignant lungtumor) Firstly ROI was extracted from the lung tumorand pretreated then 8-dimensional shape features 7-di-mensional gray features 3-dimensional Tamura features56-dimensional GLCM features and the 24-dimensionalfrequency domain features were extracted from the lungtumor ROI and 98-dimensional feature vectors are dis-creted and normalized In the decision attribute 1 rep-resents the lung malignant tumor and minus 1 represents thelung benign tumor Figure 4(a) shows four PETCT im-ages ROI of Lung malignant tumor and Figure 4(b) showsfour PETCT images ROI of lung benign tumor Table 1gives the feature values of two patients with lung cancer(one patient was a malignant tumor and the other was abenign tumor)

34Analysis ofExperimentalResults In this paper 3 kinds ofexperiments are designed according to the weight value ω

(0 1 2 3) of the fitness function and the classification errorrate β 04 02 0 (namely the inclusion degree1 minus β 06 08 1 ) For first type of experiments1 minus β 06 according to the different values of ω to do thethree groups of experiments totally For second type ofexperiments ϖ1 1ω2 1 ω3 0 according to the dif-ferent values of β to do three groups of experiments Forthird type of experiments 1 minus β 06 by increasing the ω

Mathematical Problems in Engineering 5

value to achieve the best fitness function to achieve the bestresults

341 Experiment 1mdashResearch on Different Weight Coeffi-cients under the Condition in the Same Classification ErrorRate ϖ values and β values of experiment 1 are shown inTable 2 and 1 minus β 06

(1) 1st Group Experiment ϖ1ω2ω3 1 0 0 +e al-gorithm is run 5 times according to this group weights theresults of the 5 groups are given in Table 3 including thereduction of the conditional attributes the length of re-duction the optimal fitness value the attribute dependencydegree and the time +e convergence of VPRS-GA under

the variation for fitness function value in one time is shownin Figure 5

Each reduction is classified by SVM classifier using themethod of 5-fold cross validation through changing thetraining samples and test samples the results of the fivegroups were obtained including accuracy sensitivityspecificity and time (training samples are constructed by800 malignant samples and 800 benign samples testingsamples are constructed by 200 malignant samples and 200benign samples the experiment is repeated 5 times bychanging training samples and testing samples) Finally theaverage values of these five groups are obtained as the finalresult of the reduction and shown in Table 4

+e weight value in this group experiment isϖ1ω2ω3 1 0 0 attribute dependency degree are

Output attributeset C_reduct1 C_re

duct2middotmiddotmiddotC_reductn

Indiscernibility relationfunction

Lower approximation

Relative positive domainposD

c function

Recognitionresult

SVMmodel

TrainingSVM

Reducedtraining set

Reducedtesting set

Target

Satisfycondition

Yes

No

Mutation Pm

Crossover Pc

Select Ps

F (x) = ndashω1 times target1 ndash ω2 times target2 + ω3 times target3β = 06 08 1

Initial population

Fitness value

Figure 3 Flow chart of high-dimensional feature selection based on genetic algorithm and variable precision rough set

(a) (b)

Figure 4 Part of lung tumor PETCT image ROI (a) Part of the lung malignant tumor PETCT-ROI (b) Part of the lung benign tumorPETCT-ROI

6 Mathematical Problems in Engineering

Table 1 ROI feature values of lung tumor PETCT image

Types of disease Shapefeature

Grayfeature

Tamuratexture

Texture features of GLCM Texture feature of wavelet

0 degree 45degrees

90degrees

135degrees Norm Standard

deviation Energy

Lung malignanttumor

60000 1222810 147000 00808 00779 00790 00611 6492580 371752 1000000012 14911500 309650 28937 29067 28989 31284 269473 38486 0001700000 386154 02326 02576 02820 02653 04490 93520 13355 0000200000 minus 05056 01668 01676 01659 01649 168200 24025 0000700000 24166 00792 00759 00772 00566 271143 38693 0001700000 140453 02576 02820 02653 04490 203163 29020 0001000000 70524 164110 164469 163584 164431 131755 18818 0000400000 27089 27072 27100 28066 183441 26199 00008

05755 06007 05810 073452109390 2117900 2095780 208825003064 03351 03135 03950

minus 06779 minus 06708 minus 06775 minus 0569600000 00000 00000 0000007625 07802 07658 08001

Lung benigntumor

40000 503912 101616 08087 07915 08077 07864 3799170 26741 1000000033 60006 18835 04324 04732 04370 04840 57551 08211 0000200000 24496 26329 00433 00621 00469 00679 11745 01677 0000000000 05649 94899 78127 92429 92429 34684 04955 0000100000 28589 08082 07905 08072 07853 20823 02972 0000000000 3283 00433 00621 00469 00679 21821 03117 0000000000 32559 78367 78363 78396 78363 08937 01276 0000000000 04024 04301 04045 04370 22387 03197 00000

01782 02326 01894 02481555257 550899 555291 54983100596 00873 00650 00958

minus 04707 minus 03295 minus 04351 minus 0291100000 00000 00000 0000020429 21172 20651 21394

Table 3 Results of VPRS-GA running 5 times when 1-β 06 ω1 1ω2 0ω3 0

Experimenttimes C_ reduction Reduction

lengthOptimal

fitness valueAttribute

dependency degree Time (s)

1 4 5 8 9 11 12 13 17 20 22 23 24 27 30 32 33 35 38 42 48 4952 57 59 61 62 63 64 65 68 70 72 73 75 77 78 80 87 88 91 92 41 minus 09705 09705 9719144

21 2 3 4 5 8 11 12 13 14 16 17 19 23 24 25 26 27 28 30 32 3638 39 40 42 43 44 46 47 52 53 55 61 63 66 67 69 71 72 73 77

79 80 82 84 85 87 9249 minus 09685 09685 10076907

3 4 611 12 1517 18 24 25 26 28 29 31 36 38 39 42 43 45 47 4953 56 65 68 69 72 76 77 79 80 81 83 85 88 91 92 37 minus 09695 09695 10432000

4 4 8 9 11 12 13 14 15 17 23 29 34 35 39 40 43 47 48 50 53 5556 60 61 64 68 70 75 80 81 82 83 84 86 34 minus 09790 09790 9473111

5 3 4 6 81011 12 13151719 20 21 24 26 29 31 39 42 44 45 4850 53 54 56 59 64 68 77 83 84 87 89 92 35 minus 09775 09775 9645092

Average value 392 minus 09730 09730 9869251

Table 2 Fitness function weight proportion and β value

Experiment times1 minus β 06

ω1 ω2 ω3First group experiment 1 0 0Second group experiment 1 1 0+ird group experiment 1 1 1

Mathematical Problems in Engineering 7

regarded as fitness function +e average attribute de-pendency degree is 0973 the average length of reductionis 392 and the average optimal fitness value is minus 0973+e average recognition accuracy of the experiment is9692 +e premature phenomena are shown in Fig-ure 5 and evolution progress is terminated early

(2) 2nd Group Experiment ϖ1ω2ω3 1 1 0 +isexperiment introduces an objective function to control thelength of reduction (the shorter the length of reduction thebetter it is) the influence degree of the objective functionwhich controls the reduction on the fitness function and the

final recognition accuracy is verified +e algorithm is run 5times according to this group weights and the results of the 5groups are given in Table 5 including the reduction of theconditional attributes the length of reduction the optimalfitness value the attribute dependency and the time +econvergence of VPRS-GA under the variation for fitnessfunction value in one time is shown in Figure 6

Each reduction is classified by SVM classifier using themethod of 5-fold cross validation through changing thetraining samples and test samples the results of the fivegroups were obtained including accuracy sensitivityspecificity and time (training samples are constructed by

ndash06

ndash07

ndash08

ndash09

ndash10 50 100 150

Generation stopping criteria

Best ndash09695 Mean ndash0944425

Fitn

ess v

alue

Best fitnessMean fitness

Figure 5 +e variation of fitness function value in a running process for Experiment 1-first group

Table 4 +e statistical results of the first group for experiment 1 with the SVM classifier

Experiment times Accuracy () Sensitivity () Specificity () Time (s)

Reduction 1

1 9250 8600 9900 3326072 9725 9750 9700 3450513 9900 9900 9900 3586774 9800 9950 9650 3510755 9925 10000 9850 355948

Average value 9720 9640 9800 348672

Reduction 2

1 9325 8700 9950 4365332 9725 9800 9650 4459003 9875 9850 9900 4395064 9750 9900 9600 4450645 9925 10000 9850 448513

Average value 9720 9650 9790 443103

Reduction 3

1 9275 8750 9800 3269162 9575 9750 9400 3372093 9800 9800 9800 3407014 9700 9850 9550 3331745 9850 9950 9750 333257

Average value 9640 9620 9660 334251

Reduction 4

1 9375 8850 9900 3064852 9650 9750 9550 3192403 9750 9700 9800 3240824 9775 9900 9650 3254195 9900 10000 9800 361516

Average value 9690 9640 9740 318806

Reduction 5

1 9400 8900 9900 3195572 9650 9750 9550 3369093 9725 9700 9750 3301594 9775 9900 9650 3999805 9900 10000 9800 325692

Average value 9690 9650 9730 342459

8 Mathematical Problems in Engineering

800 malignant samples and 800 benign samples testingsamples are constructed by 200 malignant samples and 200benign samples the experiment is repeated 5 times bychanging training samples and testing samples) Finally theaverage values of these five groups are obtained as the finalresult of the reduction and shown in Table 6

+e experimental weight of this group is ϖ1

ω2ω3 1 1 0 attribute dependency degree and thelength of reduction are regarded as fitness function As canbe seen from Table 5 the reduction length is 13 17 and soon +e average length of reduction was 17 which wassignificantly reduced compared with the average length ofthe reduction in Table 3 in the experiment of the first groupswhich reduced the time improved the efficiency of the al-gorithm and increased the attribute dependency of thealgorithm even up to 1 +e average recognition accuracy ofthe experimental group was 9698 which was increased by006 compared with that in the first groups

(3) 3rd Group Experiment ϖ1ω2ω3 1 1 1 On thebasis of attribute dependency degree and attribute reductionlength this experiment introduces gene coding weightfunction in order to verify the effect of gene coding weightfunction on fitness function and the final recognition ac-curacy +e algorithm are run 5 times according to thisgroup weights the results of the 5 groups are given inTable 7 including the reduction of the conditional attributesthe length of reduction the optimal fitness value the at-tribute dependency and the time +e convergence ofVPRS-GA under the variation for fitness function value inone time is shown in Figure 7

Each reduction is classified by SVM classifier using themethod of 5-fold cross validation through changing thetraining samples and test samples the results of the fivegroups were obtained including accuracy sensitivityspecificity and time (training samples are constructed by800 malignant samples and 800 benign samples testingsamples are constructed by 200 malignant samples and 200benign samples the experiment is repeated 5 times bychanging training samples and testing samples) Finally theaverage values of these five groups are obtained as the finalresult of the reduction and shown in Table 8

+e experimental weight of this group is ϖ1 ω2ω3=1 1 1 attribute dependency degree the length of re-duction and gene coding weight value are regarded as fitnessfunction However the premature phenomena are shown inFigure 7 and evolution progress is terminated early FromTable 7 we can see that the attribute dependency decreasesgradually and even the attribute dependency of Reduction 1is reduced to 0759 +e average recognition accuracy of theexperimental group was 9685+e accuracy of recognitionwas decreased compared with the second groups and henceusing gene encoding weight function in the fitness functionto improve recognition accuracy is useless only for thesamples with different results to analyze specific issues +e3 experiment runs of experiment 1 verified the necessity ofthe fitness function by continuously introducing fitnessobjective function such as target1 target2 and target3 theconclusion is that the fitness function is better when it is notbigger but after the introduction of target3 the accuracydeclines therefore the introduction of target1 and target2 inthis algorithm can get better results

Table 5 Results of VPRS-GA running 5 times when 1 minus β 06 ω1 1ω2 1ω3 0

Experiment times C_ reduction Reductionlength

Optimalfitness value

Attributedependency

degreeTime (s)

1 5 9 14 20 26 41 43 46 48 54 55 57 64 66 74 79 86 90 18 minus 46487 09965 107240722 1 4 11 12 14 24 34 40 42 43 56 60 61 65 67 68 71 72 85 19 minus 40109 1 63281223 2 13 27 29 39 42 45 56 59 63 68 70 75 13 minus 46512 09990 110239674 1 3 4 7 9 11 12 15 30 34 38 42 46 48 55 62 65 77 79 19 minus 49674 1 87946705 3 9 11 13 29 39 41 42 43 46 50 55 65 c77 85 86 16 minus 44114 09815 15075539

Average value 17 minus 45379 09954 10389274

ndash1

ndash2

ndash3

ndash4

ndash5

Fitn

ess v

alue

Best ndash496739 Mean ndash492312

0 50 100 150Generation stopping criteria

Best fitnessMean fitness

Figure 6 +e variation of fitness function value in a running process for experiment 1-second group

Mathematical Problems in Engineering 9

342 Experiment 2mdashResearch on Different ClassificationError Rates under the Condition in the Same WeightCoefficient According to experiment 1 we can see thatwhen ω1 1 ω2 1 ω3 0 the experimental results arethe best so in experiment 2 the case of the weight value ofwas unchanged ω1 1 ω2 1 ω3 0 and the β value waschanged and they are shown in Table 9

(1) 1st Group Experiment 1 minus β 06 +e algorithm is run 5times according to this group weights the results of the 5groups are shown in Table 5 including the reduction of the

conditional attributes the length of reduction the optimalfitness value the attribute dependency and the time +econvergence of VPRS-GA under the variation for fitnessfunction value for one time is shown in Figure 6 (ie notrepeated in the second group of experiment 1)

(2) 2nd Group Experiment 1 minus β 08 +e algorithm are is 5times according to this group weights the results of the 5groups are given in Table 10 including the reduction of theconditional attributes the length of reduction the optimalfitness value the attribute dependency and the time +e

Table 6 +e statistical results of the second group for experiment 1 with the SVM classifier

Experiment times Accuracy () Sensitivity () Specificity () Time (s)

Reduction 1

1 9300 8600 10000 1164882 9625 9600 9650 1255113 9850 9900 9800 1315094 9725 9850 9600 1344685 9925 10000 9850 144839

Average value 9685 9590 9780 130563

Reduction 2

1 9425 8900 9950 1210962 9725 9700 9750 1286363 9800 9800 9800 1356774 9750 9800 9700 1381965 9875 9900 9850 136691

Average value 9715 9620 9810 132059

Reduction 3

1 9300 8750 9850 877572 9725 9750 9700 1034243 9775 9800 9750 1074114 9775 9850 9700 1123445 9900 10000 9800 113006

Average value 9695 9630 9760 104788

Reduction 4

1 9375 8750 10000 1464172 9650 9750 9550 1547363 9750 9700 9800 1576214 9800 9900 9700 1613555 9925 10000 9850 163381

Average value 9700 9620 9780 156702

Reduction 5

1 9250 8650 9850 1249332 9675 9800 9550 1400573 9800 9800 9800 1451944 9800 9900 9700 1457925 9950 9950 9950 150400

Average value 9695 9620 9770 141275

Table 7 Results of VPRS-GA running 5 times when 1 minus β 06 ω1 1ω2 1ω3 1

Experimenttimes C_ reduction Reduction

lengthOptimal

fitness valueAttribute

dependency degree Time (s)

1 4 5 7 26 27 34 35 41 47 54 55 71 74 75 78 80 83 90 18 minus 14192 07590 6888635

2 4 15 16 19 22 27 28 29 30 35 38 42 45 50 52 53 59 61 6264 65 70 71 72 77 87 88 27 minus 15232 08640 8124857

3 6 17 19 24 28 31 33 34 38 39 43 45 47 48 49 51 55 56 6667 69 70 71 72 76 77 78 80 81 84 87 89 91 92 34 minus 13545 07950 9521511

4 3 6 8 91617 19 20 24 25 28 35 37 39 41 42 46 49 51 52 5459 63 65 66 74 83 86 28 minus 14703 08365 8714839

5 1 7 8 15 17 19 20 23 29 37 45 48 54 60 62 70 73 75 77 7879 86 22 minus 14990 07995 7797617

Average value 258 minus 14532 08108 8209492

10 Mathematical Problems in Engineering

convergence of VPRS-GA under the variation for fitnessfunction value for one time is shown in Figure 8

Each reduction is classified by SVM classifier using themethod of 5-fold cross validation through changing thetraining samples and test samples the results of the five

groups were obtained including accuracy sensitivityspecificity and time (training samples are constructed by800 malignant samples and 800 benign samples testingsamples are constructed by 200 malignant samples and 200benign samples the experiment is repeated 5 times by

ndash08

ndash1

ndash12

ndash14

ndash16

Fitn

ess v

alue

Best ndash141919 Mean ndash128476

0 50 100 150Generation stopping criteria

Best fitnessMean fitness

Figure 7 +e variation of fitness function value in a running process for experiment 1-third group

Table 8 +e statistical results of the third group for experiment 1 with the SVM classifier

Experiment times Accuracy () Sensitivity () Specificity () Time (s)

Reduction 1

1 9275 8600 9950 924922 9725 9750 9700 1074613 9850 9850 9850 1138114 9775 9900 9650 1155605 9875 10000 9750 117022

Average value 9700 9620 9780 109269

Reduction 2

1 9350 8750 9950 1482452 9700 9650 9750 1615353 9775 9850 9700 1664524 9800 9850 9750 1754505 9875 9950 9800 172348

Average value 9700 9610 9790 164806

Reduction 3

1 9125 8300 9950 2019042 9650 9700 9600 2185353 9800 9800 9800 2196054 9625 9900 9350 2230915 9825 10000 9650 236896

Average value 9605 9540 9670 220006

Reduction 4

1 9300 8700 9900 1654542 9675 9600 9750 1724323 9875 9850 9900 1793014 9800 9900 9700 1895605 9900 9950 9850 185249

Average value 9710 9600 9820 178399

Reduction 5

1 9275 8600 9950 1411732 9725 9800 9650 1612953 9900 9950 9850 1589924 9775 9950 9600 1648765 9875 10000 9750 166070

Average value 9710 9660 9760 158481

Table 9 Fitness function weight proportion and β value

Experiment timesω1 1 ω2 1 ω3 0

1 minus β 06 1 minus β 08 1 minus β 1First group experiment Second group experiment +ird group experiment

Mathematical Problems in Engineering 11

changing training samples and testing samples) Finally theaverage values of these five groups are obtained as the finalresult of the reduction and shown in Table 11

In the case of constant weight ϖ and classification errorrate of β 02 (which contains 1 minus β 08) the classificationerror rate is changed on the basis of the attribute dependencyand the length of control reduction +e premature phe-nomena are shown in Figure 8 and evolution progress isterminated early such that the attribute dependency ofreduction 5 was 08405 appeared in attribute dependency onless than 09 compared with first groups of experiment 2attribute dependency declined +e average recognitionaccuracy of the experimental group was 9674 Comparedwith the classification error rate of 04 and inclusion degreeof 06 the accuracy was decreased by 024

(3) 3rd Group Experiment 1 minus β1 +e algorithm is run 5times according to the group weights and the results of the 5groups are shown in Table 12 including the reduction of theconditional attributes the length of reduction the optimalfitness value the attribute dependency and the time +econvergence of VPRS-GA under the variation for fitnessfunction value for one time is shown in Figure 9

Each reduction is classified by SVM classifier using themethod of 5-fold cross validation through changing thetraining samples and test samples the results of the fivegroups were obtained including accuracy sensitivityspecificity and time (training samples are constructed by800 malignant samples and 800 benign samples testingsamples are constructed by 200 malignant samples and 200

benign samples the experiment is repeated 5 times bychanging training samples and testing samples) Finally theaverage values of these five groups are obtained as the finalresult of the reduction and shown in Table 13

In the case of constant weight ϖ and classification errorrate of β= 0 (which contains 1 minus β= 1) the classificationerror rate is reduced and the inclusion degree is improved onthe basis of the attribute dependency and the length ofcontrol reduction +e premature phenomena are shown inFigure 9 and evolution progress is terminated early +eaverage recognition accuracy of the experimental group was9573 which was decreased by 006 compared with thatin the second group In experiment 2 the effect of changingthe classification error rate on the recognition accuracy wasverified by the 3 groups of experiments By continuallyreducing the classification error rate the final recognitionaccuracy has been declining when inclusion degree is 1β= 0 variable precision rough set becomes Pawlak rough setthe recognition accuracy of the recognition accuracy of isminimum which was verified the advantages of variableprecision rough set

343 Experiment 3mdashResearch on Increasing the WeightCoefficient under the Condition in the Same ClassificationError Rate According to experiment 1 and experiment 2we can know that when β 06 ω1 1 ω2 1 ω3 0 therecognition accuracy is the best therefore in the thirdexperiment by increasing the weight of ω 3 groups ofexperiments are performed fitness goals target 1 (attribute

Table 10 Results of VPRS-GA running 5 times when 1 minus β 08 ω1 1ω2 1ω3 0

Experimenttimes C_ reduction Reduction

lengthOptimal fitness

valueAttribute

dependency degree Time (s)

1 8 9 11 12 15 16 17 18 25 26 29 31 35 39 40 41 42 48 5865 67 68 70 83 84 91 26 minus 67816 09490 10002827

2 1 6 8 9 11 12 15 17 21 23 26 28 30 31 34 44 50 56 58 5962 63 64 68 71 75 77 82 89 92 30 minus 67797 09615 9477387

3 6 8 12 14 15 16 17 21 28 35 38 39 45 49 55 58 61 62 6465 77 82 85 23 minus 68694 09070 12866181

4 4 6 7 8 11 12 13 16 17 20 25 26 31 32 34 35 41 42 44 4950 55 58 68 72 74 76 78 79 85 89 92 32 minus 67225 09540 10510220

5 3 6 8 9 10 16 17 26 27 34 36 37 38 40 42 44 46 51 52 6266 67 84 86 87 25 minus 65892 08405 8469324

Average value 272 minus 67484 09224 10265188

ndash55

ndash6

ndash65

ndash7

Fitn

ess v

alue

Best ndash686942 Mean ndash653584

0 50 100 150Generation stopping criteria

Best fitnessMean fitness

Figure 8 +e variation of fitness function value in a running process for experiment 2-second group

12 Mathematical Problems in Engineering

Table 11 +e statistical results of the second group for experiment 2 with the SVM classifier

Experiment times Accuracy () Sensitivity () Specificity () Time (s)

Reduction 1

1 9300 8650 9950 2280072 9575 9700 9450 2376463 9700 9600 9800 2332504 9750 9850 9650 2444915 9925 10000 9850 244816

Average value 9650 9560 9740 237642

Reduction 2

1 9375 8800 9950 2524032 9625 9750 9500 2652893 9800 9700 9900 2655234 9800 9900 9700 2682125 9950 10000 9900 275880

Average value 9710 9630 9790 265461

Reduction 3

1 9275 8750 9800 1807802 9675 9750 9600 1929923 9700 9600 9800 1872434 9775 9950 9600 2084825 9875 10000 9750 203507

Average value 9660 9610 9710 194601

Reduction 4

1 9200 8650 9750 2572602 9700 9750 9650 2730243 9775 9650 9900 2723164 9750 9900 9600 2815545 9900 10000 9800 291471

Average value 9665 9590 9740 275125

Reduction 5

1 9275 8750 9800 1437152 9675 9600 9750 1526373 9750 9800 9700 1589294 9775 9900 9650 1629975 9950 10000 9900 166792

Average value 9685 9610 9760 157014

Table 12 Results of VPRS-GA running 5 times when 1 minus β 1 ω1 1ω2 1ω3 0

Experimenttimes C_ reduction Reduction

lengthOptimal fitness

valueAttribute dependency

degree Time (s)

1 15 44 68 73 79 84 6 minus 27313 07965 114499012 34 51 54 75 80 90 6 minus 27047 08460 96993913 2 34 49 70 71 72 76 81 8 minus 34057 07535 112334894 12 25 78 85 4 minus 22872 09285 11668133

5 6 7 12 13 42 44 55 57 65 66 69 77 81 8687 15 minus 33230 08665 13236077

Average value 78 minus 28903 08382 11457398

ndash1

ndash2

ndash3

ndash4

Fitn

ess v

alue

0 50 100 150Generation stopping criteria

Best fitnessMean fitness

Best ndash340567 Mean ndash330598

Figure 9 +e variation of fitness function value in a running process for experiment 2-third group

Mathematical Problems in Engineering 13

dependency) target 2 (the minimum number of attributesreduction) and target 3 (gene encoding weight function)the three objective functions play an important role in theevaluation of fitness function However the importance offitness function is reduced in these three objectives+erefore in this experiment when the other conditions areunchanged the weight coefficient of the target 1 is increasedto verify the influence of the change in the weight coefficienton the experimental results and they are shown in Table 14

(1) 1st Group Experiment ω1 1 ω2 1 ω3 0 +e al-gorithm are run 5 times according to this group weights theresults of the 5 groups are given in Table 5 including thereduction of the conditional attributes the length of reduc-tion the optimal fitness value the attribute dependency andthe time +e convergence of VPRS-GA under the variationfor fitness function value in one time is shown in Figure 6 (ienot repeated for the second group of experiment 1)

(2) 2nd Group Experiment ω1 2 ω2 1 ω3 0 +ealgorithm is run 5 times according to this group weights theresults of the 5 groups are given in Table 15 including thereduction of the conditional attributes the length of re-duction the optimal fitness value the attribute dependencyand the time +e convergence of VPRS-GA under thevariation for fitness function value in one time is shown inFigure 10

Each reduction is classified by SVM classifier using themethod of 5-fold cross validation through changing thetraining samples and test samples the results of the fivegroups were obtained including accuracy sensitivityspecificity and time (training samples are constructed by800 malignant samples and 800 benign samples testingsamples are constructed by 200 malignant samples and 200benign samples the experiment is repeated 5 times bychanging training samples and testing samples) Finally theaverage values of these five groups are obtained as the finalresult of the reduction and shown in Table 16

+e experimental group in the case of 1 minus β= 06 un-changed the weight of ω1 was increased +e attributedependency and the optimal fitness function are relativelyhigh the average precision of reduction 1 reduction 2 andreduction 3 in Table 16 is more than 97 and that of re-duction 2 is even up to 9725 +e average recognitionaccuracy of the experimental group is 9703 which ishigher than that of the first group

Table 13 +e statistical results of the third group for experiment 2 with the SVM classifier

Experiment times Accuracy () Sensitivity () Specificity () Time (s)

Reduction 1

1 9225 8450 10000 812712 9550 9700 9400 945833 9575 9400 9750 881984 9600 9800 9400 937545 9725 9900 9550 98691

Average value 9535 9450 9620 91299

Reduction 2

1 9200 8450 9950 648942 9625 9550 9700 801983 9525 9300 9750 773374 9600 9750 9450 760125 9800 10000 9600 82763

Average value 9550 9410 9690 76241

Reduction 3

1 9200 8450 9950 648942 9625 9550 9700 801983 9525 9300 9750 773374 9600 9750 9450 760125 9800 10000 9600 82763

Average value 9550 9410 9690 76241

Reduction 4

1 9275 8550 10000 672642 9675 9600 9750 784673 9600 9450 9750 730224 9575 9750 9400 794605 9800 10000 9600 84184

Average value 9585 9470 9700 76479

Reduction 5

1 9200 8450 9950 1147192 9625 9750 9500 1287053 9850 9900 9800 1320494 9775 9950 9600 1335135 9850 10000 9700 133144

Average value 9660 9610 9710 128426

Table 14 Fitness function weight proportion and β value

Experiment times1 minus β 06

ω1 ω2 ω3First group experiment 1 1 0Second group experiment 2 1 0+ird group experiment 3 1 0

14 Mathematical Problems in Engineering

ndash2

ndash25

ndash3

Fitn

ess v

alue

0 50 100 150Generation stopping criteria

Best fitnessMean fitness

Best ndash2915 Mean ndash291446

Figure 10 +e variation of fitness function value in a running process for experiment 3-second group

Table 15 Results of VPRS-GA running 5 times when 1 minus β 06 ω1 2ω2 1ω3 0

Experimenttimes C_ reduction Reduction

lengthOptimal fitness

valueAttribute dependency

degree Time (s)

1 2 3 4 5 11 13 16 18 24 30 34 37 39 41 42 51 55 64 7077 78 82 22 minus 34859 09060 21515464

2 8 9 11 12 14 15 23 25 26 29 30 33 37 42 43 45 46 5060 61 69 74 80 87 89 25 minus 30845 09390 42761634

3 8 11 12 13 16 18 19 24 29 36 37 43 64 65 68 71 86 9192 19 minus 35039 09150 26197164

4 2 3 4 8 10 11 12 13 15 16 19 23 25 30 48 55 64 65 6874 77 80 81 83 84 86 89 27 minus 29150 09575 44271631

5 5 8 911 121517 23 25 29 31 36 39 41 48 54 59 63 8083 86 89 22 minus 29920 09525 43161464

Average value 23 minus 31962 09340 35581471

Table 16 +e statistical results of the second group for experiment 3 with the SVM classifier

Experiment times Accuracy () Sensitivity () Specificity () Time (s)

Reduction 1

1 9275 8600 9950 1884972 9725 9800 9650 1571623 9850 9900 9800 1586914 9800 9900 9700 1646035 9950 10000 9900 161914

Average value 9720 9640 9800 166173

Reduction 2

1 9450 8950 9950 1908132 9675 9800 9550 2002513 9775 9800 9750 1970084 9850 9900 9800 2009245 9875 9900 9850 209245

Average value 9725 9670 9780 199648

Reduction 3

1 9400 8800 10000 1313692 9725 9800 9650 1447973 9800 9800 9800 1426624 9725 9850 9600 1471905 9925 10000 9850 148799

Average value 9715 9650 9780 142963

Reduction 4

1 9350 8750 9950 2404562 9700 9750 9650 2520823 9800 9800 9800 2511754 9775 9950 9600 2701885 9825 10000 9650 267471

Average value 9690 9650 9730 256274

Reduction 5

1 9325 8800 9850 1809592 9600 9800 9400 1965633 9750 9750 9750 1967234 9800 9900 9700 2078295 9850 9950 9750 219703

Average value 9665 9640 9690 200355

Mathematical Problems in Engineering 15

Table 17 Results of VPRS-GA running 5 times when 1 minus β 1 ω1 1ω2 1ω3 0

Experimenttimes C_ reduction Reduction

lengthOptimal fitness

valueAttribute

dependency degree Time (s)

1 3 4 5 8 9 11 12 17 19 29 34 35 38 46 52 53 55 59 63 6672 75 77 78 79 87 92 27 minus 38867 09550 28981789

2 4 8 9 11 12 15 17 29 33 37 38 39 42 43 48 55 67 73 7881 83 84 88 89 90 25 minus 38167 09715 55783772

3 2 3 4 8 9 10 11 12 13 15 16 19 24 25 30 36 49 54 55 6064 67 68 70 74 77 83 85 86 91 30 minus 38807 09530 34831096

4 4 5 7 11 12 14 15 17 25 29 33 36 39 41 42 47 48 50 5556 58 62 67 69 72 74 77 84 86 90 91 31 minus 39430 09665 35742822

5 3 4 5 8 9 11 12 17 19 29 34 35 38 46 52 53 55 59 63 6672 75 77 78 79 87 92 27 minus 38867 09550 27919582

Average value 28 minus 38827 09602 36651812

ndash3

ndash35

ndash40 50 100 150

Generation stopping criteria

Fitn

ess v

alue

Best fitnessMean fitness

Best ndash394298 Mean ndash393327

Figure 11 +e variation of fitness function value in a running process for experiment 3-third group

Table 18 +e statistical results of the Second group for experiment 3 with the SVM classifier

Experiment times Accuracy () Sensitivity () Specificity () Time (s)

Reduction 1

1 9200 8700 9700 2187172 9750 9750 9750 2105503 9850 9850 9850 2032064 9800 9900 9700 2211645 9925 10000 9850 272536

Average value 9705 9640 9770 225235

Reduction 2

1 9400 8850 9950 2331232 9575 9750 9400 2433493 9750 9700 9800 2442024 9775 9900 9650 2566075 9900 9950 9850 259071

Average value 9680 9630 9730 247270

Reduction 3

1 9275 8650 9900 2525842 9625 9750 9500 2624123 9775 9800 9750 2601274 9775 9900 9650 2686705 9875 10000 9750 265387

Average value 9665 9620 9710 261836

Reduction 4

1 9150 8550 9750 2532312 9625 9750 9500 2649433 9750 9700 9800 2752834 9800 9950 9650 3229545 9825 9950 9700 277432

Average value 9630 9580 9680 278769

Reduction 5

1 9200 8800 9600 1951962 9700 9700 9700 2148893 9825 9800 9850 2036124 9850 10000 9700 2133615 9900 9900 9900 225526

Average value 9695 9640 9750 210517

16 Mathematical Problems in Engineering

(3) 3rd Group Experiment ω1 3 ω2 1 ω3 0 +e al-gorithm is run 5 times according to the group weights andthe results of the 5 groups are given in Table 17 including thereduction of the conditional attributes the length of re-duction the optimal fitness value the attribute dependencyand the time +e convergence of VPRS-GA under thevariation for fitness function value for one time is shown inFigure 11

Each reduction is classified by SVM classifier using themethod of 5-fold cross validation through changing thetraining samples and test samples the results of the fivegroups were obtained including accuracy sensitivityspecificity and time (training samples are constructed by800 malignant samples and 800 benign samples testingsamples are constructed by 200 malignant samples and 200benign samples the experiment is repeated 5 times bychanging training samples and testing samples) Finally theaverage values of these five groups are obtained as the finalresult of the reduction and shown in Table 18

+e experiment in the case of 1 minus β 06 unchangedincrease the weight of the ω1 ω1 3 ω2 1 ω3 0 InTable 18 the recognition accuracy of reduction 1 is over 97only +e average recognition accuracy of the experimentalgroup is 9675 and the accuracy is decreased by 028compared with that in the other second groups +e threegroups of experiment 3 the purpose is to verify whether theexperimental accuracy is influenced by increasing theweight +e experimental results show that the accuracy ofsecond group for experimental weight 2 1 0 comparedwith first group experiment when 1 1 0 is high but thethird groups of experimental weight was 3 1 0 and theaccuracy declined therefore the weight of 2 1 0 is the bestchoice for this experiment

4 Conclusions

Aiming at the deficiency of the traditional rough set modelthis paper proposes a new feature selection model based ongenetic algorithm and variable precision rough set by in-troducing the β value the rigid inclusion of the approxi-mation for the traditional rough set is relaxed and then wedesign the 3 kinds of experiments by constructing the de-cision information table of the PETCT feature for lungtumor ROI +e first type of experiment is the inclusion of1 minus β 06 and different values of ω made a total of threegroups of experiments the experimental results show thatthe better recognition accuracy can be obtained when theweight is 1 1 0 and the results show that the gene codingweight function has no effect on the fitness function For thesecond type of experiments ϖ1 1ω2 1 ω3 0according to the different values of β to do three groups ofexperiments the results show that the recognition accuracyof 1 minus β 06 is the best which shows that the larger the βvalue is the lower approximate cardinality will be largerthen the relative accuracy will increase For the third type ofexperiments 1 minus β 06 ω value is increased to achieve thebest fitness function in order to achieve the best results +eexperimental results show that the recognition accuracy isbetter than the others when the weight value is 2 1 0 so it

is better to solve the problem by increasing the proportion ofattribute dependency +rough the above experiments it isshown that the high-dimensional feature selection algorithmbased on genetic algorithm and variable precision rough setcan solve the multiobjective optimization problem wellHowever when the fitness function and its parameters areapplied in the specific application it is necessary to analyzethe specific problems

Data Availability

+e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

+e authors declare no conflicts of interest

Acknowledgments

+is work was supported by National Natural ScienceFoundation of China (Grant nos 61561040 and 61876121)First-Class Disciplines Foundation of Ningxia (NoNXYLXK2017B09)

References

[1] S Luo D Miao Z Zhang Y Zhang and S Hu ldquoA neigh-borhood rough set model with nominal metric embeddingrdquoInformation Sciences vol 520 pp 373ndash388 2020

[2] B Barman and S Patra ldquoVariable precision rough set basedunsupervised band selection technique for hyperspectralimage classificationrdquo Knowledge-Based Systems vol 1936Article ID 105414 2020

[3] Y Chenyi and L Jinjin ldquoApproximate attribute reductionunder variable precision rough set βrdquo Journal of ShandongUniversity vol 11 pp 17ndash21 2011

[4] S Xiaowei Research on Hierarchical Model of Attribute Re-duction in Variable Precision Rough Set Central SouthUniversity Changsha China 2013

[5] Z Jie and W Jiayang ldquoAnalysis of reduction feature ofvariable precision rough set modelrdquo Computer ApplicationResearch vol 7 pp 12ndash15 2007

[6] Z Pei and Z Qinghua ldquoFCM clustering algorithm based onvariable precision rough setrdquo Journal of Shanxi Universityvol 3 pp 342ndash348 2016

[7] C Hao and Y Junan ldquoAttribute kernel and minimum at-tribute reduction algorithm of variable precision rough setrdquoActa Sinica Sinica vol 5 pp 1011ndash1017 2012

[8] S Xu X Yang H Yu D-J Yu J Yang and E CC TsangldquoMulti-label learning with label-specific feature reductionrdquoKnowledge-Based Systems vol 104 pp 52ndash61 2016

[9] I Maryam and G Hassan ldquoFeature space discriminantanalysis for hyperspectral data feature reductionrdquo ISPRSJournal of Photogrammetry and Remote Sensing vol 102pp 1ndash13 2015

[10] S Q Wang C Y Gao C Luo G M Zheng and Y N ZhouldquoResearch on feature selectionattribute reduction methodbased on rough set theoryrdquo Procedia Computer Sciencevol 154 pp 194ndash198e 2019

[11] A W Omar M Azzam O Hadi and B Jamal ldquoCEAP SVM-based intelligent detection model for clustered vehicular ad

Mathematical Problems in Engineering 17

hoc networksrdquo Expert Systems with Applications vol 50pp 40ndash54 2016

[12] H Lee and Y-P P Chen ldquoImage based computer aideddiagnosis system for cancer detectionrdquo Expert Systems withApplications vol 42 no 12 pp 5356ndash5365 2015

[13] J A Guy and P L Harold ldquoAfter detection the improvedaccuracy of lung cancer assessment using radiologic com-puter-aided diagnosisrdquo Academic Radiology vol 23 no 2pp 186ndash191 2016

[14] E Kiyonori T Shodayu J Binghu et al ldquoPleural invasion byperipheral lung cancer prediction with three-dimensionalCTrdquo Academic Radiology vol 3 pp 310ndash319 2015

[15] B Koohestani ldquoA crossover operator for improving the ef-ficiency of permutation-based genetic algorithmsrdquo ExpertSystems with Applications vol 1511 Article ID 113381 2020

[16] N K Lee X Li and D Wang ldquoA comprehensive survey ongenetic algorithms for DNA motif predictionrdquo InformationSciences vol 466 pp 25ndash43 2018

[17] S Shibao and Y Leilei ldquoResearch on variable precision roughset model and its applicationrdquo Computer Engineering andApplication vol 07 pp 10ndash13 2009

[18] T Xiaolong Several Problems of Multi Granularity VariablePrecision Rough Set Guangxi University For NationalitiesNanning China 2015

[19] W Xueming Research on Several Rough Set Models andNeural Network University of Electronic Science and Tech-nology of China Chengdu China 2013

[20] T Sun J Wang X Li et al ldquoComparative evaluation ofsupport vector machines for computer aided diagnosis of lungcancer in CT based on a multi-dimensional data setrdquo Com-puter Methods and Programs in Biomedicine vol 111 no 2pp 519ndash524 2013

[21] Z Yang T Ouyang X Fu and X Peng ldquoA decision-makingalgorithm for online shopping using deep-learning-basedopinion pairs mining and q -rung orthopair fuzzy interactionHeronianmean operatorsrdquo International Journal of IntelligentSystems vol 35 no 5 pp 783ndash825 2020

[22] W Chen C Lin C Li et al ldquoTracing the evolution of 3Dprinting technology in China using LDA-based patent ab-stract miningrdquo IEEE Transactions on Engineering Manage-men vol 36 pp 1ndash11 2020

18 Mathematical Problems in Engineering

value to achieve the best fitness function to achieve the bestresults

341 Experiment 1mdashResearch on Different Weight Coeffi-cients under the Condition in the Same Classification ErrorRate ϖ values and β values of experiment 1 are shown inTable 2 and 1 minus β 06

(1) 1st Group Experiment ϖ1ω2ω3 1 0 0 +e al-gorithm is run 5 times according to this group weights theresults of the 5 groups are given in Table 3 including thereduction of the conditional attributes the length of re-duction the optimal fitness value the attribute dependencydegree and the time +e convergence of VPRS-GA under

the variation for fitness function value in one time is shownin Figure 5

Each reduction is classified by SVM classifier using themethod of 5-fold cross validation through changing thetraining samples and test samples the results of the fivegroups were obtained including accuracy sensitivityspecificity and time (training samples are constructed by800 malignant samples and 800 benign samples testingsamples are constructed by 200 malignant samples and 200benign samples the experiment is repeated 5 times bychanging training samples and testing samples) Finally theaverage values of these five groups are obtained as the finalresult of the reduction and shown in Table 4

+e weight value in this group experiment isϖ1ω2ω3 1 0 0 attribute dependency degree are

Output attributeset C_reduct1 C_re

duct2middotmiddotmiddotC_reductn

Indiscernibility relationfunction

Lower approximation

Relative positive domainposD

c function

Recognitionresult

SVMmodel

TrainingSVM

Reducedtraining set

Reducedtesting set

Target

Satisfycondition

Yes

No

Mutation Pm

Crossover Pc

Select Ps

F (x) = ndashω1 times target1 ndash ω2 times target2 + ω3 times target3β = 06 08 1

Initial population

Fitness value

Figure 3 Flow chart of high-dimensional feature selection based on genetic algorithm and variable precision rough set

(a) (b)

Figure 4 Part of lung tumor PETCT image ROI (a) Part of the lung malignant tumor PETCT-ROI (b) Part of the lung benign tumorPETCT-ROI

6 Mathematical Problems in Engineering

Table 1 ROI feature values of lung tumor PETCT image

Types of disease Shapefeature

Grayfeature

Tamuratexture

Texture features of GLCM Texture feature of wavelet

0 degree 45degrees

90degrees

135degrees Norm Standard

deviation Energy

Lung malignanttumor

60000 1222810 147000 00808 00779 00790 00611 6492580 371752 1000000012 14911500 309650 28937 29067 28989 31284 269473 38486 0001700000 386154 02326 02576 02820 02653 04490 93520 13355 0000200000 minus 05056 01668 01676 01659 01649 168200 24025 0000700000 24166 00792 00759 00772 00566 271143 38693 0001700000 140453 02576 02820 02653 04490 203163 29020 0001000000 70524 164110 164469 163584 164431 131755 18818 0000400000 27089 27072 27100 28066 183441 26199 00008

05755 06007 05810 073452109390 2117900 2095780 208825003064 03351 03135 03950

minus 06779 minus 06708 minus 06775 minus 0569600000 00000 00000 0000007625 07802 07658 08001

Lung benigntumor

40000 503912 101616 08087 07915 08077 07864 3799170 26741 1000000033 60006 18835 04324 04732 04370 04840 57551 08211 0000200000 24496 26329 00433 00621 00469 00679 11745 01677 0000000000 05649 94899 78127 92429 92429 34684 04955 0000100000 28589 08082 07905 08072 07853 20823 02972 0000000000 3283 00433 00621 00469 00679 21821 03117 0000000000 32559 78367 78363 78396 78363 08937 01276 0000000000 04024 04301 04045 04370 22387 03197 00000

01782 02326 01894 02481555257 550899 555291 54983100596 00873 00650 00958

minus 04707 minus 03295 minus 04351 minus 0291100000 00000 00000 0000020429 21172 20651 21394

Table 3 Results of VPRS-GA running 5 times when 1-β 06 ω1 1ω2 0ω3 0

Experimenttimes C_ reduction Reduction

lengthOptimal

fitness valueAttribute

dependency degree Time (s)

1 4 5 8 9 11 12 13 17 20 22 23 24 27 30 32 33 35 38 42 48 4952 57 59 61 62 63 64 65 68 70 72 73 75 77 78 80 87 88 91 92 41 minus 09705 09705 9719144

21 2 3 4 5 8 11 12 13 14 16 17 19 23 24 25 26 27 28 30 32 3638 39 40 42 43 44 46 47 52 53 55 61 63 66 67 69 71 72 73 77

79 80 82 84 85 87 9249 minus 09685 09685 10076907

3 4 611 12 1517 18 24 25 26 28 29 31 36 38 39 42 43 45 47 4953 56 65 68 69 72 76 77 79 80 81 83 85 88 91 92 37 minus 09695 09695 10432000

4 4 8 9 11 12 13 14 15 17 23 29 34 35 39 40 43 47 48 50 53 5556 60 61 64 68 70 75 80 81 82 83 84 86 34 minus 09790 09790 9473111

5 3 4 6 81011 12 13151719 20 21 24 26 29 31 39 42 44 45 4850 53 54 56 59 64 68 77 83 84 87 89 92 35 minus 09775 09775 9645092

Average value 392 minus 09730 09730 9869251

Table 2 Fitness function weight proportion and β value

Experiment times1 minus β 06

ω1 ω2 ω3First group experiment 1 0 0Second group experiment 1 1 0+ird group experiment 1 1 1

Mathematical Problems in Engineering 7

regarded as fitness function +e average attribute de-pendency degree is 0973 the average length of reductionis 392 and the average optimal fitness value is minus 0973+e average recognition accuracy of the experiment is9692 +e premature phenomena are shown in Fig-ure 5 and evolution progress is terminated early

(2) 2nd Group Experiment ϖ1ω2ω3 1 1 0 +isexperiment introduces an objective function to control thelength of reduction (the shorter the length of reduction thebetter it is) the influence degree of the objective functionwhich controls the reduction on the fitness function and the

final recognition accuracy is verified +e algorithm is run 5times according to this group weights and the results of the 5groups are given in Table 5 including the reduction of theconditional attributes the length of reduction the optimalfitness value the attribute dependency and the time +econvergence of VPRS-GA under the variation for fitnessfunction value in one time is shown in Figure 6

Each reduction is classified by SVM classifier using themethod of 5-fold cross validation through changing thetraining samples and test samples the results of the fivegroups were obtained including accuracy sensitivityspecificity and time (training samples are constructed by

ndash06

ndash07

ndash08

ndash09

ndash10 50 100 150

Generation stopping criteria

Best ndash09695 Mean ndash0944425

Fitn

ess v

alue

Best fitnessMean fitness

Figure 5 +e variation of fitness function value in a running process for Experiment 1-first group

Table 4 +e statistical results of the first group for experiment 1 with the SVM classifier

Experiment times Accuracy () Sensitivity () Specificity () Time (s)

Reduction 1

1 9250 8600 9900 3326072 9725 9750 9700 3450513 9900 9900 9900 3586774 9800 9950 9650 3510755 9925 10000 9850 355948

Average value 9720 9640 9800 348672

Reduction 2

1 9325 8700 9950 4365332 9725 9800 9650 4459003 9875 9850 9900 4395064 9750 9900 9600 4450645 9925 10000 9850 448513

Average value 9720 9650 9790 443103

Reduction 3

1 9275 8750 9800 3269162 9575 9750 9400 3372093 9800 9800 9800 3407014 9700 9850 9550 3331745 9850 9950 9750 333257

Average value 9640 9620 9660 334251

Reduction 4

1 9375 8850 9900 3064852 9650 9750 9550 3192403 9750 9700 9800 3240824 9775 9900 9650 3254195 9900 10000 9800 361516

Average value 9690 9640 9740 318806

Reduction 5

1 9400 8900 9900 3195572 9650 9750 9550 3369093 9725 9700 9750 3301594 9775 9900 9650 3999805 9900 10000 9800 325692

Average value 9690 9650 9730 342459

8 Mathematical Problems in Engineering

800 malignant samples and 800 benign samples testingsamples are constructed by 200 malignant samples and 200benign samples the experiment is repeated 5 times bychanging training samples and testing samples) Finally theaverage values of these five groups are obtained as the finalresult of the reduction and shown in Table 6

+e experimental weight of this group is ϖ1

ω2ω3 1 1 0 attribute dependency degree and thelength of reduction are regarded as fitness function As canbe seen from Table 5 the reduction length is 13 17 and soon +e average length of reduction was 17 which wassignificantly reduced compared with the average length ofthe reduction in Table 3 in the experiment of the first groupswhich reduced the time improved the efficiency of the al-gorithm and increased the attribute dependency of thealgorithm even up to 1 +e average recognition accuracy ofthe experimental group was 9698 which was increased by006 compared with that in the first groups

(3) 3rd Group Experiment ϖ1ω2ω3 1 1 1 On thebasis of attribute dependency degree and attribute reductionlength this experiment introduces gene coding weightfunction in order to verify the effect of gene coding weightfunction on fitness function and the final recognition ac-curacy +e algorithm are run 5 times according to thisgroup weights the results of the 5 groups are given inTable 7 including the reduction of the conditional attributesthe length of reduction the optimal fitness value the at-tribute dependency and the time +e convergence ofVPRS-GA under the variation for fitness function value inone time is shown in Figure 7

Each reduction is classified by SVM classifier using themethod of 5-fold cross validation through changing thetraining samples and test samples the results of the fivegroups were obtained including accuracy sensitivityspecificity and time (training samples are constructed by800 malignant samples and 800 benign samples testingsamples are constructed by 200 malignant samples and 200benign samples the experiment is repeated 5 times bychanging training samples and testing samples) Finally theaverage values of these five groups are obtained as the finalresult of the reduction and shown in Table 8

+e experimental weight of this group is ϖ1 ω2ω3=1 1 1 attribute dependency degree the length of re-duction and gene coding weight value are regarded as fitnessfunction However the premature phenomena are shown inFigure 7 and evolution progress is terminated early FromTable 7 we can see that the attribute dependency decreasesgradually and even the attribute dependency of Reduction 1is reduced to 0759 +e average recognition accuracy of theexperimental group was 9685+e accuracy of recognitionwas decreased compared with the second groups and henceusing gene encoding weight function in the fitness functionto improve recognition accuracy is useless only for thesamples with different results to analyze specific issues +e3 experiment runs of experiment 1 verified the necessity ofthe fitness function by continuously introducing fitnessobjective function such as target1 target2 and target3 theconclusion is that the fitness function is better when it is notbigger but after the introduction of target3 the accuracydeclines therefore the introduction of target1 and target2 inthis algorithm can get better results

Table 5 Results of VPRS-GA running 5 times when 1 minus β 06 ω1 1ω2 1ω3 0

Experiment times C_ reduction Reductionlength

Optimalfitness value

Attributedependency

degreeTime (s)

1 5 9 14 20 26 41 43 46 48 54 55 57 64 66 74 79 86 90 18 minus 46487 09965 107240722 1 4 11 12 14 24 34 40 42 43 56 60 61 65 67 68 71 72 85 19 minus 40109 1 63281223 2 13 27 29 39 42 45 56 59 63 68 70 75 13 minus 46512 09990 110239674 1 3 4 7 9 11 12 15 30 34 38 42 46 48 55 62 65 77 79 19 minus 49674 1 87946705 3 9 11 13 29 39 41 42 43 46 50 55 65 c77 85 86 16 minus 44114 09815 15075539

Average value 17 minus 45379 09954 10389274

ndash1

ndash2

ndash3

ndash4

ndash5

Fitn

ess v

alue

Best ndash496739 Mean ndash492312

0 50 100 150Generation stopping criteria

Best fitnessMean fitness

Figure 6 +e variation of fitness function value in a running process for experiment 1-second group

Mathematical Problems in Engineering 9

342 Experiment 2mdashResearch on Different ClassificationError Rates under the Condition in the Same WeightCoefficient According to experiment 1 we can see thatwhen ω1 1 ω2 1 ω3 0 the experimental results arethe best so in experiment 2 the case of the weight value ofwas unchanged ω1 1 ω2 1 ω3 0 and the β value waschanged and they are shown in Table 9

(1) 1st Group Experiment 1 minus β 06 +e algorithm is run 5times according to this group weights the results of the 5groups are shown in Table 5 including the reduction of the

conditional attributes the length of reduction the optimalfitness value the attribute dependency and the time +econvergence of VPRS-GA under the variation for fitnessfunction value for one time is shown in Figure 6 (ie notrepeated in the second group of experiment 1)

(2) 2nd Group Experiment 1 minus β 08 +e algorithm are is 5times according to this group weights the results of the 5groups are given in Table 10 including the reduction of theconditional attributes the length of reduction the optimalfitness value the attribute dependency and the time +e

Table 6 +e statistical results of the second group for experiment 1 with the SVM classifier

Experiment times Accuracy () Sensitivity () Specificity () Time (s)

Reduction 1

1 9300 8600 10000 1164882 9625 9600 9650 1255113 9850 9900 9800 1315094 9725 9850 9600 1344685 9925 10000 9850 144839

Average value 9685 9590 9780 130563

Reduction 2

1 9425 8900 9950 1210962 9725 9700 9750 1286363 9800 9800 9800 1356774 9750 9800 9700 1381965 9875 9900 9850 136691

Average value 9715 9620 9810 132059

Reduction 3

1 9300 8750 9850 877572 9725 9750 9700 1034243 9775 9800 9750 1074114 9775 9850 9700 1123445 9900 10000 9800 113006

Average value 9695 9630 9760 104788

Reduction 4

1 9375 8750 10000 1464172 9650 9750 9550 1547363 9750 9700 9800 1576214 9800 9900 9700 1613555 9925 10000 9850 163381

Average value 9700 9620 9780 156702

Reduction 5

1 9250 8650 9850 1249332 9675 9800 9550 1400573 9800 9800 9800 1451944 9800 9900 9700 1457925 9950 9950 9950 150400

Average value 9695 9620 9770 141275

Table 7 Results of VPRS-GA running 5 times when 1 minus β 06 ω1 1ω2 1ω3 1

Experimenttimes C_ reduction Reduction

lengthOptimal

fitness valueAttribute

dependency degree Time (s)

1 4 5 7 26 27 34 35 41 47 54 55 71 74 75 78 80 83 90 18 minus 14192 07590 6888635

2 4 15 16 19 22 27 28 29 30 35 38 42 45 50 52 53 59 61 6264 65 70 71 72 77 87 88 27 minus 15232 08640 8124857

3 6 17 19 24 28 31 33 34 38 39 43 45 47 48 49 51 55 56 6667 69 70 71 72 76 77 78 80 81 84 87 89 91 92 34 minus 13545 07950 9521511

4 3 6 8 91617 19 20 24 25 28 35 37 39 41 42 46 49 51 52 5459 63 65 66 74 83 86 28 minus 14703 08365 8714839

5 1 7 8 15 17 19 20 23 29 37 45 48 54 60 62 70 73 75 77 7879 86 22 minus 14990 07995 7797617

Average value 258 minus 14532 08108 8209492

10 Mathematical Problems in Engineering

convergence of VPRS-GA under the variation for fitnessfunction value for one time is shown in Figure 8

Each reduction is classified by SVM classifier using themethod of 5-fold cross validation through changing thetraining samples and test samples the results of the five

groups were obtained including accuracy sensitivityspecificity and time (training samples are constructed by800 malignant samples and 800 benign samples testingsamples are constructed by 200 malignant samples and 200benign samples the experiment is repeated 5 times by

ndash08

ndash1

ndash12

ndash14

ndash16

Fitn

ess v

alue

Best ndash141919 Mean ndash128476

0 50 100 150Generation stopping criteria

Best fitnessMean fitness

Figure 7 +e variation of fitness function value in a running process for experiment 1-third group

Table 8 +e statistical results of the third group for experiment 1 with the SVM classifier

Experiment times Accuracy () Sensitivity () Specificity () Time (s)

Reduction 1

1 9275 8600 9950 924922 9725 9750 9700 1074613 9850 9850 9850 1138114 9775 9900 9650 1155605 9875 10000 9750 117022

Average value 9700 9620 9780 109269

Reduction 2

1 9350 8750 9950 1482452 9700 9650 9750 1615353 9775 9850 9700 1664524 9800 9850 9750 1754505 9875 9950 9800 172348

Average value 9700 9610 9790 164806

Reduction 3

1 9125 8300 9950 2019042 9650 9700 9600 2185353 9800 9800 9800 2196054 9625 9900 9350 2230915 9825 10000 9650 236896

Average value 9605 9540 9670 220006

Reduction 4

1 9300 8700 9900 1654542 9675 9600 9750 1724323 9875 9850 9900 1793014 9800 9900 9700 1895605 9900 9950 9850 185249

Average value 9710 9600 9820 178399

Reduction 5

1 9275 8600 9950 1411732 9725 9800 9650 1612953 9900 9950 9850 1589924 9775 9950 9600 1648765 9875 10000 9750 166070

Average value 9710 9660 9760 158481

Table 9 Fitness function weight proportion and β value

Experiment timesω1 1 ω2 1 ω3 0

1 minus β 06 1 minus β 08 1 minus β 1First group experiment Second group experiment +ird group experiment

Mathematical Problems in Engineering 11

changing training samples and testing samples) Finally theaverage values of these five groups are obtained as the finalresult of the reduction and shown in Table 11

In the case of constant weight ϖ and classification errorrate of β 02 (which contains 1 minus β 08) the classificationerror rate is changed on the basis of the attribute dependencyand the length of control reduction +e premature phe-nomena are shown in Figure 8 and evolution progress isterminated early such that the attribute dependency ofreduction 5 was 08405 appeared in attribute dependency onless than 09 compared with first groups of experiment 2attribute dependency declined +e average recognitionaccuracy of the experimental group was 9674 Comparedwith the classification error rate of 04 and inclusion degreeof 06 the accuracy was decreased by 024

(3) 3rd Group Experiment 1 minus β1 +e algorithm is run 5times according to the group weights and the results of the 5groups are shown in Table 12 including the reduction of theconditional attributes the length of reduction the optimalfitness value the attribute dependency and the time +econvergence of VPRS-GA under the variation for fitnessfunction value for one time is shown in Figure 9

Each reduction is classified by SVM classifier using themethod of 5-fold cross validation through changing thetraining samples and test samples the results of the fivegroups were obtained including accuracy sensitivityspecificity and time (training samples are constructed by800 malignant samples and 800 benign samples testingsamples are constructed by 200 malignant samples and 200

benign samples the experiment is repeated 5 times bychanging training samples and testing samples) Finally theaverage values of these five groups are obtained as the finalresult of the reduction and shown in Table 13

In the case of constant weight ϖ and classification errorrate of β= 0 (which contains 1 minus β= 1) the classificationerror rate is reduced and the inclusion degree is improved onthe basis of the attribute dependency and the length ofcontrol reduction +e premature phenomena are shown inFigure 9 and evolution progress is terminated early +eaverage recognition accuracy of the experimental group was9573 which was decreased by 006 compared with thatin the second group In experiment 2 the effect of changingthe classification error rate on the recognition accuracy wasverified by the 3 groups of experiments By continuallyreducing the classification error rate the final recognitionaccuracy has been declining when inclusion degree is 1β= 0 variable precision rough set becomes Pawlak rough setthe recognition accuracy of the recognition accuracy of isminimum which was verified the advantages of variableprecision rough set

343 Experiment 3mdashResearch on Increasing the WeightCoefficient under the Condition in the Same ClassificationError Rate According to experiment 1 and experiment 2we can know that when β 06 ω1 1 ω2 1 ω3 0 therecognition accuracy is the best therefore in the thirdexperiment by increasing the weight of ω 3 groups ofexperiments are performed fitness goals target 1 (attribute

Table 10 Results of VPRS-GA running 5 times when 1 minus β 08 ω1 1ω2 1ω3 0

Experimenttimes C_ reduction Reduction

lengthOptimal fitness

valueAttribute

dependency degree Time (s)

1 8 9 11 12 15 16 17 18 25 26 29 31 35 39 40 41 42 48 5865 67 68 70 83 84 91 26 minus 67816 09490 10002827

2 1 6 8 9 11 12 15 17 21 23 26 28 30 31 34 44 50 56 58 5962 63 64 68 71 75 77 82 89 92 30 minus 67797 09615 9477387

3 6 8 12 14 15 16 17 21 28 35 38 39 45 49 55 58 61 62 6465 77 82 85 23 minus 68694 09070 12866181

4 4 6 7 8 11 12 13 16 17 20 25 26 31 32 34 35 41 42 44 4950 55 58 68 72 74 76 78 79 85 89 92 32 minus 67225 09540 10510220

5 3 6 8 9 10 16 17 26 27 34 36 37 38 40 42 44 46 51 52 6266 67 84 86 87 25 minus 65892 08405 8469324

Average value 272 minus 67484 09224 10265188

ndash55

ndash6

ndash65

ndash7

Fitn

ess v

alue

Best ndash686942 Mean ndash653584

0 50 100 150Generation stopping criteria

Best fitnessMean fitness

Figure 8 +e variation of fitness function value in a running process for experiment 2-second group

12 Mathematical Problems in Engineering

Table 11 +e statistical results of the second group for experiment 2 with the SVM classifier

Experiment times Accuracy () Sensitivity () Specificity () Time (s)

Reduction 1

1 9300 8650 9950 2280072 9575 9700 9450 2376463 9700 9600 9800 2332504 9750 9850 9650 2444915 9925 10000 9850 244816

Average value 9650 9560 9740 237642

Reduction 2

1 9375 8800 9950 2524032 9625 9750 9500 2652893 9800 9700 9900 2655234 9800 9900 9700 2682125 9950 10000 9900 275880

Average value 9710 9630 9790 265461

Reduction 3

1 9275 8750 9800 1807802 9675 9750 9600 1929923 9700 9600 9800 1872434 9775 9950 9600 2084825 9875 10000 9750 203507

Average value 9660 9610 9710 194601

Reduction 4

1 9200 8650 9750 2572602 9700 9750 9650 2730243 9775 9650 9900 2723164 9750 9900 9600 2815545 9900 10000 9800 291471

Average value 9665 9590 9740 275125

Reduction 5

1 9275 8750 9800 1437152 9675 9600 9750 1526373 9750 9800 9700 1589294 9775 9900 9650 1629975 9950 10000 9900 166792

Average value 9685 9610 9760 157014

Table 12 Results of VPRS-GA running 5 times when 1 minus β 1 ω1 1ω2 1ω3 0

Experimenttimes C_ reduction Reduction

lengthOptimal fitness

valueAttribute dependency

degree Time (s)

1 15 44 68 73 79 84 6 minus 27313 07965 114499012 34 51 54 75 80 90 6 minus 27047 08460 96993913 2 34 49 70 71 72 76 81 8 minus 34057 07535 112334894 12 25 78 85 4 minus 22872 09285 11668133

5 6 7 12 13 42 44 55 57 65 66 69 77 81 8687 15 minus 33230 08665 13236077

Average value 78 minus 28903 08382 11457398

ndash1

ndash2

ndash3

ndash4

Fitn

ess v

alue

0 50 100 150Generation stopping criteria

Best fitnessMean fitness

Best ndash340567 Mean ndash330598

Figure 9 +e variation of fitness function value in a running process for experiment 2-third group

Mathematical Problems in Engineering 13

dependency) target 2 (the minimum number of attributesreduction) and target 3 (gene encoding weight function)the three objective functions play an important role in theevaluation of fitness function However the importance offitness function is reduced in these three objectives+erefore in this experiment when the other conditions areunchanged the weight coefficient of the target 1 is increasedto verify the influence of the change in the weight coefficienton the experimental results and they are shown in Table 14

(1) 1st Group Experiment ω1 1 ω2 1 ω3 0 +e al-gorithm are run 5 times according to this group weights theresults of the 5 groups are given in Table 5 including thereduction of the conditional attributes the length of reduc-tion the optimal fitness value the attribute dependency andthe time +e convergence of VPRS-GA under the variationfor fitness function value in one time is shown in Figure 6 (ienot repeated for the second group of experiment 1)

(2) 2nd Group Experiment ω1 2 ω2 1 ω3 0 +ealgorithm is run 5 times according to this group weights theresults of the 5 groups are given in Table 15 including thereduction of the conditional attributes the length of re-duction the optimal fitness value the attribute dependencyand the time +e convergence of VPRS-GA under thevariation for fitness function value in one time is shown inFigure 10

Each reduction is classified by SVM classifier using themethod of 5-fold cross validation through changing thetraining samples and test samples the results of the fivegroups were obtained including accuracy sensitivityspecificity and time (training samples are constructed by800 malignant samples and 800 benign samples testingsamples are constructed by 200 malignant samples and 200benign samples the experiment is repeated 5 times bychanging training samples and testing samples) Finally theaverage values of these five groups are obtained as the finalresult of the reduction and shown in Table 16

+e experimental group in the case of 1 minus β= 06 un-changed the weight of ω1 was increased +e attributedependency and the optimal fitness function are relativelyhigh the average precision of reduction 1 reduction 2 andreduction 3 in Table 16 is more than 97 and that of re-duction 2 is even up to 9725 +e average recognitionaccuracy of the experimental group is 9703 which ishigher than that of the first group

Table 13 +e statistical results of the third group for experiment 2 with the SVM classifier

Experiment times Accuracy () Sensitivity () Specificity () Time (s)

Reduction 1

1 9225 8450 10000 812712 9550 9700 9400 945833 9575 9400 9750 881984 9600 9800 9400 937545 9725 9900 9550 98691

Average value 9535 9450 9620 91299

Reduction 2

1 9200 8450 9950 648942 9625 9550 9700 801983 9525 9300 9750 773374 9600 9750 9450 760125 9800 10000 9600 82763

Average value 9550 9410 9690 76241

Reduction 3

1 9200 8450 9950 648942 9625 9550 9700 801983 9525 9300 9750 773374 9600 9750 9450 760125 9800 10000 9600 82763

Average value 9550 9410 9690 76241

Reduction 4

1 9275 8550 10000 672642 9675 9600 9750 784673 9600 9450 9750 730224 9575 9750 9400 794605 9800 10000 9600 84184

Average value 9585 9470 9700 76479

Reduction 5

1 9200 8450 9950 1147192 9625 9750 9500 1287053 9850 9900 9800 1320494 9775 9950 9600 1335135 9850 10000 9700 133144

Average value 9660 9610 9710 128426

Table 14 Fitness function weight proportion and β value

Experiment times1 minus β 06

ω1 ω2 ω3First group experiment 1 1 0Second group experiment 2 1 0+ird group experiment 3 1 0

14 Mathematical Problems in Engineering

ndash2

ndash25

ndash3

Fitn

ess v

alue

0 50 100 150Generation stopping criteria

Best fitnessMean fitness

Best ndash2915 Mean ndash291446

Figure 10 +e variation of fitness function value in a running process for experiment 3-second group

Table 15 Results of VPRS-GA running 5 times when 1 minus β 06 ω1 2ω2 1ω3 0

Experimenttimes C_ reduction Reduction

lengthOptimal fitness

valueAttribute dependency

degree Time (s)

1 2 3 4 5 11 13 16 18 24 30 34 37 39 41 42 51 55 64 7077 78 82 22 minus 34859 09060 21515464

2 8 9 11 12 14 15 23 25 26 29 30 33 37 42 43 45 46 5060 61 69 74 80 87 89 25 minus 30845 09390 42761634

3 8 11 12 13 16 18 19 24 29 36 37 43 64 65 68 71 86 9192 19 minus 35039 09150 26197164

4 2 3 4 8 10 11 12 13 15 16 19 23 25 30 48 55 64 65 6874 77 80 81 83 84 86 89 27 minus 29150 09575 44271631

5 5 8 911 121517 23 25 29 31 36 39 41 48 54 59 63 8083 86 89 22 minus 29920 09525 43161464

Average value 23 minus 31962 09340 35581471

Table 16 +e statistical results of the second group for experiment 3 with the SVM classifier

Experiment times Accuracy () Sensitivity () Specificity () Time (s)

Reduction 1

1 9275 8600 9950 1884972 9725 9800 9650 1571623 9850 9900 9800 1586914 9800 9900 9700 1646035 9950 10000 9900 161914

Average value 9720 9640 9800 166173

Reduction 2

1 9450 8950 9950 1908132 9675 9800 9550 2002513 9775 9800 9750 1970084 9850 9900 9800 2009245 9875 9900 9850 209245

Average value 9725 9670 9780 199648

Reduction 3

1 9400 8800 10000 1313692 9725 9800 9650 1447973 9800 9800 9800 1426624 9725 9850 9600 1471905 9925 10000 9850 148799

Average value 9715 9650 9780 142963

Reduction 4

1 9350 8750 9950 2404562 9700 9750 9650 2520823 9800 9800 9800 2511754 9775 9950 9600 2701885 9825 10000 9650 267471

Average value 9690 9650 9730 256274

Reduction 5

1 9325 8800 9850 1809592 9600 9800 9400 1965633 9750 9750 9750 1967234 9800 9900 9700 2078295 9850 9950 9750 219703

Average value 9665 9640 9690 200355

Mathematical Problems in Engineering 15

Table 17 Results of VPRS-GA running 5 times when 1 minus β 1 ω1 1ω2 1ω3 0

Experimenttimes C_ reduction Reduction

lengthOptimal fitness

valueAttribute

dependency degree Time (s)

1 3 4 5 8 9 11 12 17 19 29 34 35 38 46 52 53 55 59 63 6672 75 77 78 79 87 92 27 minus 38867 09550 28981789

2 4 8 9 11 12 15 17 29 33 37 38 39 42 43 48 55 67 73 7881 83 84 88 89 90 25 minus 38167 09715 55783772

3 2 3 4 8 9 10 11 12 13 15 16 19 24 25 30 36 49 54 55 6064 67 68 70 74 77 83 85 86 91 30 minus 38807 09530 34831096

4 4 5 7 11 12 14 15 17 25 29 33 36 39 41 42 47 48 50 5556 58 62 67 69 72 74 77 84 86 90 91 31 minus 39430 09665 35742822

5 3 4 5 8 9 11 12 17 19 29 34 35 38 46 52 53 55 59 63 6672 75 77 78 79 87 92 27 minus 38867 09550 27919582

Average value 28 minus 38827 09602 36651812

ndash3

ndash35

ndash40 50 100 150

Generation stopping criteria

Fitn

ess v

alue

Best fitnessMean fitness

Best ndash394298 Mean ndash393327

Figure 11 +e variation of fitness function value in a running process for experiment 3-third group

Table 18 +e statistical results of the Second group for experiment 3 with the SVM classifier

Experiment times Accuracy () Sensitivity () Specificity () Time (s)

Reduction 1

1 9200 8700 9700 2187172 9750 9750 9750 2105503 9850 9850 9850 2032064 9800 9900 9700 2211645 9925 10000 9850 272536

Average value 9705 9640 9770 225235

Reduction 2

1 9400 8850 9950 2331232 9575 9750 9400 2433493 9750 9700 9800 2442024 9775 9900 9650 2566075 9900 9950 9850 259071

Average value 9680 9630 9730 247270

Reduction 3

1 9275 8650 9900 2525842 9625 9750 9500 2624123 9775 9800 9750 2601274 9775 9900 9650 2686705 9875 10000 9750 265387

Average value 9665 9620 9710 261836

Reduction 4

1 9150 8550 9750 2532312 9625 9750 9500 2649433 9750 9700 9800 2752834 9800 9950 9650 3229545 9825 9950 9700 277432

Average value 9630 9580 9680 278769

Reduction 5

1 9200 8800 9600 1951962 9700 9700 9700 2148893 9825 9800 9850 2036124 9850 10000 9700 2133615 9900 9900 9900 225526

Average value 9695 9640 9750 210517

16 Mathematical Problems in Engineering

(3) 3rd Group Experiment ω1 3 ω2 1 ω3 0 +e al-gorithm is run 5 times according to the group weights andthe results of the 5 groups are given in Table 17 including thereduction of the conditional attributes the length of re-duction the optimal fitness value the attribute dependencyand the time +e convergence of VPRS-GA under thevariation for fitness function value for one time is shown inFigure 11

Each reduction is classified by SVM classifier using themethod of 5-fold cross validation through changing thetraining samples and test samples the results of the fivegroups were obtained including accuracy sensitivityspecificity and time (training samples are constructed by800 malignant samples and 800 benign samples testingsamples are constructed by 200 malignant samples and 200benign samples the experiment is repeated 5 times bychanging training samples and testing samples) Finally theaverage values of these five groups are obtained as the finalresult of the reduction and shown in Table 18

+e experiment in the case of 1 minus β 06 unchangedincrease the weight of the ω1 ω1 3 ω2 1 ω3 0 InTable 18 the recognition accuracy of reduction 1 is over 97only +e average recognition accuracy of the experimentalgroup is 9675 and the accuracy is decreased by 028compared with that in the other second groups +e threegroups of experiment 3 the purpose is to verify whether theexperimental accuracy is influenced by increasing theweight +e experimental results show that the accuracy ofsecond group for experimental weight 2 1 0 comparedwith first group experiment when 1 1 0 is high but thethird groups of experimental weight was 3 1 0 and theaccuracy declined therefore the weight of 2 1 0 is the bestchoice for this experiment

4 Conclusions

Aiming at the deficiency of the traditional rough set modelthis paper proposes a new feature selection model based ongenetic algorithm and variable precision rough set by in-troducing the β value the rigid inclusion of the approxi-mation for the traditional rough set is relaxed and then wedesign the 3 kinds of experiments by constructing the de-cision information table of the PETCT feature for lungtumor ROI +e first type of experiment is the inclusion of1 minus β 06 and different values of ω made a total of threegroups of experiments the experimental results show thatthe better recognition accuracy can be obtained when theweight is 1 1 0 and the results show that the gene codingweight function has no effect on the fitness function For thesecond type of experiments ϖ1 1ω2 1 ω3 0according to the different values of β to do three groups ofexperiments the results show that the recognition accuracyof 1 minus β 06 is the best which shows that the larger the βvalue is the lower approximate cardinality will be largerthen the relative accuracy will increase For the third type ofexperiments 1 minus β 06 ω value is increased to achieve thebest fitness function in order to achieve the best results +eexperimental results show that the recognition accuracy isbetter than the others when the weight value is 2 1 0 so it

is better to solve the problem by increasing the proportion ofattribute dependency +rough the above experiments it isshown that the high-dimensional feature selection algorithmbased on genetic algorithm and variable precision rough setcan solve the multiobjective optimization problem wellHowever when the fitness function and its parameters areapplied in the specific application it is necessary to analyzethe specific problems

Data Availability

+e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

+e authors declare no conflicts of interest

Acknowledgments

+is work was supported by National Natural ScienceFoundation of China (Grant nos 61561040 and 61876121)First-Class Disciplines Foundation of Ningxia (NoNXYLXK2017B09)

References

[1] S Luo D Miao Z Zhang Y Zhang and S Hu ldquoA neigh-borhood rough set model with nominal metric embeddingrdquoInformation Sciences vol 520 pp 373ndash388 2020

[2] B Barman and S Patra ldquoVariable precision rough set basedunsupervised band selection technique for hyperspectralimage classificationrdquo Knowledge-Based Systems vol 1936Article ID 105414 2020

[3] Y Chenyi and L Jinjin ldquoApproximate attribute reductionunder variable precision rough set βrdquo Journal of ShandongUniversity vol 11 pp 17ndash21 2011

[4] S Xiaowei Research on Hierarchical Model of Attribute Re-duction in Variable Precision Rough Set Central SouthUniversity Changsha China 2013

[5] Z Jie and W Jiayang ldquoAnalysis of reduction feature ofvariable precision rough set modelrdquo Computer ApplicationResearch vol 7 pp 12ndash15 2007

[6] Z Pei and Z Qinghua ldquoFCM clustering algorithm based onvariable precision rough setrdquo Journal of Shanxi Universityvol 3 pp 342ndash348 2016

[7] C Hao and Y Junan ldquoAttribute kernel and minimum at-tribute reduction algorithm of variable precision rough setrdquoActa Sinica Sinica vol 5 pp 1011ndash1017 2012

[8] S Xu X Yang H Yu D-J Yu J Yang and E CC TsangldquoMulti-label learning with label-specific feature reductionrdquoKnowledge-Based Systems vol 104 pp 52ndash61 2016

[9] I Maryam and G Hassan ldquoFeature space discriminantanalysis for hyperspectral data feature reductionrdquo ISPRSJournal of Photogrammetry and Remote Sensing vol 102pp 1ndash13 2015

[10] S Q Wang C Y Gao C Luo G M Zheng and Y N ZhouldquoResearch on feature selectionattribute reduction methodbased on rough set theoryrdquo Procedia Computer Sciencevol 154 pp 194ndash198e 2019

[11] A W Omar M Azzam O Hadi and B Jamal ldquoCEAP SVM-based intelligent detection model for clustered vehicular ad

Mathematical Problems in Engineering 17

hoc networksrdquo Expert Systems with Applications vol 50pp 40ndash54 2016

[12] H Lee and Y-P P Chen ldquoImage based computer aideddiagnosis system for cancer detectionrdquo Expert Systems withApplications vol 42 no 12 pp 5356ndash5365 2015

[13] J A Guy and P L Harold ldquoAfter detection the improvedaccuracy of lung cancer assessment using radiologic com-puter-aided diagnosisrdquo Academic Radiology vol 23 no 2pp 186ndash191 2016

[14] E Kiyonori T Shodayu J Binghu et al ldquoPleural invasion byperipheral lung cancer prediction with three-dimensionalCTrdquo Academic Radiology vol 3 pp 310ndash319 2015

[15] B Koohestani ldquoA crossover operator for improving the ef-ficiency of permutation-based genetic algorithmsrdquo ExpertSystems with Applications vol 1511 Article ID 113381 2020

[16] N K Lee X Li and D Wang ldquoA comprehensive survey ongenetic algorithms for DNA motif predictionrdquo InformationSciences vol 466 pp 25ndash43 2018

[17] S Shibao and Y Leilei ldquoResearch on variable precision roughset model and its applicationrdquo Computer Engineering andApplication vol 07 pp 10ndash13 2009

[18] T Xiaolong Several Problems of Multi Granularity VariablePrecision Rough Set Guangxi University For NationalitiesNanning China 2015

[19] W Xueming Research on Several Rough Set Models andNeural Network University of Electronic Science and Tech-nology of China Chengdu China 2013

[20] T Sun J Wang X Li et al ldquoComparative evaluation ofsupport vector machines for computer aided diagnosis of lungcancer in CT based on a multi-dimensional data setrdquo Com-puter Methods and Programs in Biomedicine vol 111 no 2pp 519ndash524 2013

[21] Z Yang T Ouyang X Fu and X Peng ldquoA decision-makingalgorithm for online shopping using deep-learning-basedopinion pairs mining and q -rung orthopair fuzzy interactionHeronianmean operatorsrdquo International Journal of IntelligentSystems vol 35 no 5 pp 783ndash825 2020

[22] W Chen C Lin C Li et al ldquoTracing the evolution of 3Dprinting technology in China using LDA-based patent ab-stract miningrdquo IEEE Transactions on Engineering Manage-men vol 36 pp 1ndash11 2020

18 Mathematical Problems in Engineering

Table 1 ROI feature values of lung tumor PETCT image

Types of disease Shapefeature

Grayfeature

Tamuratexture

Texture features of GLCM Texture feature of wavelet

0 degree 45degrees

90degrees

135degrees Norm Standard

deviation Energy

Lung malignanttumor

60000 1222810 147000 00808 00779 00790 00611 6492580 371752 1000000012 14911500 309650 28937 29067 28989 31284 269473 38486 0001700000 386154 02326 02576 02820 02653 04490 93520 13355 0000200000 minus 05056 01668 01676 01659 01649 168200 24025 0000700000 24166 00792 00759 00772 00566 271143 38693 0001700000 140453 02576 02820 02653 04490 203163 29020 0001000000 70524 164110 164469 163584 164431 131755 18818 0000400000 27089 27072 27100 28066 183441 26199 00008

05755 06007 05810 073452109390 2117900 2095780 208825003064 03351 03135 03950

minus 06779 minus 06708 minus 06775 minus 0569600000 00000 00000 0000007625 07802 07658 08001

Lung benigntumor

40000 503912 101616 08087 07915 08077 07864 3799170 26741 1000000033 60006 18835 04324 04732 04370 04840 57551 08211 0000200000 24496 26329 00433 00621 00469 00679 11745 01677 0000000000 05649 94899 78127 92429 92429 34684 04955 0000100000 28589 08082 07905 08072 07853 20823 02972 0000000000 3283 00433 00621 00469 00679 21821 03117 0000000000 32559 78367 78363 78396 78363 08937 01276 0000000000 04024 04301 04045 04370 22387 03197 00000

01782 02326 01894 02481555257 550899 555291 54983100596 00873 00650 00958

minus 04707 minus 03295 minus 04351 minus 0291100000 00000 00000 0000020429 21172 20651 21394

Table 3 Results of VPRS-GA running 5 times when 1-β 06 ω1 1ω2 0ω3 0

Experimenttimes C_ reduction Reduction

lengthOptimal

fitness valueAttribute

dependency degree Time (s)

1 4 5 8 9 11 12 13 17 20 22 23 24 27 30 32 33 35 38 42 48 4952 57 59 61 62 63 64 65 68 70 72 73 75 77 78 80 87 88 91 92 41 minus 09705 09705 9719144

21 2 3 4 5 8 11 12 13 14 16 17 19 23 24 25 26 27 28 30 32 3638 39 40 42 43 44 46 47 52 53 55 61 63 66 67 69 71 72 73 77

79 80 82 84 85 87 9249 minus 09685 09685 10076907

3 4 611 12 1517 18 24 25 26 28 29 31 36 38 39 42 43 45 47 4953 56 65 68 69 72 76 77 79 80 81 83 85 88 91 92 37 minus 09695 09695 10432000

4 4 8 9 11 12 13 14 15 17 23 29 34 35 39 40 43 47 48 50 53 5556 60 61 64 68 70 75 80 81 82 83 84 86 34 minus 09790 09790 9473111

5 3 4 6 81011 12 13151719 20 21 24 26 29 31 39 42 44 45 4850 53 54 56 59 64 68 77 83 84 87 89 92 35 minus 09775 09775 9645092

Average value 392 minus 09730 09730 9869251

Table 2 Fitness function weight proportion and β value

Experiment times1 minus β 06

ω1 ω2 ω3First group experiment 1 0 0Second group experiment 1 1 0+ird group experiment 1 1 1

Mathematical Problems in Engineering 7

regarded as fitness function +e average attribute de-pendency degree is 0973 the average length of reductionis 392 and the average optimal fitness value is minus 0973+e average recognition accuracy of the experiment is9692 +e premature phenomena are shown in Fig-ure 5 and evolution progress is terminated early

(2) 2nd Group Experiment ϖ1ω2ω3 1 1 0 +isexperiment introduces an objective function to control thelength of reduction (the shorter the length of reduction thebetter it is) the influence degree of the objective functionwhich controls the reduction on the fitness function and the

final recognition accuracy is verified +e algorithm is run 5times according to this group weights and the results of the 5groups are given in Table 5 including the reduction of theconditional attributes the length of reduction the optimalfitness value the attribute dependency and the time +econvergence of VPRS-GA under the variation for fitnessfunction value in one time is shown in Figure 6

Each reduction is classified by SVM classifier using themethod of 5-fold cross validation through changing thetraining samples and test samples the results of the fivegroups were obtained including accuracy sensitivityspecificity and time (training samples are constructed by

ndash06

ndash07

ndash08

ndash09

ndash10 50 100 150

Generation stopping criteria

Best ndash09695 Mean ndash0944425

Fitn

ess v

alue

Best fitnessMean fitness

Figure 5 +e variation of fitness function value in a running process for Experiment 1-first group

Table 4 +e statistical results of the first group for experiment 1 with the SVM classifier

Experiment times Accuracy () Sensitivity () Specificity () Time (s)

Reduction 1

1 9250 8600 9900 3326072 9725 9750 9700 3450513 9900 9900 9900 3586774 9800 9950 9650 3510755 9925 10000 9850 355948

Average value 9720 9640 9800 348672

Reduction 2

1 9325 8700 9950 4365332 9725 9800 9650 4459003 9875 9850 9900 4395064 9750 9900 9600 4450645 9925 10000 9850 448513

Average value 9720 9650 9790 443103

Reduction 3

1 9275 8750 9800 3269162 9575 9750 9400 3372093 9800 9800 9800 3407014 9700 9850 9550 3331745 9850 9950 9750 333257

Average value 9640 9620 9660 334251

Reduction 4

1 9375 8850 9900 3064852 9650 9750 9550 3192403 9750 9700 9800 3240824 9775 9900 9650 3254195 9900 10000 9800 361516

Average value 9690 9640 9740 318806

Reduction 5

1 9400 8900 9900 3195572 9650 9750 9550 3369093 9725 9700 9750 3301594 9775 9900 9650 3999805 9900 10000 9800 325692

Average value 9690 9650 9730 342459

8 Mathematical Problems in Engineering

800 malignant samples and 800 benign samples testingsamples are constructed by 200 malignant samples and 200benign samples the experiment is repeated 5 times bychanging training samples and testing samples) Finally theaverage values of these five groups are obtained as the finalresult of the reduction and shown in Table 6

+e experimental weight of this group is ϖ1

ω2ω3 1 1 0 attribute dependency degree and thelength of reduction are regarded as fitness function As canbe seen from Table 5 the reduction length is 13 17 and soon +e average length of reduction was 17 which wassignificantly reduced compared with the average length ofthe reduction in Table 3 in the experiment of the first groupswhich reduced the time improved the efficiency of the al-gorithm and increased the attribute dependency of thealgorithm even up to 1 +e average recognition accuracy ofthe experimental group was 9698 which was increased by006 compared with that in the first groups

(3) 3rd Group Experiment ϖ1ω2ω3 1 1 1 On thebasis of attribute dependency degree and attribute reductionlength this experiment introduces gene coding weightfunction in order to verify the effect of gene coding weightfunction on fitness function and the final recognition ac-curacy +e algorithm are run 5 times according to thisgroup weights the results of the 5 groups are given inTable 7 including the reduction of the conditional attributesthe length of reduction the optimal fitness value the at-tribute dependency and the time +e convergence ofVPRS-GA under the variation for fitness function value inone time is shown in Figure 7

Each reduction is classified by SVM classifier using themethod of 5-fold cross validation through changing thetraining samples and test samples the results of the fivegroups were obtained including accuracy sensitivityspecificity and time (training samples are constructed by800 malignant samples and 800 benign samples testingsamples are constructed by 200 malignant samples and 200benign samples the experiment is repeated 5 times bychanging training samples and testing samples) Finally theaverage values of these five groups are obtained as the finalresult of the reduction and shown in Table 8

+e experimental weight of this group is ϖ1 ω2ω3=1 1 1 attribute dependency degree the length of re-duction and gene coding weight value are regarded as fitnessfunction However the premature phenomena are shown inFigure 7 and evolution progress is terminated early FromTable 7 we can see that the attribute dependency decreasesgradually and even the attribute dependency of Reduction 1is reduced to 0759 +e average recognition accuracy of theexperimental group was 9685+e accuracy of recognitionwas decreased compared with the second groups and henceusing gene encoding weight function in the fitness functionto improve recognition accuracy is useless only for thesamples with different results to analyze specific issues +e3 experiment runs of experiment 1 verified the necessity ofthe fitness function by continuously introducing fitnessobjective function such as target1 target2 and target3 theconclusion is that the fitness function is better when it is notbigger but after the introduction of target3 the accuracydeclines therefore the introduction of target1 and target2 inthis algorithm can get better results

Table 5 Results of VPRS-GA running 5 times when 1 minus β 06 ω1 1ω2 1ω3 0

Experiment times C_ reduction Reductionlength

Optimalfitness value

Attributedependency

degreeTime (s)

1 5 9 14 20 26 41 43 46 48 54 55 57 64 66 74 79 86 90 18 minus 46487 09965 107240722 1 4 11 12 14 24 34 40 42 43 56 60 61 65 67 68 71 72 85 19 minus 40109 1 63281223 2 13 27 29 39 42 45 56 59 63 68 70 75 13 minus 46512 09990 110239674 1 3 4 7 9 11 12 15 30 34 38 42 46 48 55 62 65 77 79 19 minus 49674 1 87946705 3 9 11 13 29 39 41 42 43 46 50 55 65 c77 85 86 16 minus 44114 09815 15075539

Average value 17 minus 45379 09954 10389274

ndash1

ndash2

ndash3

ndash4

ndash5

Fitn

ess v

alue

Best ndash496739 Mean ndash492312

0 50 100 150Generation stopping criteria

Best fitnessMean fitness

Figure 6 +e variation of fitness function value in a running process for experiment 1-second group

Mathematical Problems in Engineering 9

342 Experiment 2mdashResearch on Different ClassificationError Rates under the Condition in the Same WeightCoefficient According to experiment 1 we can see thatwhen ω1 1 ω2 1 ω3 0 the experimental results arethe best so in experiment 2 the case of the weight value ofwas unchanged ω1 1 ω2 1 ω3 0 and the β value waschanged and they are shown in Table 9

(1) 1st Group Experiment 1 minus β 06 +e algorithm is run 5times according to this group weights the results of the 5groups are shown in Table 5 including the reduction of the

conditional attributes the length of reduction the optimalfitness value the attribute dependency and the time +econvergence of VPRS-GA under the variation for fitnessfunction value for one time is shown in Figure 6 (ie notrepeated in the second group of experiment 1)

(2) 2nd Group Experiment 1 minus β 08 +e algorithm are is 5times according to this group weights the results of the 5groups are given in Table 10 including the reduction of theconditional attributes the length of reduction the optimalfitness value the attribute dependency and the time +e

Table 6 +e statistical results of the second group for experiment 1 with the SVM classifier

Experiment times Accuracy () Sensitivity () Specificity () Time (s)

Reduction 1

1 9300 8600 10000 1164882 9625 9600 9650 1255113 9850 9900 9800 1315094 9725 9850 9600 1344685 9925 10000 9850 144839

Average value 9685 9590 9780 130563

Reduction 2

1 9425 8900 9950 1210962 9725 9700 9750 1286363 9800 9800 9800 1356774 9750 9800 9700 1381965 9875 9900 9850 136691

Average value 9715 9620 9810 132059

Reduction 3

1 9300 8750 9850 877572 9725 9750 9700 1034243 9775 9800 9750 1074114 9775 9850 9700 1123445 9900 10000 9800 113006

Average value 9695 9630 9760 104788

Reduction 4

1 9375 8750 10000 1464172 9650 9750 9550 1547363 9750 9700 9800 1576214 9800 9900 9700 1613555 9925 10000 9850 163381

Average value 9700 9620 9780 156702

Reduction 5

1 9250 8650 9850 1249332 9675 9800 9550 1400573 9800 9800 9800 1451944 9800 9900 9700 1457925 9950 9950 9950 150400

Average value 9695 9620 9770 141275

Table 7 Results of VPRS-GA running 5 times when 1 minus β 06 ω1 1ω2 1ω3 1

Experimenttimes C_ reduction Reduction

lengthOptimal

fitness valueAttribute

dependency degree Time (s)

1 4 5 7 26 27 34 35 41 47 54 55 71 74 75 78 80 83 90 18 minus 14192 07590 6888635

2 4 15 16 19 22 27 28 29 30 35 38 42 45 50 52 53 59 61 6264 65 70 71 72 77 87 88 27 minus 15232 08640 8124857

3 6 17 19 24 28 31 33 34 38 39 43 45 47 48 49 51 55 56 6667 69 70 71 72 76 77 78 80 81 84 87 89 91 92 34 minus 13545 07950 9521511

4 3 6 8 91617 19 20 24 25 28 35 37 39 41 42 46 49 51 52 5459 63 65 66 74 83 86 28 minus 14703 08365 8714839

5 1 7 8 15 17 19 20 23 29 37 45 48 54 60 62 70 73 75 77 7879 86 22 minus 14990 07995 7797617

Average value 258 minus 14532 08108 8209492

10 Mathematical Problems in Engineering

convergence of VPRS-GA under the variation for fitnessfunction value for one time is shown in Figure 8

Each reduction is classified by SVM classifier using themethod of 5-fold cross validation through changing thetraining samples and test samples the results of the five

groups were obtained including accuracy sensitivityspecificity and time (training samples are constructed by800 malignant samples and 800 benign samples testingsamples are constructed by 200 malignant samples and 200benign samples the experiment is repeated 5 times by

ndash08

ndash1

ndash12

ndash14

ndash16

Fitn

ess v

alue

Best ndash141919 Mean ndash128476

0 50 100 150Generation stopping criteria

Best fitnessMean fitness

Figure 7 +e variation of fitness function value in a running process for experiment 1-third group

Table 8 +e statistical results of the third group for experiment 1 with the SVM classifier

Experiment times Accuracy () Sensitivity () Specificity () Time (s)

Reduction 1

1 9275 8600 9950 924922 9725 9750 9700 1074613 9850 9850 9850 1138114 9775 9900 9650 1155605 9875 10000 9750 117022

Average value 9700 9620 9780 109269

Reduction 2

1 9350 8750 9950 1482452 9700 9650 9750 1615353 9775 9850 9700 1664524 9800 9850 9750 1754505 9875 9950 9800 172348

Average value 9700 9610 9790 164806

Reduction 3

1 9125 8300 9950 2019042 9650 9700 9600 2185353 9800 9800 9800 2196054 9625 9900 9350 2230915 9825 10000 9650 236896

Average value 9605 9540 9670 220006

Reduction 4

1 9300 8700 9900 1654542 9675 9600 9750 1724323 9875 9850 9900 1793014 9800 9900 9700 1895605 9900 9950 9850 185249

Average value 9710 9600 9820 178399

Reduction 5

1 9275 8600 9950 1411732 9725 9800 9650 1612953 9900 9950 9850 1589924 9775 9950 9600 1648765 9875 10000 9750 166070

Average value 9710 9660 9760 158481

Table 9 Fitness function weight proportion and β value

Experiment timesω1 1 ω2 1 ω3 0

1 minus β 06 1 minus β 08 1 minus β 1First group experiment Second group experiment +ird group experiment

Mathematical Problems in Engineering 11

changing training samples and testing samples) Finally theaverage values of these five groups are obtained as the finalresult of the reduction and shown in Table 11

In the case of constant weight ϖ and classification errorrate of β 02 (which contains 1 minus β 08) the classificationerror rate is changed on the basis of the attribute dependencyand the length of control reduction +e premature phe-nomena are shown in Figure 8 and evolution progress isterminated early such that the attribute dependency ofreduction 5 was 08405 appeared in attribute dependency onless than 09 compared with first groups of experiment 2attribute dependency declined +e average recognitionaccuracy of the experimental group was 9674 Comparedwith the classification error rate of 04 and inclusion degreeof 06 the accuracy was decreased by 024

(3) 3rd Group Experiment 1 minus β1 +e algorithm is run 5times according to the group weights and the results of the 5groups are shown in Table 12 including the reduction of theconditional attributes the length of reduction the optimalfitness value the attribute dependency and the time +econvergence of VPRS-GA under the variation for fitnessfunction value for one time is shown in Figure 9

Each reduction is classified by SVM classifier using themethod of 5-fold cross validation through changing thetraining samples and test samples the results of the fivegroups were obtained including accuracy sensitivityspecificity and time (training samples are constructed by800 malignant samples and 800 benign samples testingsamples are constructed by 200 malignant samples and 200

benign samples the experiment is repeated 5 times bychanging training samples and testing samples) Finally theaverage values of these five groups are obtained as the finalresult of the reduction and shown in Table 13

In the case of constant weight ϖ and classification errorrate of β= 0 (which contains 1 minus β= 1) the classificationerror rate is reduced and the inclusion degree is improved onthe basis of the attribute dependency and the length ofcontrol reduction +e premature phenomena are shown inFigure 9 and evolution progress is terminated early +eaverage recognition accuracy of the experimental group was9573 which was decreased by 006 compared with thatin the second group In experiment 2 the effect of changingthe classification error rate on the recognition accuracy wasverified by the 3 groups of experiments By continuallyreducing the classification error rate the final recognitionaccuracy has been declining when inclusion degree is 1β= 0 variable precision rough set becomes Pawlak rough setthe recognition accuracy of the recognition accuracy of isminimum which was verified the advantages of variableprecision rough set

343 Experiment 3mdashResearch on Increasing the WeightCoefficient under the Condition in the Same ClassificationError Rate According to experiment 1 and experiment 2we can know that when β 06 ω1 1 ω2 1 ω3 0 therecognition accuracy is the best therefore in the thirdexperiment by increasing the weight of ω 3 groups ofexperiments are performed fitness goals target 1 (attribute

Table 10 Results of VPRS-GA running 5 times when 1 minus β 08 ω1 1ω2 1ω3 0

Experimenttimes C_ reduction Reduction

lengthOptimal fitness

valueAttribute

dependency degree Time (s)

1 8 9 11 12 15 16 17 18 25 26 29 31 35 39 40 41 42 48 5865 67 68 70 83 84 91 26 minus 67816 09490 10002827

2 1 6 8 9 11 12 15 17 21 23 26 28 30 31 34 44 50 56 58 5962 63 64 68 71 75 77 82 89 92 30 minus 67797 09615 9477387

3 6 8 12 14 15 16 17 21 28 35 38 39 45 49 55 58 61 62 6465 77 82 85 23 minus 68694 09070 12866181

4 4 6 7 8 11 12 13 16 17 20 25 26 31 32 34 35 41 42 44 4950 55 58 68 72 74 76 78 79 85 89 92 32 minus 67225 09540 10510220

5 3 6 8 9 10 16 17 26 27 34 36 37 38 40 42 44 46 51 52 6266 67 84 86 87 25 minus 65892 08405 8469324

Average value 272 minus 67484 09224 10265188

ndash55

ndash6

ndash65

ndash7

Fitn

ess v

alue

Best ndash686942 Mean ndash653584

0 50 100 150Generation stopping criteria

Best fitnessMean fitness

Figure 8 +e variation of fitness function value in a running process for experiment 2-second group

12 Mathematical Problems in Engineering

Table 11 +e statistical results of the second group for experiment 2 with the SVM classifier

Experiment times Accuracy () Sensitivity () Specificity () Time (s)

Reduction 1

1 9300 8650 9950 2280072 9575 9700 9450 2376463 9700 9600 9800 2332504 9750 9850 9650 2444915 9925 10000 9850 244816

Average value 9650 9560 9740 237642

Reduction 2

1 9375 8800 9950 2524032 9625 9750 9500 2652893 9800 9700 9900 2655234 9800 9900 9700 2682125 9950 10000 9900 275880

Average value 9710 9630 9790 265461

Reduction 3

1 9275 8750 9800 1807802 9675 9750 9600 1929923 9700 9600 9800 1872434 9775 9950 9600 2084825 9875 10000 9750 203507

Average value 9660 9610 9710 194601

Reduction 4

1 9200 8650 9750 2572602 9700 9750 9650 2730243 9775 9650 9900 2723164 9750 9900 9600 2815545 9900 10000 9800 291471

Average value 9665 9590 9740 275125

Reduction 5

1 9275 8750 9800 1437152 9675 9600 9750 1526373 9750 9800 9700 1589294 9775 9900 9650 1629975 9950 10000 9900 166792

Average value 9685 9610 9760 157014

Table 12 Results of VPRS-GA running 5 times when 1 minus β 1 ω1 1ω2 1ω3 0

Experimenttimes C_ reduction Reduction

lengthOptimal fitness

valueAttribute dependency

degree Time (s)

1 15 44 68 73 79 84 6 minus 27313 07965 114499012 34 51 54 75 80 90 6 minus 27047 08460 96993913 2 34 49 70 71 72 76 81 8 minus 34057 07535 112334894 12 25 78 85 4 minus 22872 09285 11668133

5 6 7 12 13 42 44 55 57 65 66 69 77 81 8687 15 minus 33230 08665 13236077

Average value 78 minus 28903 08382 11457398

ndash1

ndash2

ndash3

ndash4

Fitn

ess v

alue

0 50 100 150Generation stopping criteria

Best fitnessMean fitness

Best ndash340567 Mean ndash330598

Figure 9 +e variation of fitness function value in a running process for experiment 2-third group

Mathematical Problems in Engineering 13

dependency) target 2 (the minimum number of attributesreduction) and target 3 (gene encoding weight function)the three objective functions play an important role in theevaluation of fitness function However the importance offitness function is reduced in these three objectives+erefore in this experiment when the other conditions areunchanged the weight coefficient of the target 1 is increasedto verify the influence of the change in the weight coefficienton the experimental results and they are shown in Table 14

(1) 1st Group Experiment ω1 1 ω2 1 ω3 0 +e al-gorithm are run 5 times according to this group weights theresults of the 5 groups are given in Table 5 including thereduction of the conditional attributes the length of reduc-tion the optimal fitness value the attribute dependency andthe time +e convergence of VPRS-GA under the variationfor fitness function value in one time is shown in Figure 6 (ienot repeated for the second group of experiment 1)

(2) 2nd Group Experiment ω1 2 ω2 1 ω3 0 +ealgorithm is run 5 times according to this group weights theresults of the 5 groups are given in Table 15 including thereduction of the conditional attributes the length of re-duction the optimal fitness value the attribute dependencyand the time +e convergence of VPRS-GA under thevariation for fitness function value in one time is shown inFigure 10

Each reduction is classified by SVM classifier using themethod of 5-fold cross validation through changing thetraining samples and test samples the results of the fivegroups were obtained including accuracy sensitivityspecificity and time (training samples are constructed by800 malignant samples and 800 benign samples testingsamples are constructed by 200 malignant samples and 200benign samples the experiment is repeated 5 times bychanging training samples and testing samples) Finally theaverage values of these five groups are obtained as the finalresult of the reduction and shown in Table 16

+e experimental group in the case of 1 minus β= 06 un-changed the weight of ω1 was increased +e attributedependency and the optimal fitness function are relativelyhigh the average precision of reduction 1 reduction 2 andreduction 3 in Table 16 is more than 97 and that of re-duction 2 is even up to 9725 +e average recognitionaccuracy of the experimental group is 9703 which ishigher than that of the first group

Table 13 +e statistical results of the third group for experiment 2 with the SVM classifier

Experiment times Accuracy () Sensitivity () Specificity () Time (s)

Reduction 1

1 9225 8450 10000 812712 9550 9700 9400 945833 9575 9400 9750 881984 9600 9800 9400 937545 9725 9900 9550 98691

Average value 9535 9450 9620 91299

Reduction 2

1 9200 8450 9950 648942 9625 9550 9700 801983 9525 9300 9750 773374 9600 9750 9450 760125 9800 10000 9600 82763

Average value 9550 9410 9690 76241

Reduction 3

1 9200 8450 9950 648942 9625 9550 9700 801983 9525 9300 9750 773374 9600 9750 9450 760125 9800 10000 9600 82763

Average value 9550 9410 9690 76241

Reduction 4

1 9275 8550 10000 672642 9675 9600 9750 784673 9600 9450 9750 730224 9575 9750 9400 794605 9800 10000 9600 84184

Average value 9585 9470 9700 76479

Reduction 5

1 9200 8450 9950 1147192 9625 9750 9500 1287053 9850 9900 9800 1320494 9775 9950 9600 1335135 9850 10000 9700 133144

Average value 9660 9610 9710 128426

Table 14 Fitness function weight proportion and β value

Experiment times1 minus β 06

ω1 ω2 ω3First group experiment 1 1 0Second group experiment 2 1 0+ird group experiment 3 1 0

14 Mathematical Problems in Engineering

ndash2

ndash25

ndash3

Fitn

ess v

alue

0 50 100 150Generation stopping criteria

Best fitnessMean fitness

Best ndash2915 Mean ndash291446

Figure 10 +e variation of fitness function value in a running process for experiment 3-second group

Table 15 Results of VPRS-GA running 5 times when 1 minus β 06 ω1 2ω2 1ω3 0

Experimenttimes C_ reduction Reduction

lengthOptimal fitness

valueAttribute dependency

degree Time (s)

1 2 3 4 5 11 13 16 18 24 30 34 37 39 41 42 51 55 64 7077 78 82 22 minus 34859 09060 21515464

2 8 9 11 12 14 15 23 25 26 29 30 33 37 42 43 45 46 5060 61 69 74 80 87 89 25 minus 30845 09390 42761634

3 8 11 12 13 16 18 19 24 29 36 37 43 64 65 68 71 86 9192 19 minus 35039 09150 26197164

4 2 3 4 8 10 11 12 13 15 16 19 23 25 30 48 55 64 65 6874 77 80 81 83 84 86 89 27 minus 29150 09575 44271631

5 5 8 911 121517 23 25 29 31 36 39 41 48 54 59 63 8083 86 89 22 minus 29920 09525 43161464

Average value 23 minus 31962 09340 35581471

Table 16 +e statistical results of the second group for experiment 3 with the SVM classifier

Experiment times Accuracy () Sensitivity () Specificity () Time (s)

Reduction 1

1 9275 8600 9950 1884972 9725 9800 9650 1571623 9850 9900 9800 1586914 9800 9900 9700 1646035 9950 10000 9900 161914

Average value 9720 9640 9800 166173

Reduction 2

1 9450 8950 9950 1908132 9675 9800 9550 2002513 9775 9800 9750 1970084 9850 9900 9800 2009245 9875 9900 9850 209245

Average value 9725 9670 9780 199648

Reduction 3

1 9400 8800 10000 1313692 9725 9800 9650 1447973 9800 9800 9800 1426624 9725 9850 9600 1471905 9925 10000 9850 148799

Average value 9715 9650 9780 142963

Reduction 4

1 9350 8750 9950 2404562 9700 9750 9650 2520823 9800 9800 9800 2511754 9775 9950 9600 2701885 9825 10000 9650 267471

Average value 9690 9650 9730 256274

Reduction 5

1 9325 8800 9850 1809592 9600 9800 9400 1965633 9750 9750 9750 1967234 9800 9900 9700 2078295 9850 9950 9750 219703

Average value 9665 9640 9690 200355

Mathematical Problems in Engineering 15

Table 17 Results of VPRS-GA running 5 times when 1 minus β 1 ω1 1ω2 1ω3 0

Experimenttimes C_ reduction Reduction

lengthOptimal fitness

valueAttribute

dependency degree Time (s)

1 3 4 5 8 9 11 12 17 19 29 34 35 38 46 52 53 55 59 63 6672 75 77 78 79 87 92 27 minus 38867 09550 28981789

2 4 8 9 11 12 15 17 29 33 37 38 39 42 43 48 55 67 73 7881 83 84 88 89 90 25 minus 38167 09715 55783772

3 2 3 4 8 9 10 11 12 13 15 16 19 24 25 30 36 49 54 55 6064 67 68 70 74 77 83 85 86 91 30 minus 38807 09530 34831096

4 4 5 7 11 12 14 15 17 25 29 33 36 39 41 42 47 48 50 5556 58 62 67 69 72 74 77 84 86 90 91 31 minus 39430 09665 35742822

5 3 4 5 8 9 11 12 17 19 29 34 35 38 46 52 53 55 59 63 6672 75 77 78 79 87 92 27 minus 38867 09550 27919582

Average value 28 minus 38827 09602 36651812

ndash3

ndash35

ndash40 50 100 150

Generation stopping criteria

Fitn

ess v

alue

Best fitnessMean fitness

Best ndash394298 Mean ndash393327

Figure 11 +e variation of fitness function value in a running process for experiment 3-third group

Table 18 +e statistical results of the Second group for experiment 3 with the SVM classifier

Experiment times Accuracy () Sensitivity () Specificity () Time (s)

Reduction 1

1 9200 8700 9700 2187172 9750 9750 9750 2105503 9850 9850 9850 2032064 9800 9900 9700 2211645 9925 10000 9850 272536

Average value 9705 9640 9770 225235

Reduction 2

1 9400 8850 9950 2331232 9575 9750 9400 2433493 9750 9700 9800 2442024 9775 9900 9650 2566075 9900 9950 9850 259071

Average value 9680 9630 9730 247270

Reduction 3

1 9275 8650 9900 2525842 9625 9750 9500 2624123 9775 9800 9750 2601274 9775 9900 9650 2686705 9875 10000 9750 265387

Average value 9665 9620 9710 261836

Reduction 4

1 9150 8550 9750 2532312 9625 9750 9500 2649433 9750 9700 9800 2752834 9800 9950 9650 3229545 9825 9950 9700 277432

Average value 9630 9580 9680 278769

Reduction 5

1 9200 8800 9600 1951962 9700 9700 9700 2148893 9825 9800 9850 2036124 9850 10000 9700 2133615 9900 9900 9900 225526

Average value 9695 9640 9750 210517

16 Mathematical Problems in Engineering

(3) 3rd Group Experiment ω1 3 ω2 1 ω3 0 +e al-gorithm is run 5 times according to the group weights andthe results of the 5 groups are given in Table 17 including thereduction of the conditional attributes the length of re-duction the optimal fitness value the attribute dependencyand the time +e convergence of VPRS-GA under thevariation for fitness function value for one time is shown inFigure 11

Each reduction is classified by SVM classifier using themethod of 5-fold cross validation through changing thetraining samples and test samples the results of the fivegroups were obtained including accuracy sensitivityspecificity and time (training samples are constructed by800 malignant samples and 800 benign samples testingsamples are constructed by 200 malignant samples and 200benign samples the experiment is repeated 5 times bychanging training samples and testing samples) Finally theaverage values of these five groups are obtained as the finalresult of the reduction and shown in Table 18

+e experiment in the case of 1 minus β 06 unchangedincrease the weight of the ω1 ω1 3 ω2 1 ω3 0 InTable 18 the recognition accuracy of reduction 1 is over 97only +e average recognition accuracy of the experimentalgroup is 9675 and the accuracy is decreased by 028compared with that in the other second groups +e threegroups of experiment 3 the purpose is to verify whether theexperimental accuracy is influenced by increasing theweight +e experimental results show that the accuracy ofsecond group for experimental weight 2 1 0 comparedwith first group experiment when 1 1 0 is high but thethird groups of experimental weight was 3 1 0 and theaccuracy declined therefore the weight of 2 1 0 is the bestchoice for this experiment

4 Conclusions

Aiming at the deficiency of the traditional rough set modelthis paper proposes a new feature selection model based ongenetic algorithm and variable precision rough set by in-troducing the β value the rigid inclusion of the approxi-mation for the traditional rough set is relaxed and then wedesign the 3 kinds of experiments by constructing the de-cision information table of the PETCT feature for lungtumor ROI +e first type of experiment is the inclusion of1 minus β 06 and different values of ω made a total of threegroups of experiments the experimental results show thatthe better recognition accuracy can be obtained when theweight is 1 1 0 and the results show that the gene codingweight function has no effect on the fitness function For thesecond type of experiments ϖ1 1ω2 1 ω3 0according to the different values of β to do three groups ofexperiments the results show that the recognition accuracyof 1 minus β 06 is the best which shows that the larger the βvalue is the lower approximate cardinality will be largerthen the relative accuracy will increase For the third type ofexperiments 1 minus β 06 ω value is increased to achieve thebest fitness function in order to achieve the best results +eexperimental results show that the recognition accuracy isbetter than the others when the weight value is 2 1 0 so it

is better to solve the problem by increasing the proportion ofattribute dependency +rough the above experiments it isshown that the high-dimensional feature selection algorithmbased on genetic algorithm and variable precision rough setcan solve the multiobjective optimization problem wellHowever when the fitness function and its parameters areapplied in the specific application it is necessary to analyzethe specific problems

Data Availability

+e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

+e authors declare no conflicts of interest

Acknowledgments

+is work was supported by National Natural ScienceFoundation of China (Grant nos 61561040 and 61876121)First-Class Disciplines Foundation of Ningxia (NoNXYLXK2017B09)

References

[1] S Luo D Miao Z Zhang Y Zhang and S Hu ldquoA neigh-borhood rough set model with nominal metric embeddingrdquoInformation Sciences vol 520 pp 373ndash388 2020

[2] B Barman and S Patra ldquoVariable precision rough set basedunsupervised band selection technique for hyperspectralimage classificationrdquo Knowledge-Based Systems vol 1936Article ID 105414 2020

[3] Y Chenyi and L Jinjin ldquoApproximate attribute reductionunder variable precision rough set βrdquo Journal of ShandongUniversity vol 11 pp 17ndash21 2011

[4] S Xiaowei Research on Hierarchical Model of Attribute Re-duction in Variable Precision Rough Set Central SouthUniversity Changsha China 2013

[5] Z Jie and W Jiayang ldquoAnalysis of reduction feature ofvariable precision rough set modelrdquo Computer ApplicationResearch vol 7 pp 12ndash15 2007

[6] Z Pei and Z Qinghua ldquoFCM clustering algorithm based onvariable precision rough setrdquo Journal of Shanxi Universityvol 3 pp 342ndash348 2016

[7] C Hao and Y Junan ldquoAttribute kernel and minimum at-tribute reduction algorithm of variable precision rough setrdquoActa Sinica Sinica vol 5 pp 1011ndash1017 2012

[8] S Xu X Yang H Yu D-J Yu J Yang and E CC TsangldquoMulti-label learning with label-specific feature reductionrdquoKnowledge-Based Systems vol 104 pp 52ndash61 2016

[9] I Maryam and G Hassan ldquoFeature space discriminantanalysis for hyperspectral data feature reductionrdquo ISPRSJournal of Photogrammetry and Remote Sensing vol 102pp 1ndash13 2015

[10] S Q Wang C Y Gao C Luo G M Zheng and Y N ZhouldquoResearch on feature selectionattribute reduction methodbased on rough set theoryrdquo Procedia Computer Sciencevol 154 pp 194ndash198e 2019

[11] A W Omar M Azzam O Hadi and B Jamal ldquoCEAP SVM-based intelligent detection model for clustered vehicular ad

Mathematical Problems in Engineering 17

hoc networksrdquo Expert Systems with Applications vol 50pp 40ndash54 2016

[12] H Lee and Y-P P Chen ldquoImage based computer aideddiagnosis system for cancer detectionrdquo Expert Systems withApplications vol 42 no 12 pp 5356ndash5365 2015

[13] J A Guy and P L Harold ldquoAfter detection the improvedaccuracy of lung cancer assessment using radiologic com-puter-aided diagnosisrdquo Academic Radiology vol 23 no 2pp 186ndash191 2016

[14] E Kiyonori T Shodayu J Binghu et al ldquoPleural invasion byperipheral lung cancer prediction with three-dimensionalCTrdquo Academic Radiology vol 3 pp 310ndash319 2015

[15] B Koohestani ldquoA crossover operator for improving the ef-ficiency of permutation-based genetic algorithmsrdquo ExpertSystems with Applications vol 1511 Article ID 113381 2020

[16] N K Lee X Li and D Wang ldquoA comprehensive survey ongenetic algorithms for DNA motif predictionrdquo InformationSciences vol 466 pp 25ndash43 2018

[17] S Shibao and Y Leilei ldquoResearch on variable precision roughset model and its applicationrdquo Computer Engineering andApplication vol 07 pp 10ndash13 2009

[18] T Xiaolong Several Problems of Multi Granularity VariablePrecision Rough Set Guangxi University For NationalitiesNanning China 2015

[19] W Xueming Research on Several Rough Set Models andNeural Network University of Electronic Science and Tech-nology of China Chengdu China 2013

[20] T Sun J Wang X Li et al ldquoComparative evaluation ofsupport vector machines for computer aided diagnosis of lungcancer in CT based on a multi-dimensional data setrdquo Com-puter Methods and Programs in Biomedicine vol 111 no 2pp 519ndash524 2013

[21] Z Yang T Ouyang X Fu and X Peng ldquoA decision-makingalgorithm for online shopping using deep-learning-basedopinion pairs mining and q -rung orthopair fuzzy interactionHeronianmean operatorsrdquo International Journal of IntelligentSystems vol 35 no 5 pp 783ndash825 2020

[22] W Chen C Lin C Li et al ldquoTracing the evolution of 3Dprinting technology in China using LDA-based patent ab-stract miningrdquo IEEE Transactions on Engineering Manage-men vol 36 pp 1ndash11 2020

18 Mathematical Problems in Engineering

regarded as fitness function +e average attribute de-pendency degree is 0973 the average length of reductionis 392 and the average optimal fitness value is minus 0973+e average recognition accuracy of the experiment is9692 +e premature phenomena are shown in Fig-ure 5 and evolution progress is terminated early

(2) 2nd Group Experiment ϖ1ω2ω3 1 1 0 +isexperiment introduces an objective function to control thelength of reduction (the shorter the length of reduction thebetter it is) the influence degree of the objective functionwhich controls the reduction on the fitness function and the

final recognition accuracy is verified +e algorithm is run 5times according to this group weights and the results of the 5groups are given in Table 5 including the reduction of theconditional attributes the length of reduction the optimalfitness value the attribute dependency and the time +econvergence of VPRS-GA under the variation for fitnessfunction value in one time is shown in Figure 6

Each reduction is classified by SVM classifier using themethod of 5-fold cross validation through changing thetraining samples and test samples the results of the fivegroups were obtained including accuracy sensitivityspecificity and time (training samples are constructed by

ndash06

ndash07

ndash08

ndash09

ndash10 50 100 150

Generation stopping criteria

Best ndash09695 Mean ndash0944425

Fitn

ess v

alue

Best fitnessMean fitness

Figure 5 +e variation of fitness function value in a running process for Experiment 1-first group

Table 4 +e statistical results of the first group for experiment 1 with the SVM classifier

Experiment times Accuracy () Sensitivity () Specificity () Time (s)

Reduction 1

1 9250 8600 9900 3326072 9725 9750 9700 3450513 9900 9900 9900 3586774 9800 9950 9650 3510755 9925 10000 9850 355948

Average value 9720 9640 9800 348672

Reduction 2

1 9325 8700 9950 4365332 9725 9800 9650 4459003 9875 9850 9900 4395064 9750 9900 9600 4450645 9925 10000 9850 448513

Average value 9720 9650 9790 443103

Reduction 3

1 9275 8750 9800 3269162 9575 9750 9400 3372093 9800 9800 9800 3407014 9700 9850 9550 3331745 9850 9950 9750 333257

Average value 9640 9620 9660 334251

Reduction 4

1 9375 8850 9900 3064852 9650 9750 9550 3192403 9750 9700 9800 3240824 9775 9900 9650 3254195 9900 10000 9800 361516

Average value 9690 9640 9740 318806

Reduction 5

1 9400 8900 9900 3195572 9650 9750 9550 3369093 9725 9700 9750 3301594 9775 9900 9650 3999805 9900 10000 9800 325692

Average value 9690 9650 9730 342459

8 Mathematical Problems in Engineering

800 malignant samples and 800 benign samples testingsamples are constructed by 200 malignant samples and 200benign samples the experiment is repeated 5 times bychanging training samples and testing samples) Finally theaverage values of these five groups are obtained as the finalresult of the reduction and shown in Table 6

+e experimental weight of this group is ϖ1

ω2ω3 1 1 0 attribute dependency degree and thelength of reduction are regarded as fitness function As canbe seen from Table 5 the reduction length is 13 17 and soon +e average length of reduction was 17 which wassignificantly reduced compared with the average length ofthe reduction in Table 3 in the experiment of the first groupswhich reduced the time improved the efficiency of the al-gorithm and increased the attribute dependency of thealgorithm even up to 1 +e average recognition accuracy ofthe experimental group was 9698 which was increased by006 compared with that in the first groups

(3) 3rd Group Experiment ϖ1ω2ω3 1 1 1 On thebasis of attribute dependency degree and attribute reductionlength this experiment introduces gene coding weightfunction in order to verify the effect of gene coding weightfunction on fitness function and the final recognition ac-curacy +e algorithm are run 5 times according to thisgroup weights the results of the 5 groups are given inTable 7 including the reduction of the conditional attributesthe length of reduction the optimal fitness value the at-tribute dependency and the time +e convergence ofVPRS-GA under the variation for fitness function value inone time is shown in Figure 7

Each reduction is classified by SVM classifier using themethod of 5-fold cross validation through changing thetraining samples and test samples the results of the fivegroups were obtained including accuracy sensitivityspecificity and time (training samples are constructed by800 malignant samples and 800 benign samples testingsamples are constructed by 200 malignant samples and 200benign samples the experiment is repeated 5 times bychanging training samples and testing samples) Finally theaverage values of these five groups are obtained as the finalresult of the reduction and shown in Table 8

+e experimental weight of this group is ϖ1 ω2ω3=1 1 1 attribute dependency degree the length of re-duction and gene coding weight value are regarded as fitnessfunction However the premature phenomena are shown inFigure 7 and evolution progress is terminated early FromTable 7 we can see that the attribute dependency decreasesgradually and even the attribute dependency of Reduction 1is reduced to 0759 +e average recognition accuracy of theexperimental group was 9685+e accuracy of recognitionwas decreased compared with the second groups and henceusing gene encoding weight function in the fitness functionto improve recognition accuracy is useless only for thesamples with different results to analyze specific issues +e3 experiment runs of experiment 1 verified the necessity ofthe fitness function by continuously introducing fitnessobjective function such as target1 target2 and target3 theconclusion is that the fitness function is better when it is notbigger but after the introduction of target3 the accuracydeclines therefore the introduction of target1 and target2 inthis algorithm can get better results

Table 5 Results of VPRS-GA running 5 times when 1 minus β 06 ω1 1ω2 1ω3 0

Experiment times C_ reduction Reductionlength

Optimalfitness value

Attributedependency

degreeTime (s)

1 5 9 14 20 26 41 43 46 48 54 55 57 64 66 74 79 86 90 18 minus 46487 09965 107240722 1 4 11 12 14 24 34 40 42 43 56 60 61 65 67 68 71 72 85 19 minus 40109 1 63281223 2 13 27 29 39 42 45 56 59 63 68 70 75 13 minus 46512 09990 110239674 1 3 4 7 9 11 12 15 30 34 38 42 46 48 55 62 65 77 79 19 minus 49674 1 87946705 3 9 11 13 29 39 41 42 43 46 50 55 65 c77 85 86 16 minus 44114 09815 15075539

Average value 17 minus 45379 09954 10389274

ndash1

ndash2

ndash3

ndash4

ndash5

Fitn

ess v

alue

Best ndash496739 Mean ndash492312

0 50 100 150Generation stopping criteria

Best fitnessMean fitness

Figure 6 +e variation of fitness function value in a running process for experiment 1-second group

Mathematical Problems in Engineering 9

342 Experiment 2mdashResearch on Different ClassificationError Rates under the Condition in the Same WeightCoefficient According to experiment 1 we can see thatwhen ω1 1 ω2 1 ω3 0 the experimental results arethe best so in experiment 2 the case of the weight value ofwas unchanged ω1 1 ω2 1 ω3 0 and the β value waschanged and they are shown in Table 9

(1) 1st Group Experiment 1 minus β 06 +e algorithm is run 5times according to this group weights the results of the 5groups are shown in Table 5 including the reduction of the

conditional attributes the length of reduction the optimalfitness value the attribute dependency and the time +econvergence of VPRS-GA under the variation for fitnessfunction value for one time is shown in Figure 6 (ie notrepeated in the second group of experiment 1)

(2) 2nd Group Experiment 1 minus β 08 +e algorithm are is 5times according to this group weights the results of the 5groups are given in Table 10 including the reduction of theconditional attributes the length of reduction the optimalfitness value the attribute dependency and the time +e

Table 6 +e statistical results of the second group for experiment 1 with the SVM classifier

Experiment times Accuracy () Sensitivity () Specificity () Time (s)

Reduction 1

1 9300 8600 10000 1164882 9625 9600 9650 1255113 9850 9900 9800 1315094 9725 9850 9600 1344685 9925 10000 9850 144839

Average value 9685 9590 9780 130563

Reduction 2

1 9425 8900 9950 1210962 9725 9700 9750 1286363 9800 9800 9800 1356774 9750 9800 9700 1381965 9875 9900 9850 136691

Average value 9715 9620 9810 132059

Reduction 3

1 9300 8750 9850 877572 9725 9750 9700 1034243 9775 9800 9750 1074114 9775 9850 9700 1123445 9900 10000 9800 113006

Average value 9695 9630 9760 104788

Reduction 4

1 9375 8750 10000 1464172 9650 9750 9550 1547363 9750 9700 9800 1576214 9800 9900 9700 1613555 9925 10000 9850 163381

Average value 9700 9620 9780 156702

Reduction 5

1 9250 8650 9850 1249332 9675 9800 9550 1400573 9800 9800 9800 1451944 9800 9900 9700 1457925 9950 9950 9950 150400

Average value 9695 9620 9770 141275

Table 7 Results of VPRS-GA running 5 times when 1 minus β 06 ω1 1ω2 1ω3 1

Experimenttimes C_ reduction Reduction

lengthOptimal

fitness valueAttribute

dependency degree Time (s)

1 4 5 7 26 27 34 35 41 47 54 55 71 74 75 78 80 83 90 18 minus 14192 07590 6888635

2 4 15 16 19 22 27 28 29 30 35 38 42 45 50 52 53 59 61 6264 65 70 71 72 77 87 88 27 minus 15232 08640 8124857

3 6 17 19 24 28 31 33 34 38 39 43 45 47 48 49 51 55 56 6667 69 70 71 72 76 77 78 80 81 84 87 89 91 92 34 minus 13545 07950 9521511

4 3 6 8 91617 19 20 24 25 28 35 37 39 41 42 46 49 51 52 5459 63 65 66 74 83 86 28 minus 14703 08365 8714839

5 1 7 8 15 17 19 20 23 29 37 45 48 54 60 62 70 73 75 77 7879 86 22 minus 14990 07995 7797617

Average value 258 minus 14532 08108 8209492

10 Mathematical Problems in Engineering

convergence of VPRS-GA under the variation for fitnessfunction value for one time is shown in Figure 8

Each reduction is classified by SVM classifier using themethod of 5-fold cross validation through changing thetraining samples and test samples the results of the five

groups were obtained including accuracy sensitivityspecificity and time (training samples are constructed by800 malignant samples and 800 benign samples testingsamples are constructed by 200 malignant samples and 200benign samples the experiment is repeated 5 times by

ndash08

ndash1

ndash12

ndash14

ndash16

Fitn

ess v

alue

Best ndash141919 Mean ndash128476

0 50 100 150Generation stopping criteria

Best fitnessMean fitness

Figure 7 +e variation of fitness function value in a running process for experiment 1-third group

Table 8 +e statistical results of the third group for experiment 1 with the SVM classifier

Experiment times Accuracy () Sensitivity () Specificity () Time (s)

Reduction 1

1 9275 8600 9950 924922 9725 9750 9700 1074613 9850 9850 9850 1138114 9775 9900 9650 1155605 9875 10000 9750 117022

Average value 9700 9620 9780 109269

Reduction 2

1 9350 8750 9950 1482452 9700 9650 9750 1615353 9775 9850 9700 1664524 9800 9850 9750 1754505 9875 9950 9800 172348

Average value 9700 9610 9790 164806

Reduction 3

1 9125 8300 9950 2019042 9650 9700 9600 2185353 9800 9800 9800 2196054 9625 9900 9350 2230915 9825 10000 9650 236896

Average value 9605 9540 9670 220006

Reduction 4

1 9300 8700 9900 1654542 9675 9600 9750 1724323 9875 9850 9900 1793014 9800 9900 9700 1895605 9900 9950 9850 185249

Average value 9710 9600 9820 178399

Reduction 5

1 9275 8600 9950 1411732 9725 9800 9650 1612953 9900 9950 9850 1589924 9775 9950 9600 1648765 9875 10000 9750 166070

Average value 9710 9660 9760 158481

Table 9 Fitness function weight proportion and β value

Experiment timesω1 1 ω2 1 ω3 0

1 minus β 06 1 minus β 08 1 minus β 1First group experiment Second group experiment +ird group experiment

Mathematical Problems in Engineering 11

changing training samples and testing samples) Finally theaverage values of these five groups are obtained as the finalresult of the reduction and shown in Table 11

In the case of constant weight ϖ and classification errorrate of β 02 (which contains 1 minus β 08) the classificationerror rate is changed on the basis of the attribute dependencyand the length of control reduction +e premature phe-nomena are shown in Figure 8 and evolution progress isterminated early such that the attribute dependency ofreduction 5 was 08405 appeared in attribute dependency onless than 09 compared with first groups of experiment 2attribute dependency declined +e average recognitionaccuracy of the experimental group was 9674 Comparedwith the classification error rate of 04 and inclusion degreeof 06 the accuracy was decreased by 024

(3) 3rd Group Experiment 1 minus β1 +e algorithm is run 5times according to the group weights and the results of the 5groups are shown in Table 12 including the reduction of theconditional attributes the length of reduction the optimalfitness value the attribute dependency and the time +econvergence of VPRS-GA under the variation for fitnessfunction value for one time is shown in Figure 9

Each reduction is classified by SVM classifier using themethod of 5-fold cross validation through changing thetraining samples and test samples the results of the fivegroups were obtained including accuracy sensitivityspecificity and time (training samples are constructed by800 malignant samples and 800 benign samples testingsamples are constructed by 200 malignant samples and 200

benign samples the experiment is repeated 5 times bychanging training samples and testing samples) Finally theaverage values of these five groups are obtained as the finalresult of the reduction and shown in Table 13

In the case of constant weight ϖ and classification errorrate of β= 0 (which contains 1 minus β= 1) the classificationerror rate is reduced and the inclusion degree is improved onthe basis of the attribute dependency and the length ofcontrol reduction +e premature phenomena are shown inFigure 9 and evolution progress is terminated early +eaverage recognition accuracy of the experimental group was9573 which was decreased by 006 compared with thatin the second group In experiment 2 the effect of changingthe classification error rate on the recognition accuracy wasverified by the 3 groups of experiments By continuallyreducing the classification error rate the final recognitionaccuracy has been declining when inclusion degree is 1β= 0 variable precision rough set becomes Pawlak rough setthe recognition accuracy of the recognition accuracy of isminimum which was verified the advantages of variableprecision rough set

343 Experiment 3mdashResearch on Increasing the WeightCoefficient under the Condition in the Same ClassificationError Rate According to experiment 1 and experiment 2we can know that when β 06 ω1 1 ω2 1 ω3 0 therecognition accuracy is the best therefore in the thirdexperiment by increasing the weight of ω 3 groups ofexperiments are performed fitness goals target 1 (attribute

Table 10 Results of VPRS-GA running 5 times when 1 minus β 08 ω1 1ω2 1ω3 0

Experimenttimes C_ reduction Reduction

lengthOptimal fitness

valueAttribute

dependency degree Time (s)

1 8 9 11 12 15 16 17 18 25 26 29 31 35 39 40 41 42 48 5865 67 68 70 83 84 91 26 minus 67816 09490 10002827

2 1 6 8 9 11 12 15 17 21 23 26 28 30 31 34 44 50 56 58 5962 63 64 68 71 75 77 82 89 92 30 minus 67797 09615 9477387

3 6 8 12 14 15 16 17 21 28 35 38 39 45 49 55 58 61 62 6465 77 82 85 23 minus 68694 09070 12866181

4 4 6 7 8 11 12 13 16 17 20 25 26 31 32 34 35 41 42 44 4950 55 58 68 72 74 76 78 79 85 89 92 32 minus 67225 09540 10510220

5 3 6 8 9 10 16 17 26 27 34 36 37 38 40 42 44 46 51 52 6266 67 84 86 87 25 minus 65892 08405 8469324

Average value 272 minus 67484 09224 10265188

ndash55

ndash6

ndash65

ndash7

Fitn

ess v

alue

Best ndash686942 Mean ndash653584

0 50 100 150Generation stopping criteria

Best fitnessMean fitness

Figure 8 +e variation of fitness function value in a running process for experiment 2-second group

12 Mathematical Problems in Engineering

Table 11 +e statistical results of the second group for experiment 2 with the SVM classifier

Experiment times Accuracy () Sensitivity () Specificity () Time (s)

Reduction 1

1 9300 8650 9950 2280072 9575 9700 9450 2376463 9700 9600 9800 2332504 9750 9850 9650 2444915 9925 10000 9850 244816

Average value 9650 9560 9740 237642

Reduction 2

1 9375 8800 9950 2524032 9625 9750 9500 2652893 9800 9700 9900 2655234 9800 9900 9700 2682125 9950 10000 9900 275880

Average value 9710 9630 9790 265461

Reduction 3

1 9275 8750 9800 1807802 9675 9750 9600 1929923 9700 9600 9800 1872434 9775 9950 9600 2084825 9875 10000 9750 203507

Average value 9660 9610 9710 194601

Reduction 4

1 9200 8650 9750 2572602 9700 9750 9650 2730243 9775 9650 9900 2723164 9750 9900 9600 2815545 9900 10000 9800 291471

Average value 9665 9590 9740 275125

Reduction 5

1 9275 8750 9800 1437152 9675 9600 9750 1526373 9750 9800 9700 1589294 9775 9900 9650 1629975 9950 10000 9900 166792

Average value 9685 9610 9760 157014

Table 12 Results of VPRS-GA running 5 times when 1 minus β 1 ω1 1ω2 1ω3 0

Experimenttimes C_ reduction Reduction

lengthOptimal fitness

valueAttribute dependency

degree Time (s)

1 15 44 68 73 79 84 6 minus 27313 07965 114499012 34 51 54 75 80 90 6 minus 27047 08460 96993913 2 34 49 70 71 72 76 81 8 minus 34057 07535 112334894 12 25 78 85 4 minus 22872 09285 11668133

5 6 7 12 13 42 44 55 57 65 66 69 77 81 8687 15 minus 33230 08665 13236077

Average value 78 minus 28903 08382 11457398

ndash1

ndash2

ndash3

ndash4

Fitn

ess v

alue

0 50 100 150Generation stopping criteria

Best fitnessMean fitness

Best ndash340567 Mean ndash330598

Figure 9 +e variation of fitness function value in a running process for experiment 2-third group

Mathematical Problems in Engineering 13

dependency) target 2 (the minimum number of attributesreduction) and target 3 (gene encoding weight function)the three objective functions play an important role in theevaluation of fitness function However the importance offitness function is reduced in these three objectives+erefore in this experiment when the other conditions areunchanged the weight coefficient of the target 1 is increasedto verify the influence of the change in the weight coefficienton the experimental results and they are shown in Table 14

(1) 1st Group Experiment ω1 1 ω2 1 ω3 0 +e al-gorithm are run 5 times according to this group weights theresults of the 5 groups are given in Table 5 including thereduction of the conditional attributes the length of reduc-tion the optimal fitness value the attribute dependency andthe time +e convergence of VPRS-GA under the variationfor fitness function value in one time is shown in Figure 6 (ienot repeated for the second group of experiment 1)

(2) 2nd Group Experiment ω1 2 ω2 1 ω3 0 +ealgorithm is run 5 times according to this group weights theresults of the 5 groups are given in Table 15 including thereduction of the conditional attributes the length of re-duction the optimal fitness value the attribute dependencyand the time +e convergence of VPRS-GA under thevariation for fitness function value in one time is shown inFigure 10

Each reduction is classified by SVM classifier using themethod of 5-fold cross validation through changing thetraining samples and test samples the results of the fivegroups were obtained including accuracy sensitivityspecificity and time (training samples are constructed by800 malignant samples and 800 benign samples testingsamples are constructed by 200 malignant samples and 200benign samples the experiment is repeated 5 times bychanging training samples and testing samples) Finally theaverage values of these five groups are obtained as the finalresult of the reduction and shown in Table 16

+e experimental group in the case of 1 minus β= 06 un-changed the weight of ω1 was increased +e attributedependency and the optimal fitness function are relativelyhigh the average precision of reduction 1 reduction 2 andreduction 3 in Table 16 is more than 97 and that of re-duction 2 is even up to 9725 +e average recognitionaccuracy of the experimental group is 9703 which ishigher than that of the first group

Table 13 +e statistical results of the third group for experiment 2 with the SVM classifier

Experiment times Accuracy () Sensitivity () Specificity () Time (s)

Reduction 1

1 9225 8450 10000 812712 9550 9700 9400 945833 9575 9400 9750 881984 9600 9800 9400 937545 9725 9900 9550 98691

Average value 9535 9450 9620 91299

Reduction 2

1 9200 8450 9950 648942 9625 9550 9700 801983 9525 9300 9750 773374 9600 9750 9450 760125 9800 10000 9600 82763

Average value 9550 9410 9690 76241

Reduction 3

1 9200 8450 9950 648942 9625 9550 9700 801983 9525 9300 9750 773374 9600 9750 9450 760125 9800 10000 9600 82763

Average value 9550 9410 9690 76241

Reduction 4

1 9275 8550 10000 672642 9675 9600 9750 784673 9600 9450 9750 730224 9575 9750 9400 794605 9800 10000 9600 84184

Average value 9585 9470 9700 76479

Reduction 5

1 9200 8450 9950 1147192 9625 9750 9500 1287053 9850 9900 9800 1320494 9775 9950 9600 1335135 9850 10000 9700 133144

Average value 9660 9610 9710 128426

Table 14 Fitness function weight proportion and β value

Experiment times1 minus β 06

ω1 ω2 ω3First group experiment 1 1 0Second group experiment 2 1 0+ird group experiment 3 1 0

14 Mathematical Problems in Engineering

ndash2

ndash25

ndash3

Fitn

ess v

alue

0 50 100 150Generation stopping criteria

Best fitnessMean fitness

Best ndash2915 Mean ndash291446

Figure 10 +e variation of fitness function value in a running process for experiment 3-second group

Table 15 Results of VPRS-GA running 5 times when 1 minus β 06 ω1 2ω2 1ω3 0

Experimenttimes C_ reduction Reduction

lengthOptimal fitness

valueAttribute dependency

degree Time (s)

1 2 3 4 5 11 13 16 18 24 30 34 37 39 41 42 51 55 64 7077 78 82 22 minus 34859 09060 21515464

2 8 9 11 12 14 15 23 25 26 29 30 33 37 42 43 45 46 5060 61 69 74 80 87 89 25 minus 30845 09390 42761634

3 8 11 12 13 16 18 19 24 29 36 37 43 64 65 68 71 86 9192 19 minus 35039 09150 26197164

4 2 3 4 8 10 11 12 13 15 16 19 23 25 30 48 55 64 65 6874 77 80 81 83 84 86 89 27 minus 29150 09575 44271631

5 5 8 911 121517 23 25 29 31 36 39 41 48 54 59 63 8083 86 89 22 minus 29920 09525 43161464

Average value 23 minus 31962 09340 35581471

Table 16 +e statistical results of the second group for experiment 3 with the SVM classifier

Experiment times Accuracy () Sensitivity () Specificity () Time (s)

Reduction 1

1 9275 8600 9950 1884972 9725 9800 9650 1571623 9850 9900 9800 1586914 9800 9900 9700 1646035 9950 10000 9900 161914

Average value 9720 9640 9800 166173

Reduction 2

1 9450 8950 9950 1908132 9675 9800 9550 2002513 9775 9800 9750 1970084 9850 9900 9800 2009245 9875 9900 9850 209245

Average value 9725 9670 9780 199648

Reduction 3

1 9400 8800 10000 1313692 9725 9800 9650 1447973 9800 9800 9800 1426624 9725 9850 9600 1471905 9925 10000 9850 148799

Average value 9715 9650 9780 142963

Reduction 4

1 9350 8750 9950 2404562 9700 9750 9650 2520823 9800 9800 9800 2511754 9775 9950 9600 2701885 9825 10000 9650 267471

Average value 9690 9650 9730 256274

Reduction 5

1 9325 8800 9850 1809592 9600 9800 9400 1965633 9750 9750 9750 1967234 9800 9900 9700 2078295 9850 9950 9750 219703

Average value 9665 9640 9690 200355

Mathematical Problems in Engineering 15

Table 17 Results of VPRS-GA running 5 times when 1 minus β 1 ω1 1ω2 1ω3 0

Experimenttimes C_ reduction Reduction

lengthOptimal fitness

valueAttribute

dependency degree Time (s)

1 3 4 5 8 9 11 12 17 19 29 34 35 38 46 52 53 55 59 63 6672 75 77 78 79 87 92 27 minus 38867 09550 28981789

2 4 8 9 11 12 15 17 29 33 37 38 39 42 43 48 55 67 73 7881 83 84 88 89 90 25 minus 38167 09715 55783772

3 2 3 4 8 9 10 11 12 13 15 16 19 24 25 30 36 49 54 55 6064 67 68 70 74 77 83 85 86 91 30 minus 38807 09530 34831096

4 4 5 7 11 12 14 15 17 25 29 33 36 39 41 42 47 48 50 5556 58 62 67 69 72 74 77 84 86 90 91 31 minus 39430 09665 35742822

5 3 4 5 8 9 11 12 17 19 29 34 35 38 46 52 53 55 59 63 6672 75 77 78 79 87 92 27 minus 38867 09550 27919582

Average value 28 minus 38827 09602 36651812

ndash3

ndash35

ndash40 50 100 150

Generation stopping criteria

Fitn

ess v

alue

Best fitnessMean fitness

Best ndash394298 Mean ndash393327

Figure 11 +e variation of fitness function value in a running process for experiment 3-third group

Table 18 +e statistical results of the Second group for experiment 3 with the SVM classifier

Experiment times Accuracy () Sensitivity () Specificity () Time (s)

Reduction 1

1 9200 8700 9700 2187172 9750 9750 9750 2105503 9850 9850 9850 2032064 9800 9900 9700 2211645 9925 10000 9850 272536

Average value 9705 9640 9770 225235

Reduction 2

1 9400 8850 9950 2331232 9575 9750 9400 2433493 9750 9700 9800 2442024 9775 9900 9650 2566075 9900 9950 9850 259071

Average value 9680 9630 9730 247270

Reduction 3

1 9275 8650 9900 2525842 9625 9750 9500 2624123 9775 9800 9750 2601274 9775 9900 9650 2686705 9875 10000 9750 265387

Average value 9665 9620 9710 261836

Reduction 4

1 9150 8550 9750 2532312 9625 9750 9500 2649433 9750 9700 9800 2752834 9800 9950 9650 3229545 9825 9950 9700 277432

Average value 9630 9580 9680 278769

Reduction 5

1 9200 8800 9600 1951962 9700 9700 9700 2148893 9825 9800 9850 2036124 9850 10000 9700 2133615 9900 9900 9900 225526

Average value 9695 9640 9750 210517

16 Mathematical Problems in Engineering

(3) 3rd Group Experiment ω1 3 ω2 1 ω3 0 +e al-gorithm is run 5 times according to the group weights andthe results of the 5 groups are given in Table 17 including thereduction of the conditional attributes the length of re-duction the optimal fitness value the attribute dependencyand the time +e convergence of VPRS-GA under thevariation for fitness function value for one time is shown inFigure 11

Each reduction is classified by SVM classifier using themethod of 5-fold cross validation through changing thetraining samples and test samples the results of the fivegroups were obtained including accuracy sensitivityspecificity and time (training samples are constructed by800 malignant samples and 800 benign samples testingsamples are constructed by 200 malignant samples and 200benign samples the experiment is repeated 5 times bychanging training samples and testing samples) Finally theaverage values of these five groups are obtained as the finalresult of the reduction and shown in Table 18

+e experiment in the case of 1 minus β 06 unchangedincrease the weight of the ω1 ω1 3 ω2 1 ω3 0 InTable 18 the recognition accuracy of reduction 1 is over 97only +e average recognition accuracy of the experimentalgroup is 9675 and the accuracy is decreased by 028compared with that in the other second groups +e threegroups of experiment 3 the purpose is to verify whether theexperimental accuracy is influenced by increasing theweight +e experimental results show that the accuracy ofsecond group for experimental weight 2 1 0 comparedwith first group experiment when 1 1 0 is high but thethird groups of experimental weight was 3 1 0 and theaccuracy declined therefore the weight of 2 1 0 is the bestchoice for this experiment

4 Conclusions

Aiming at the deficiency of the traditional rough set modelthis paper proposes a new feature selection model based ongenetic algorithm and variable precision rough set by in-troducing the β value the rigid inclusion of the approxi-mation for the traditional rough set is relaxed and then wedesign the 3 kinds of experiments by constructing the de-cision information table of the PETCT feature for lungtumor ROI +e first type of experiment is the inclusion of1 minus β 06 and different values of ω made a total of threegroups of experiments the experimental results show thatthe better recognition accuracy can be obtained when theweight is 1 1 0 and the results show that the gene codingweight function has no effect on the fitness function For thesecond type of experiments ϖ1 1ω2 1 ω3 0according to the different values of β to do three groups ofexperiments the results show that the recognition accuracyof 1 minus β 06 is the best which shows that the larger the βvalue is the lower approximate cardinality will be largerthen the relative accuracy will increase For the third type ofexperiments 1 minus β 06 ω value is increased to achieve thebest fitness function in order to achieve the best results +eexperimental results show that the recognition accuracy isbetter than the others when the weight value is 2 1 0 so it

is better to solve the problem by increasing the proportion ofattribute dependency +rough the above experiments it isshown that the high-dimensional feature selection algorithmbased on genetic algorithm and variable precision rough setcan solve the multiobjective optimization problem wellHowever when the fitness function and its parameters areapplied in the specific application it is necessary to analyzethe specific problems

Data Availability

+e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

+e authors declare no conflicts of interest

Acknowledgments

+is work was supported by National Natural ScienceFoundation of China (Grant nos 61561040 and 61876121)First-Class Disciplines Foundation of Ningxia (NoNXYLXK2017B09)

References

[1] S Luo D Miao Z Zhang Y Zhang and S Hu ldquoA neigh-borhood rough set model with nominal metric embeddingrdquoInformation Sciences vol 520 pp 373ndash388 2020

[2] B Barman and S Patra ldquoVariable precision rough set basedunsupervised band selection technique for hyperspectralimage classificationrdquo Knowledge-Based Systems vol 1936Article ID 105414 2020

[3] Y Chenyi and L Jinjin ldquoApproximate attribute reductionunder variable precision rough set βrdquo Journal of ShandongUniversity vol 11 pp 17ndash21 2011

[4] S Xiaowei Research on Hierarchical Model of Attribute Re-duction in Variable Precision Rough Set Central SouthUniversity Changsha China 2013

[5] Z Jie and W Jiayang ldquoAnalysis of reduction feature ofvariable precision rough set modelrdquo Computer ApplicationResearch vol 7 pp 12ndash15 2007

[6] Z Pei and Z Qinghua ldquoFCM clustering algorithm based onvariable precision rough setrdquo Journal of Shanxi Universityvol 3 pp 342ndash348 2016

[7] C Hao and Y Junan ldquoAttribute kernel and minimum at-tribute reduction algorithm of variable precision rough setrdquoActa Sinica Sinica vol 5 pp 1011ndash1017 2012

[8] S Xu X Yang H Yu D-J Yu J Yang and E CC TsangldquoMulti-label learning with label-specific feature reductionrdquoKnowledge-Based Systems vol 104 pp 52ndash61 2016

[9] I Maryam and G Hassan ldquoFeature space discriminantanalysis for hyperspectral data feature reductionrdquo ISPRSJournal of Photogrammetry and Remote Sensing vol 102pp 1ndash13 2015

[10] S Q Wang C Y Gao C Luo G M Zheng and Y N ZhouldquoResearch on feature selectionattribute reduction methodbased on rough set theoryrdquo Procedia Computer Sciencevol 154 pp 194ndash198e 2019

[11] A W Omar M Azzam O Hadi and B Jamal ldquoCEAP SVM-based intelligent detection model for clustered vehicular ad

Mathematical Problems in Engineering 17

hoc networksrdquo Expert Systems with Applications vol 50pp 40ndash54 2016

[12] H Lee and Y-P P Chen ldquoImage based computer aideddiagnosis system for cancer detectionrdquo Expert Systems withApplications vol 42 no 12 pp 5356ndash5365 2015

[13] J A Guy and P L Harold ldquoAfter detection the improvedaccuracy of lung cancer assessment using radiologic com-puter-aided diagnosisrdquo Academic Radiology vol 23 no 2pp 186ndash191 2016

[14] E Kiyonori T Shodayu J Binghu et al ldquoPleural invasion byperipheral lung cancer prediction with three-dimensionalCTrdquo Academic Radiology vol 3 pp 310ndash319 2015

[15] B Koohestani ldquoA crossover operator for improving the ef-ficiency of permutation-based genetic algorithmsrdquo ExpertSystems with Applications vol 1511 Article ID 113381 2020

[16] N K Lee X Li and D Wang ldquoA comprehensive survey ongenetic algorithms for DNA motif predictionrdquo InformationSciences vol 466 pp 25ndash43 2018

[17] S Shibao and Y Leilei ldquoResearch on variable precision roughset model and its applicationrdquo Computer Engineering andApplication vol 07 pp 10ndash13 2009

[18] T Xiaolong Several Problems of Multi Granularity VariablePrecision Rough Set Guangxi University For NationalitiesNanning China 2015

[19] W Xueming Research on Several Rough Set Models andNeural Network University of Electronic Science and Tech-nology of China Chengdu China 2013

[20] T Sun J Wang X Li et al ldquoComparative evaluation ofsupport vector machines for computer aided diagnosis of lungcancer in CT based on a multi-dimensional data setrdquo Com-puter Methods and Programs in Biomedicine vol 111 no 2pp 519ndash524 2013

[21] Z Yang T Ouyang X Fu and X Peng ldquoA decision-makingalgorithm for online shopping using deep-learning-basedopinion pairs mining and q -rung orthopair fuzzy interactionHeronianmean operatorsrdquo International Journal of IntelligentSystems vol 35 no 5 pp 783ndash825 2020

[22] W Chen C Lin C Li et al ldquoTracing the evolution of 3Dprinting technology in China using LDA-based patent ab-stract miningrdquo IEEE Transactions on Engineering Manage-men vol 36 pp 1ndash11 2020

18 Mathematical Problems in Engineering

800 malignant samples and 800 benign samples testingsamples are constructed by 200 malignant samples and 200benign samples the experiment is repeated 5 times bychanging training samples and testing samples) Finally theaverage values of these five groups are obtained as the finalresult of the reduction and shown in Table 6

+e experimental weight of this group is ϖ1

ω2ω3 1 1 0 attribute dependency degree and thelength of reduction are regarded as fitness function As canbe seen from Table 5 the reduction length is 13 17 and soon +e average length of reduction was 17 which wassignificantly reduced compared with the average length ofthe reduction in Table 3 in the experiment of the first groupswhich reduced the time improved the efficiency of the al-gorithm and increased the attribute dependency of thealgorithm even up to 1 +e average recognition accuracy ofthe experimental group was 9698 which was increased by006 compared with that in the first groups

(3) 3rd Group Experiment ϖ1ω2ω3 1 1 1 On thebasis of attribute dependency degree and attribute reductionlength this experiment introduces gene coding weightfunction in order to verify the effect of gene coding weightfunction on fitness function and the final recognition ac-curacy +e algorithm are run 5 times according to thisgroup weights the results of the 5 groups are given inTable 7 including the reduction of the conditional attributesthe length of reduction the optimal fitness value the at-tribute dependency and the time +e convergence ofVPRS-GA under the variation for fitness function value inone time is shown in Figure 7

Each reduction is classified by SVM classifier using themethod of 5-fold cross validation through changing thetraining samples and test samples the results of the fivegroups were obtained including accuracy sensitivityspecificity and time (training samples are constructed by800 malignant samples and 800 benign samples testingsamples are constructed by 200 malignant samples and 200benign samples the experiment is repeated 5 times bychanging training samples and testing samples) Finally theaverage values of these five groups are obtained as the finalresult of the reduction and shown in Table 8

+e experimental weight of this group is ϖ1 ω2ω3=1 1 1 attribute dependency degree the length of re-duction and gene coding weight value are regarded as fitnessfunction However the premature phenomena are shown inFigure 7 and evolution progress is terminated early FromTable 7 we can see that the attribute dependency decreasesgradually and even the attribute dependency of Reduction 1is reduced to 0759 +e average recognition accuracy of theexperimental group was 9685+e accuracy of recognitionwas decreased compared with the second groups and henceusing gene encoding weight function in the fitness functionto improve recognition accuracy is useless only for thesamples with different results to analyze specific issues +e3 experiment runs of experiment 1 verified the necessity ofthe fitness function by continuously introducing fitnessobjective function such as target1 target2 and target3 theconclusion is that the fitness function is better when it is notbigger but after the introduction of target3 the accuracydeclines therefore the introduction of target1 and target2 inthis algorithm can get better results

Table 5 Results of VPRS-GA running 5 times when 1 minus β 06 ω1 1ω2 1ω3 0

Experiment times C_ reduction Reductionlength

Optimalfitness value

Attributedependency

degreeTime (s)

1 5 9 14 20 26 41 43 46 48 54 55 57 64 66 74 79 86 90 18 minus 46487 09965 107240722 1 4 11 12 14 24 34 40 42 43 56 60 61 65 67 68 71 72 85 19 minus 40109 1 63281223 2 13 27 29 39 42 45 56 59 63 68 70 75 13 minus 46512 09990 110239674 1 3 4 7 9 11 12 15 30 34 38 42 46 48 55 62 65 77 79 19 minus 49674 1 87946705 3 9 11 13 29 39 41 42 43 46 50 55 65 c77 85 86 16 minus 44114 09815 15075539

Average value 17 minus 45379 09954 10389274

ndash1

ndash2

ndash3

ndash4

ndash5

Fitn

ess v

alue

Best ndash496739 Mean ndash492312

0 50 100 150Generation stopping criteria

Best fitnessMean fitness

Figure 6 +e variation of fitness function value in a running process for experiment 1-second group

Mathematical Problems in Engineering 9

342 Experiment 2mdashResearch on Different ClassificationError Rates under the Condition in the Same WeightCoefficient According to experiment 1 we can see thatwhen ω1 1 ω2 1 ω3 0 the experimental results arethe best so in experiment 2 the case of the weight value ofwas unchanged ω1 1 ω2 1 ω3 0 and the β value waschanged and they are shown in Table 9

(1) 1st Group Experiment 1 minus β 06 +e algorithm is run 5times according to this group weights the results of the 5groups are shown in Table 5 including the reduction of the

conditional attributes the length of reduction the optimalfitness value the attribute dependency and the time +econvergence of VPRS-GA under the variation for fitnessfunction value for one time is shown in Figure 6 (ie notrepeated in the second group of experiment 1)

(2) 2nd Group Experiment 1 minus β 08 +e algorithm are is 5times according to this group weights the results of the 5groups are given in Table 10 including the reduction of theconditional attributes the length of reduction the optimalfitness value the attribute dependency and the time +e

Table 6 +e statistical results of the second group for experiment 1 with the SVM classifier

Experiment times Accuracy () Sensitivity () Specificity () Time (s)

Reduction 1

1 9300 8600 10000 1164882 9625 9600 9650 1255113 9850 9900 9800 1315094 9725 9850 9600 1344685 9925 10000 9850 144839

Average value 9685 9590 9780 130563

Reduction 2

1 9425 8900 9950 1210962 9725 9700 9750 1286363 9800 9800 9800 1356774 9750 9800 9700 1381965 9875 9900 9850 136691

Average value 9715 9620 9810 132059

Reduction 3

1 9300 8750 9850 877572 9725 9750 9700 1034243 9775 9800 9750 1074114 9775 9850 9700 1123445 9900 10000 9800 113006

Average value 9695 9630 9760 104788

Reduction 4

1 9375 8750 10000 1464172 9650 9750 9550 1547363 9750 9700 9800 1576214 9800 9900 9700 1613555 9925 10000 9850 163381

Average value 9700 9620 9780 156702

Reduction 5

1 9250 8650 9850 1249332 9675 9800 9550 1400573 9800 9800 9800 1451944 9800 9900 9700 1457925 9950 9950 9950 150400

Average value 9695 9620 9770 141275

Table 7 Results of VPRS-GA running 5 times when 1 minus β 06 ω1 1ω2 1ω3 1

Experimenttimes C_ reduction Reduction

lengthOptimal

fitness valueAttribute

dependency degree Time (s)

1 4 5 7 26 27 34 35 41 47 54 55 71 74 75 78 80 83 90 18 minus 14192 07590 6888635

2 4 15 16 19 22 27 28 29 30 35 38 42 45 50 52 53 59 61 6264 65 70 71 72 77 87 88 27 minus 15232 08640 8124857

3 6 17 19 24 28 31 33 34 38 39 43 45 47 48 49 51 55 56 6667 69 70 71 72 76 77 78 80 81 84 87 89 91 92 34 minus 13545 07950 9521511

4 3 6 8 91617 19 20 24 25 28 35 37 39 41 42 46 49 51 52 5459 63 65 66 74 83 86 28 minus 14703 08365 8714839

5 1 7 8 15 17 19 20 23 29 37 45 48 54 60 62 70 73 75 77 7879 86 22 minus 14990 07995 7797617

Average value 258 minus 14532 08108 8209492

10 Mathematical Problems in Engineering

convergence of VPRS-GA under the variation for fitnessfunction value for one time is shown in Figure 8

Each reduction is classified by SVM classifier using themethod of 5-fold cross validation through changing thetraining samples and test samples the results of the five

groups were obtained including accuracy sensitivityspecificity and time (training samples are constructed by800 malignant samples and 800 benign samples testingsamples are constructed by 200 malignant samples and 200benign samples the experiment is repeated 5 times by

ndash08

ndash1

ndash12

ndash14

ndash16

Fitn

ess v

alue

Best ndash141919 Mean ndash128476

0 50 100 150Generation stopping criteria

Best fitnessMean fitness

Figure 7 +e variation of fitness function value in a running process for experiment 1-third group

Table 8 +e statistical results of the third group for experiment 1 with the SVM classifier

Experiment times Accuracy () Sensitivity () Specificity () Time (s)

Reduction 1

1 9275 8600 9950 924922 9725 9750 9700 1074613 9850 9850 9850 1138114 9775 9900 9650 1155605 9875 10000 9750 117022

Average value 9700 9620 9780 109269

Reduction 2

1 9350 8750 9950 1482452 9700 9650 9750 1615353 9775 9850 9700 1664524 9800 9850 9750 1754505 9875 9950 9800 172348

Average value 9700 9610 9790 164806

Reduction 3

1 9125 8300 9950 2019042 9650 9700 9600 2185353 9800 9800 9800 2196054 9625 9900 9350 2230915 9825 10000 9650 236896

Average value 9605 9540 9670 220006

Reduction 4

1 9300 8700 9900 1654542 9675 9600 9750 1724323 9875 9850 9900 1793014 9800 9900 9700 1895605 9900 9950 9850 185249

Average value 9710 9600 9820 178399

Reduction 5

1 9275 8600 9950 1411732 9725 9800 9650 1612953 9900 9950 9850 1589924 9775 9950 9600 1648765 9875 10000 9750 166070

Average value 9710 9660 9760 158481

Table 9 Fitness function weight proportion and β value

Experiment timesω1 1 ω2 1 ω3 0

1 minus β 06 1 minus β 08 1 minus β 1First group experiment Second group experiment +ird group experiment

Mathematical Problems in Engineering 11

changing training samples and testing samples) Finally theaverage values of these five groups are obtained as the finalresult of the reduction and shown in Table 11

In the case of constant weight ϖ and classification errorrate of β 02 (which contains 1 minus β 08) the classificationerror rate is changed on the basis of the attribute dependencyand the length of control reduction +e premature phe-nomena are shown in Figure 8 and evolution progress isterminated early such that the attribute dependency ofreduction 5 was 08405 appeared in attribute dependency onless than 09 compared with first groups of experiment 2attribute dependency declined +e average recognitionaccuracy of the experimental group was 9674 Comparedwith the classification error rate of 04 and inclusion degreeof 06 the accuracy was decreased by 024

(3) 3rd Group Experiment 1 minus β1 +e algorithm is run 5times according to the group weights and the results of the 5groups are shown in Table 12 including the reduction of theconditional attributes the length of reduction the optimalfitness value the attribute dependency and the time +econvergence of VPRS-GA under the variation for fitnessfunction value for one time is shown in Figure 9

Each reduction is classified by SVM classifier using themethod of 5-fold cross validation through changing thetraining samples and test samples the results of the fivegroups were obtained including accuracy sensitivityspecificity and time (training samples are constructed by800 malignant samples and 800 benign samples testingsamples are constructed by 200 malignant samples and 200

benign samples the experiment is repeated 5 times bychanging training samples and testing samples) Finally theaverage values of these five groups are obtained as the finalresult of the reduction and shown in Table 13

In the case of constant weight ϖ and classification errorrate of β= 0 (which contains 1 minus β= 1) the classificationerror rate is reduced and the inclusion degree is improved onthe basis of the attribute dependency and the length ofcontrol reduction +e premature phenomena are shown inFigure 9 and evolution progress is terminated early +eaverage recognition accuracy of the experimental group was9573 which was decreased by 006 compared with thatin the second group In experiment 2 the effect of changingthe classification error rate on the recognition accuracy wasverified by the 3 groups of experiments By continuallyreducing the classification error rate the final recognitionaccuracy has been declining when inclusion degree is 1β= 0 variable precision rough set becomes Pawlak rough setthe recognition accuracy of the recognition accuracy of isminimum which was verified the advantages of variableprecision rough set

343 Experiment 3mdashResearch on Increasing the WeightCoefficient under the Condition in the Same ClassificationError Rate According to experiment 1 and experiment 2we can know that when β 06 ω1 1 ω2 1 ω3 0 therecognition accuracy is the best therefore in the thirdexperiment by increasing the weight of ω 3 groups ofexperiments are performed fitness goals target 1 (attribute

Table 10 Results of VPRS-GA running 5 times when 1 minus β 08 ω1 1ω2 1ω3 0

Experimenttimes C_ reduction Reduction

lengthOptimal fitness

valueAttribute

dependency degree Time (s)

1 8 9 11 12 15 16 17 18 25 26 29 31 35 39 40 41 42 48 5865 67 68 70 83 84 91 26 minus 67816 09490 10002827

2 1 6 8 9 11 12 15 17 21 23 26 28 30 31 34 44 50 56 58 5962 63 64 68 71 75 77 82 89 92 30 minus 67797 09615 9477387

3 6 8 12 14 15 16 17 21 28 35 38 39 45 49 55 58 61 62 6465 77 82 85 23 minus 68694 09070 12866181

4 4 6 7 8 11 12 13 16 17 20 25 26 31 32 34 35 41 42 44 4950 55 58 68 72 74 76 78 79 85 89 92 32 minus 67225 09540 10510220

5 3 6 8 9 10 16 17 26 27 34 36 37 38 40 42 44 46 51 52 6266 67 84 86 87 25 minus 65892 08405 8469324

Average value 272 minus 67484 09224 10265188

ndash55

ndash6

ndash65

ndash7

Fitn

ess v

alue

Best ndash686942 Mean ndash653584

0 50 100 150Generation stopping criteria

Best fitnessMean fitness

Figure 8 +e variation of fitness function value in a running process for experiment 2-second group

12 Mathematical Problems in Engineering

Table 11 +e statistical results of the second group for experiment 2 with the SVM classifier

Experiment times Accuracy () Sensitivity () Specificity () Time (s)

Reduction 1

1 9300 8650 9950 2280072 9575 9700 9450 2376463 9700 9600 9800 2332504 9750 9850 9650 2444915 9925 10000 9850 244816

Average value 9650 9560 9740 237642

Reduction 2

1 9375 8800 9950 2524032 9625 9750 9500 2652893 9800 9700 9900 2655234 9800 9900 9700 2682125 9950 10000 9900 275880

Average value 9710 9630 9790 265461

Reduction 3

1 9275 8750 9800 1807802 9675 9750 9600 1929923 9700 9600 9800 1872434 9775 9950 9600 2084825 9875 10000 9750 203507

Average value 9660 9610 9710 194601

Reduction 4

1 9200 8650 9750 2572602 9700 9750 9650 2730243 9775 9650 9900 2723164 9750 9900 9600 2815545 9900 10000 9800 291471

Average value 9665 9590 9740 275125

Reduction 5

1 9275 8750 9800 1437152 9675 9600 9750 1526373 9750 9800 9700 1589294 9775 9900 9650 1629975 9950 10000 9900 166792

Average value 9685 9610 9760 157014

Table 12 Results of VPRS-GA running 5 times when 1 minus β 1 ω1 1ω2 1ω3 0

Experimenttimes C_ reduction Reduction

lengthOptimal fitness

valueAttribute dependency

degree Time (s)

1 15 44 68 73 79 84 6 minus 27313 07965 114499012 34 51 54 75 80 90 6 minus 27047 08460 96993913 2 34 49 70 71 72 76 81 8 minus 34057 07535 112334894 12 25 78 85 4 minus 22872 09285 11668133

5 6 7 12 13 42 44 55 57 65 66 69 77 81 8687 15 minus 33230 08665 13236077

Average value 78 minus 28903 08382 11457398

ndash1

ndash2

ndash3

ndash4

Fitn

ess v

alue

0 50 100 150Generation stopping criteria

Best fitnessMean fitness

Best ndash340567 Mean ndash330598

Figure 9 +e variation of fitness function value in a running process for experiment 2-third group

Mathematical Problems in Engineering 13

dependency) target 2 (the minimum number of attributesreduction) and target 3 (gene encoding weight function)the three objective functions play an important role in theevaluation of fitness function However the importance offitness function is reduced in these three objectives+erefore in this experiment when the other conditions areunchanged the weight coefficient of the target 1 is increasedto verify the influence of the change in the weight coefficienton the experimental results and they are shown in Table 14

(1) 1st Group Experiment ω1 1 ω2 1 ω3 0 +e al-gorithm are run 5 times according to this group weights theresults of the 5 groups are given in Table 5 including thereduction of the conditional attributes the length of reduc-tion the optimal fitness value the attribute dependency andthe time +e convergence of VPRS-GA under the variationfor fitness function value in one time is shown in Figure 6 (ienot repeated for the second group of experiment 1)

(2) 2nd Group Experiment ω1 2 ω2 1 ω3 0 +ealgorithm is run 5 times according to this group weights theresults of the 5 groups are given in Table 15 including thereduction of the conditional attributes the length of re-duction the optimal fitness value the attribute dependencyand the time +e convergence of VPRS-GA under thevariation for fitness function value in one time is shown inFigure 10

Each reduction is classified by SVM classifier using themethod of 5-fold cross validation through changing thetraining samples and test samples the results of the fivegroups were obtained including accuracy sensitivityspecificity and time (training samples are constructed by800 malignant samples and 800 benign samples testingsamples are constructed by 200 malignant samples and 200benign samples the experiment is repeated 5 times bychanging training samples and testing samples) Finally theaverage values of these five groups are obtained as the finalresult of the reduction and shown in Table 16

+e experimental group in the case of 1 minus β= 06 un-changed the weight of ω1 was increased +e attributedependency and the optimal fitness function are relativelyhigh the average precision of reduction 1 reduction 2 andreduction 3 in Table 16 is more than 97 and that of re-duction 2 is even up to 9725 +e average recognitionaccuracy of the experimental group is 9703 which ishigher than that of the first group

Table 13 +e statistical results of the third group for experiment 2 with the SVM classifier

Experiment times Accuracy () Sensitivity () Specificity () Time (s)

Reduction 1

1 9225 8450 10000 812712 9550 9700 9400 945833 9575 9400 9750 881984 9600 9800 9400 937545 9725 9900 9550 98691

Average value 9535 9450 9620 91299

Reduction 2

1 9200 8450 9950 648942 9625 9550 9700 801983 9525 9300 9750 773374 9600 9750 9450 760125 9800 10000 9600 82763

Average value 9550 9410 9690 76241

Reduction 3

1 9200 8450 9950 648942 9625 9550 9700 801983 9525 9300 9750 773374 9600 9750 9450 760125 9800 10000 9600 82763

Average value 9550 9410 9690 76241

Reduction 4

1 9275 8550 10000 672642 9675 9600 9750 784673 9600 9450 9750 730224 9575 9750 9400 794605 9800 10000 9600 84184

Average value 9585 9470 9700 76479

Reduction 5

1 9200 8450 9950 1147192 9625 9750 9500 1287053 9850 9900 9800 1320494 9775 9950 9600 1335135 9850 10000 9700 133144

Average value 9660 9610 9710 128426

Table 14 Fitness function weight proportion and β value

Experiment times1 minus β 06

ω1 ω2 ω3First group experiment 1 1 0Second group experiment 2 1 0+ird group experiment 3 1 0

14 Mathematical Problems in Engineering

ndash2

ndash25

ndash3

Fitn

ess v

alue

0 50 100 150Generation stopping criteria

Best fitnessMean fitness

Best ndash2915 Mean ndash291446

Figure 10 +e variation of fitness function value in a running process for experiment 3-second group

Table 15 Results of VPRS-GA running 5 times when 1 minus β 06 ω1 2ω2 1ω3 0

Experimenttimes C_ reduction Reduction

lengthOptimal fitness

valueAttribute dependency

degree Time (s)

1 2 3 4 5 11 13 16 18 24 30 34 37 39 41 42 51 55 64 7077 78 82 22 minus 34859 09060 21515464

2 8 9 11 12 14 15 23 25 26 29 30 33 37 42 43 45 46 5060 61 69 74 80 87 89 25 minus 30845 09390 42761634

3 8 11 12 13 16 18 19 24 29 36 37 43 64 65 68 71 86 9192 19 minus 35039 09150 26197164

4 2 3 4 8 10 11 12 13 15 16 19 23 25 30 48 55 64 65 6874 77 80 81 83 84 86 89 27 minus 29150 09575 44271631

5 5 8 911 121517 23 25 29 31 36 39 41 48 54 59 63 8083 86 89 22 minus 29920 09525 43161464

Average value 23 minus 31962 09340 35581471

Table 16 +e statistical results of the second group for experiment 3 with the SVM classifier

Experiment times Accuracy () Sensitivity () Specificity () Time (s)

Reduction 1

1 9275 8600 9950 1884972 9725 9800 9650 1571623 9850 9900 9800 1586914 9800 9900 9700 1646035 9950 10000 9900 161914

Average value 9720 9640 9800 166173

Reduction 2

1 9450 8950 9950 1908132 9675 9800 9550 2002513 9775 9800 9750 1970084 9850 9900 9800 2009245 9875 9900 9850 209245

Average value 9725 9670 9780 199648

Reduction 3

1 9400 8800 10000 1313692 9725 9800 9650 1447973 9800 9800 9800 1426624 9725 9850 9600 1471905 9925 10000 9850 148799

Average value 9715 9650 9780 142963

Reduction 4

1 9350 8750 9950 2404562 9700 9750 9650 2520823 9800 9800 9800 2511754 9775 9950 9600 2701885 9825 10000 9650 267471

Average value 9690 9650 9730 256274

Reduction 5

1 9325 8800 9850 1809592 9600 9800 9400 1965633 9750 9750 9750 1967234 9800 9900 9700 2078295 9850 9950 9750 219703

Average value 9665 9640 9690 200355

Mathematical Problems in Engineering 15

Table 17 Results of VPRS-GA running 5 times when 1 minus β 1 ω1 1ω2 1ω3 0

Experimenttimes C_ reduction Reduction

lengthOptimal fitness

valueAttribute

dependency degree Time (s)

1 3 4 5 8 9 11 12 17 19 29 34 35 38 46 52 53 55 59 63 6672 75 77 78 79 87 92 27 minus 38867 09550 28981789

2 4 8 9 11 12 15 17 29 33 37 38 39 42 43 48 55 67 73 7881 83 84 88 89 90 25 minus 38167 09715 55783772

3 2 3 4 8 9 10 11 12 13 15 16 19 24 25 30 36 49 54 55 6064 67 68 70 74 77 83 85 86 91 30 minus 38807 09530 34831096

4 4 5 7 11 12 14 15 17 25 29 33 36 39 41 42 47 48 50 5556 58 62 67 69 72 74 77 84 86 90 91 31 minus 39430 09665 35742822

5 3 4 5 8 9 11 12 17 19 29 34 35 38 46 52 53 55 59 63 6672 75 77 78 79 87 92 27 minus 38867 09550 27919582

Average value 28 minus 38827 09602 36651812

ndash3

ndash35

ndash40 50 100 150

Generation stopping criteria

Fitn

ess v

alue

Best fitnessMean fitness

Best ndash394298 Mean ndash393327

Figure 11 +e variation of fitness function value in a running process for experiment 3-third group

Table 18 +e statistical results of the Second group for experiment 3 with the SVM classifier

Experiment times Accuracy () Sensitivity () Specificity () Time (s)

Reduction 1

1 9200 8700 9700 2187172 9750 9750 9750 2105503 9850 9850 9850 2032064 9800 9900 9700 2211645 9925 10000 9850 272536

Average value 9705 9640 9770 225235

Reduction 2

1 9400 8850 9950 2331232 9575 9750 9400 2433493 9750 9700 9800 2442024 9775 9900 9650 2566075 9900 9950 9850 259071

Average value 9680 9630 9730 247270

Reduction 3

1 9275 8650 9900 2525842 9625 9750 9500 2624123 9775 9800 9750 2601274 9775 9900 9650 2686705 9875 10000 9750 265387

Average value 9665 9620 9710 261836

Reduction 4

1 9150 8550 9750 2532312 9625 9750 9500 2649433 9750 9700 9800 2752834 9800 9950 9650 3229545 9825 9950 9700 277432

Average value 9630 9580 9680 278769

Reduction 5

1 9200 8800 9600 1951962 9700 9700 9700 2148893 9825 9800 9850 2036124 9850 10000 9700 2133615 9900 9900 9900 225526

Average value 9695 9640 9750 210517

16 Mathematical Problems in Engineering

(3) 3rd Group Experiment ω1 3 ω2 1 ω3 0 +e al-gorithm is run 5 times according to the group weights andthe results of the 5 groups are given in Table 17 including thereduction of the conditional attributes the length of re-duction the optimal fitness value the attribute dependencyand the time +e convergence of VPRS-GA under thevariation for fitness function value for one time is shown inFigure 11

Each reduction is classified by SVM classifier using themethod of 5-fold cross validation through changing thetraining samples and test samples the results of the fivegroups were obtained including accuracy sensitivityspecificity and time (training samples are constructed by800 malignant samples and 800 benign samples testingsamples are constructed by 200 malignant samples and 200benign samples the experiment is repeated 5 times bychanging training samples and testing samples) Finally theaverage values of these five groups are obtained as the finalresult of the reduction and shown in Table 18

+e experiment in the case of 1 minus β 06 unchangedincrease the weight of the ω1 ω1 3 ω2 1 ω3 0 InTable 18 the recognition accuracy of reduction 1 is over 97only +e average recognition accuracy of the experimentalgroup is 9675 and the accuracy is decreased by 028compared with that in the other second groups +e threegroups of experiment 3 the purpose is to verify whether theexperimental accuracy is influenced by increasing theweight +e experimental results show that the accuracy ofsecond group for experimental weight 2 1 0 comparedwith first group experiment when 1 1 0 is high but thethird groups of experimental weight was 3 1 0 and theaccuracy declined therefore the weight of 2 1 0 is the bestchoice for this experiment

4 Conclusions

Aiming at the deficiency of the traditional rough set modelthis paper proposes a new feature selection model based ongenetic algorithm and variable precision rough set by in-troducing the β value the rigid inclusion of the approxi-mation for the traditional rough set is relaxed and then wedesign the 3 kinds of experiments by constructing the de-cision information table of the PETCT feature for lungtumor ROI +e first type of experiment is the inclusion of1 minus β 06 and different values of ω made a total of threegroups of experiments the experimental results show thatthe better recognition accuracy can be obtained when theweight is 1 1 0 and the results show that the gene codingweight function has no effect on the fitness function For thesecond type of experiments ϖ1 1ω2 1 ω3 0according to the different values of β to do three groups ofexperiments the results show that the recognition accuracyof 1 minus β 06 is the best which shows that the larger the βvalue is the lower approximate cardinality will be largerthen the relative accuracy will increase For the third type ofexperiments 1 minus β 06 ω value is increased to achieve thebest fitness function in order to achieve the best results +eexperimental results show that the recognition accuracy isbetter than the others when the weight value is 2 1 0 so it

is better to solve the problem by increasing the proportion ofattribute dependency +rough the above experiments it isshown that the high-dimensional feature selection algorithmbased on genetic algorithm and variable precision rough setcan solve the multiobjective optimization problem wellHowever when the fitness function and its parameters areapplied in the specific application it is necessary to analyzethe specific problems

Data Availability

+e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

+e authors declare no conflicts of interest

Acknowledgments

+is work was supported by National Natural ScienceFoundation of China (Grant nos 61561040 and 61876121)First-Class Disciplines Foundation of Ningxia (NoNXYLXK2017B09)

References

[1] S Luo D Miao Z Zhang Y Zhang and S Hu ldquoA neigh-borhood rough set model with nominal metric embeddingrdquoInformation Sciences vol 520 pp 373ndash388 2020

[2] B Barman and S Patra ldquoVariable precision rough set basedunsupervised band selection technique for hyperspectralimage classificationrdquo Knowledge-Based Systems vol 1936Article ID 105414 2020

[3] Y Chenyi and L Jinjin ldquoApproximate attribute reductionunder variable precision rough set βrdquo Journal of ShandongUniversity vol 11 pp 17ndash21 2011

[4] S Xiaowei Research on Hierarchical Model of Attribute Re-duction in Variable Precision Rough Set Central SouthUniversity Changsha China 2013

[5] Z Jie and W Jiayang ldquoAnalysis of reduction feature ofvariable precision rough set modelrdquo Computer ApplicationResearch vol 7 pp 12ndash15 2007

[6] Z Pei and Z Qinghua ldquoFCM clustering algorithm based onvariable precision rough setrdquo Journal of Shanxi Universityvol 3 pp 342ndash348 2016

[7] C Hao and Y Junan ldquoAttribute kernel and minimum at-tribute reduction algorithm of variable precision rough setrdquoActa Sinica Sinica vol 5 pp 1011ndash1017 2012

[8] S Xu X Yang H Yu D-J Yu J Yang and E CC TsangldquoMulti-label learning with label-specific feature reductionrdquoKnowledge-Based Systems vol 104 pp 52ndash61 2016

[9] I Maryam and G Hassan ldquoFeature space discriminantanalysis for hyperspectral data feature reductionrdquo ISPRSJournal of Photogrammetry and Remote Sensing vol 102pp 1ndash13 2015

[10] S Q Wang C Y Gao C Luo G M Zheng and Y N ZhouldquoResearch on feature selectionattribute reduction methodbased on rough set theoryrdquo Procedia Computer Sciencevol 154 pp 194ndash198e 2019

[11] A W Omar M Azzam O Hadi and B Jamal ldquoCEAP SVM-based intelligent detection model for clustered vehicular ad

Mathematical Problems in Engineering 17

hoc networksrdquo Expert Systems with Applications vol 50pp 40ndash54 2016

[12] H Lee and Y-P P Chen ldquoImage based computer aideddiagnosis system for cancer detectionrdquo Expert Systems withApplications vol 42 no 12 pp 5356ndash5365 2015

[13] J A Guy and P L Harold ldquoAfter detection the improvedaccuracy of lung cancer assessment using radiologic com-puter-aided diagnosisrdquo Academic Radiology vol 23 no 2pp 186ndash191 2016

[14] E Kiyonori T Shodayu J Binghu et al ldquoPleural invasion byperipheral lung cancer prediction with three-dimensionalCTrdquo Academic Radiology vol 3 pp 310ndash319 2015

[15] B Koohestani ldquoA crossover operator for improving the ef-ficiency of permutation-based genetic algorithmsrdquo ExpertSystems with Applications vol 1511 Article ID 113381 2020

[16] N K Lee X Li and D Wang ldquoA comprehensive survey ongenetic algorithms for DNA motif predictionrdquo InformationSciences vol 466 pp 25ndash43 2018

[17] S Shibao and Y Leilei ldquoResearch on variable precision roughset model and its applicationrdquo Computer Engineering andApplication vol 07 pp 10ndash13 2009

[18] T Xiaolong Several Problems of Multi Granularity VariablePrecision Rough Set Guangxi University For NationalitiesNanning China 2015

[19] W Xueming Research on Several Rough Set Models andNeural Network University of Electronic Science and Tech-nology of China Chengdu China 2013

[20] T Sun J Wang X Li et al ldquoComparative evaluation ofsupport vector machines for computer aided diagnosis of lungcancer in CT based on a multi-dimensional data setrdquo Com-puter Methods and Programs in Biomedicine vol 111 no 2pp 519ndash524 2013

[21] Z Yang T Ouyang X Fu and X Peng ldquoA decision-makingalgorithm for online shopping using deep-learning-basedopinion pairs mining and q -rung orthopair fuzzy interactionHeronianmean operatorsrdquo International Journal of IntelligentSystems vol 35 no 5 pp 783ndash825 2020

[22] W Chen C Lin C Li et al ldquoTracing the evolution of 3Dprinting technology in China using LDA-based patent ab-stract miningrdquo IEEE Transactions on Engineering Manage-men vol 36 pp 1ndash11 2020

18 Mathematical Problems in Engineering

342 Experiment 2mdashResearch on Different ClassificationError Rates under the Condition in the Same WeightCoefficient According to experiment 1 we can see thatwhen ω1 1 ω2 1 ω3 0 the experimental results arethe best so in experiment 2 the case of the weight value ofwas unchanged ω1 1 ω2 1 ω3 0 and the β value waschanged and they are shown in Table 9

(1) 1st Group Experiment 1 minus β 06 +e algorithm is run 5times according to this group weights the results of the 5groups are shown in Table 5 including the reduction of the

conditional attributes the length of reduction the optimalfitness value the attribute dependency and the time +econvergence of VPRS-GA under the variation for fitnessfunction value for one time is shown in Figure 6 (ie notrepeated in the second group of experiment 1)

(2) 2nd Group Experiment 1 minus β 08 +e algorithm are is 5times according to this group weights the results of the 5groups are given in Table 10 including the reduction of theconditional attributes the length of reduction the optimalfitness value the attribute dependency and the time +e

Table 6 +e statistical results of the second group for experiment 1 with the SVM classifier

Experiment times Accuracy () Sensitivity () Specificity () Time (s)

Reduction 1

1 9300 8600 10000 1164882 9625 9600 9650 1255113 9850 9900 9800 1315094 9725 9850 9600 1344685 9925 10000 9850 144839

Average value 9685 9590 9780 130563

Reduction 2

1 9425 8900 9950 1210962 9725 9700 9750 1286363 9800 9800 9800 1356774 9750 9800 9700 1381965 9875 9900 9850 136691

Average value 9715 9620 9810 132059

Reduction 3

1 9300 8750 9850 877572 9725 9750 9700 1034243 9775 9800 9750 1074114 9775 9850 9700 1123445 9900 10000 9800 113006

Average value 9695 9630 9760 104788

Reduction 4

1 9375 8750 10000 1464172 9650 9750 9550 1547363 9750 9700 9800 1576214 9800 9900 9700 1613555 9925 10000 9850 163381

Average value 9700 9620 9780 156702

Reduction 5

1 9250 8650 9850 1249332 9675 9800 9550 1400573 9800 9800 9800 1451944 9800 9900 9700 1457925 9950 9950 9950 150400

Average value 9695 9620 9770 141275

Table 7 Results of VPRS-GA running 5 times when 1 minus β 06 ω1 1ω2 1ω3 1

Experimenttimes C_ reduction Reduction

lengthOptimal

fitness valueAttribute

dependency degree Time (s)

1 4 5 7 26 27 34 35 41 47 54 55 71 74 75 78 80 83 90 18 minus 14192 07590 6888635

2 4 15 16 19 22 27 28 29 30 35 38 42 45 50 52 53 59 61 6264 65 70 71 72 77 87 88 27 minus 15232 08640 8124857

3 6 17 19 24 28 31 33 34 38 39 43 45 47 48 49 51 55 56 6667 69 70 71 72 76 77 78 80 81 84 87 89 91 92 34 minus 13545 07950 9521511

4 3 6 8 91617 19 20 24 25 28 35 37 39 41 42 46 49 51 52 5459 63 65 66 74 83 86 28 minus 14703 08365 8714839

5 1 7 8 15 17 19 20 23 29 37 45 48 54 60 62 70 73 75 77 7879 86 22 minus 14990 07995 7797617

Average value 258 minus 14532 08108 8209492

10 Mathematical Problems in Engineering

convergence of VPRS-GA under the variation for fitnessfunction value for one time is shown in Figure 8

Each reduction is classified by SVM classifier using themethod of 5-fold cross validation through changing thetraining samples and test samples the results of the five

groups were obtained including accuracy sensitivityspecificity and time (training samples are constructed by800 malignant samples and 800 benign samples testingsamples are constructed by 200 malignant samples and 200benign samples the experiment is repeated 5 times by

ndash08

ndash1

ndash12

ndash14

ndash16

Fitn

ess v

alue

Best ndash141919 Mean ndash128476

0 50 100 150Generation stopping criteria

Best fitnessMean fitness

Figure 7 +e variation of fitness function value in a running process for experiment 1-third group

Table 8 +e statistical results of the third group for experiment 1 with the SVM classifier

Experiment times Accuracy () Sensitivity () Specificity () Time (s)

Reduction 1

1 9275 8600 9950 924922 9725 9750 9700 1074613 9850 9850 9850 1138114 9775 9900 9650 1155605 9875 10000 9750 117022

Average value 9700 9620 9780 109269

Reduction 2

1 9350 8750 9950 1482452 9700 9650 9750 1615353 9775 9850 9700 1664524 9800 9850 9750 1754505 9875 9950 9800 172348

Average value 9700 9610 9790 164806

Reduction 3

1 9125 8300 9950 2019042 9650 9700 9600 2185353 9800 9800 9800 2196054 9625 9900 9350 2230915 9825 10000 9650 236896

Average value 9605 9540 9670 220006

Reduction 4

1 9300 8700 9900 1654542 9675 9600 9750 1724323 9875 9850 9900 1793014 9800 9900 9700 1895605 9900 9950 9850 185249

Average value 9710 9600 9820 178399

Reduction 5

1 9275 8600 9950 1411732 9725 9800 9650 1612953 9900 9950 9850 1589924 9775 9950 9600 1648765 9875 10000 9750 166070

Average value 9710 9660 9760 158481

Table 9 Fitness function weight proportion and β value

Experiment timesω1 1 ω2 1 ω3 0

1 minus β 06 1 minus β 08 1 minus β 1First group experiment Second group experiment +ird group experiment

Mathematical Problems in Engineering 11

changing training samples and testing samples) Finally theaverage values of these five groups are obtained as the finalresult of the reduction and shown in Table 11

In the case of constant weight ϖ and classification errorrate of β 02 (which contains 1 minus β 08) the classificationerror rate is changed on the basis of the attribute dependencyand the length of control reduction +e premature phe-nomena are shown in Figure 8 and evolution progress isterminated early such that the attribute dependency ofreduction 5 was 08405 appeared in attribute dependency onless than 09 compared with first groups of experiment 2attribute dependency declined +e average recognitionaccuracy of the experimental group was 9674 Comparedwith the classification error rate of 04 and inclusion degreeof 06 the accuracy was decreased by 024

(3) 3rd Group Experiment 1 minus β1 +e algorithm is run 5times according to the group weights and the results of the 5groups are shown in Table 12 including the reduction of theconditional attributes the length of reduction the optimalfitness value the attribute dependency and the time +econvergence of VPRS-GA under the variation for fitnessfunction value for one time is shown in Figure 9

Each reduction is classified by SVM classifier using themethod of 5-fold cross validation through changing thetraining samples and test samples the results of the fivegroups were obtained including accuracy sensitivityspecificity and time (training samples are constructed by800 malignant samples and 800 benign samples testingsamples are constructed by 200 malignant samples and 200

benign samples the experiment is repeated 5 times bychanging training samples and testing samples) Finally theaverage values of these five groups are obtained as the finalresult of the reduction and shown in Table 13

In the case of constant weight ϖ and classification errorrate of β= 0 (which contains 1 minus β= 1) the classificationerror rate is reduced and the inclusion degree is improved onthe basis of the attribute dependency and the length ofcontrol reduction +e premature phenomena are shown inFigure 9 and evolution progress is terminated early +eaverage recognition accuracy of the experimental group was9573 which was decreased by 006 compared with thatin the second group In experiment 2 the effect of changingthe classification error rate on the recognition accuracy wasverified by the 3 groups of experiments By continuallyreducing the classification error rate the final recognitionaccuracy has been declining when inclusion degree is 1β= 0 variable precision rough set becomes Pawlak rough setthe recognition accuracy of the recognition accuracy of isminimum which was verified the advantages of variableprecision rough set

343 Experiment 3mdashResearch on Increasing the WeightCoefficient under the Condition in the Same ClassificationError Rate According to experiment 1 and experiment 2we can know that when β 06 ω1 1 ω2 1 ω3 0 therecognition accuracy is the best therefore in the thirdexperiment by increasing the weight of ω 3 groups ofexperiments are performed fitness goals target 1 (attribute

Table 10 Results of VPRS-GA running 5 times when 1 minus β 08 ω1 1ω2 1ω3 0

Experimenttimes C_ reduction Reduction

lengthOptimal fitness

valueAttribute

dependency degree Time (s)

1 8 9 11 12 15 16 17 18 25 26 29 31 35 39 40 41 42 48 5865 67 68 70 83 84 91 26 minus 67816 09490 10002827

2 1 6 8 9 11 12 15 17 21 23 26 28 30 31 34 44 50 56 58 5962 63 64 68 71 75 77 82 89 92 30 minus 67797 09615 9477387

3 6 8 12 14 15 16 17 21 28 35 38 39 45 49 55 58 61 62 6465 77 82 85 23 minus 68694 09070 12866181

4 4 6 7 8 11 12 13 16 17 20 25 26 31 32 34 35 41 42 44 4950 55 58 68 72 74 76 78 79 85 89 92 32 minus 67225 09540 10510220

5 3 6 8 9 10 16 17 26 27 34 36 37 38 40 42 44 46 51 52 6266 67 84 86 87 25 minus 65892 08405 8469324

Average value 272 minus 67484 09224 10265188

ndash55

ndash6

ndash65

ndash7

Fitn

ess v

alue

Best ndash686942 Mean ndash653584

0 50 100 150Generation stopping criteria

Best fitnessMean fitness

Figure 8 +e variation of fitness function value in a running process for experiment 2-second group

12 Mathematical Problems in Engineering

Table 11 +e statistical results of the second group for experiment 2 with the SVM classifier

Experiment times Accuracy () Sensitivity () Specificity () Time (s)

Reduction 1

1 9300 8650 9950 2280072 9575 9700 9450 2376463 9700 9600 9800 2332504 9750 9850 9650 2444915 9925 10000 9850 244816

Average value 9650 9560 9740 237642

Reduction 2

1 9375 8800 9950 2524032 9625 9750 9500 2652893 9800 9700 9900 2655234 9800 9900 9700 2682125 9950 10000 9900 275880

Average value 9710 9630 9790 265461

Reduction 3

1 9275 8750 9800 1807802 9675 9750 9600 1929923 9700 9600 9800 1872434 9775 9950 9600 2084825 9875 10000 9750 203507

Average value 9660 9610 9710 194601

Reduction 4

1 9200 8650 9750 2572602 9700 9750 9650 2730243 9775 9650 9900 2723164 9750 9900 9600 2815545 9900 10000 9800 291471

Average value 9665 9590 9740 275125

Reduction 5

1 9275 8750 9800 1437152 9675 9600 9750 1526373 9750 9800 9700 1589294 9775 9900 9650 1629975 9950 10000 9900 166792

Average value 9685 9610 9760 157014

Table 12 Results of VPRS-GA running 5 times when 1 minus β 1 ω1 1ω2 1ω3 0

Experimenttimes C_ reduction Reduction

lengthOptimal fitness

valueAttribute dependency

degree Time (s)

1 15 44 68 73 79 84 6 minus 27313 07965 114499012 34 51 54 75 80 90 6 minus 27047 08460 96993913 2 34 49 70 71 72 76 81 8 minus 34057 07535 112334894 12 25 78 85 4 minus 22872 09285 11668133

5 6 7 12 13 42 44 55 57 65 66 69 77 81 8687 15 minus 33230 08665 13236077

Average value 78 minus 28903 08382 11457398

ndash1

ndash2

ndash3

ndash4

Fitn

ess v

alue

0 50 100 150Generation stopping criteria

Best fitnessMean fitness

Best ndash340567 Mean ndash330598

Figure 9 +e variation of fitness function value in a running process for experiment 2-third group

Mathematical Problems in Engineering 13

dependency) target 2 (the minimum number of attributesreduction) and target 3 (gene encoding weight function)the three objective functions play an important role in theevaluation of fitness function However the importance offitness function is reduced in these three objectives+erefore in this experiment when the other conditions areunchanged the weight coefficient of the target 1 is increasedto verify the influence of the change in the weight coefficienton the experimental results and they are shown in Table 14

(1) 1st Group Experiment ω1 1 ω2 1 ω3 0 +e al-gorithm are run 5 times according to this group weights theresults of the 5 groups are given in Table 5 including thereduction of the conditional attributes the length of reduc-tion the optimal fitness value the attribute dependency andthe time +e convergence of VPRS-GA under the variationfor fitness function value in one time is shown in Figure 6 (ienot repeated for the second group of experiment 1)

(2) 2nd Group Experiment ω1 2 ω2 1 ω3 0 +ealgorithm is run 5 times according to this group weights theresults of the 5 groups are given in Table 15 including thereduction of the conditional attributes the length of re-duction the optimal fitness value the attribute dependencyand the time +e convergence of VPRS-GA under thevariation for fitness function value in one time is shown inFigure 10

Each reduction is classified by SVM classifier using themethod of 5-fold cross validation through changing thetraining samples and test samples the results of the fivegroups were obtained including accuracy sensitivityspecificity and time (training samples are constructed by800 malignant samples and 800 benign samples testingsamples are constructed by 200 malignant samples and 200benign samples the experiment is repeated 5 times bychanging training samples and testing samples) Finally theaverage values of these five groups are obtained as the finalresult of the reduction and shown in Table 16

+e experimental group in the case of 1 minus β= 06 un-changed the weight of ω1 was increased +e attributedependency and the optimal fitness function are relativelyhigh the average precision of reduction 1 reduction 2 andreduction 3 in Table 16 is more than 97 and that of re-duction 2 is even up to 9725 +e average recognitionaccuracy of the experimental group is 9703 which ishigher than that of the first group

Table 13 +e statistical results of the third group for experiment 2 with the SVM classifier

Experiment times Accuracy () Sensitivity () Specificity () Time (s)

Reduction 1

1 9225 8450 10000 812712 9550 9700 9400 945833 9575 9400 9750 881984 9600 9800 9400 937545 9725 9900 9550 98691

Average value 9535 9450 9620 91299

Reduction 2

1 9200 8450 9950 648942 9625 9550 9700 801983 9525 9300 9750 773374 9600 9750 9450 760125 9800 10000 9600 82763

Average value 9550 9410 9690 76241

Reduction 3

1 9200 8450 9950 648942 9625 9550 9700 801983 9525 9300 9750 773374 9600 9750 9450 760125 9800 10000 9600 82763

Average value 9550 9410 9690 76241

Reduction 4

1 9275 8550 10000 672642 9675 9600 9750 784673 9600 9450 9750 730224 9575 9750 9400 794605 9800 10000 9600 84184

Average value 9585 9470 9700 76479

Reduction 5

1 9200 8450 9950 1147192 9625 9750 9500 1287053 9850 9900 9800 1320494 9775 9950 9600 1335135 9850 10000 9700 133144

Average value 9660 9610 9710 128426

Table 14 Fitness function weight proportion and β value

Experiment times1 minus β 06

ω1 ω2 ω3First group experiment 1 1 0Second group experiment 2 1 0+ird group experiment 3 1 0

14 Mathematical Problems in Engineering

ndash2

ndash25

ndash3

Fitn

ess v

alue

0 50 100 150Generation stopping criteria

Best fitnessMean fitness

Best ndash2915 Mean ndash291446

Figure 10 +e variation of fitness function value in a running process for experiment 3-second group

Table 15 Results of VPRS-GA running 5 times when 1 minus β 06 ω1 2ω2 1ω3 0

Experimenttimes C_ reduction Reduction

lengthOptimal fitness

valueAttribute dependency

degree Time (s)

1 2 3 4 5 11 13 16 18 24 30 34 37 39 41 42 51 55 64 7077 78 82 22 minus 34859 09060 21515464

2 8 9 11 12 14 15 23 25 26 29 30 33 37 42 43 45 46 5060 61 69 74 80 87 89 25 minus 30845 09390 42761634

3 8 11 12 13 16 18 19 24 29 36 37 43 64 65 68 71 86 9192 19 minus 35039 09150 26197164

4 2 3 4 8 10 11 12 13 15 16 19 23 25 30 48 55 64 65 6874 77 80 81 83 84 86 89 27 minus 29150 09575 44271631

5 5 8 911 121517 23 25 29 31 36 39 41 48 54 59 63 8083 86 89 22 minus 29920 09525 43161464

Average value 23 minus 31962 09340 35581471

Table 16 +e statistical results of the second group for experiment 3 with the SVM classifier

Experiment times Accuracy () Sensitivity () Specificity () Time (s)

Reduction 1

1 9275 8600 9950 1884972 9725 9800 9650 1571623 9850 9900 9800 1586914 9800 9900 9700 1646035 9950 10000 9900 161914

Average value 9720 9640 9800 166173

Reduction 2

1 9450 8950 9950 1908132 9675 9800 9550 2002513 9775 9800 9750 1970084 9850 9900 9800 2009245 9875 9900 9850 209245

Average value 9725 9670 9780 199648

Reduction 3

1 9400 8800 10000 1313692 9725 9800 9650 1447973 9800 9800 9800 1426624 9725 9850 9600 1471905 9925 10000 9850 148799

Average value 9715 9650 9780 142963

Reduction 4

1 9350 8750 9950 2404562 9700 9750 9650 2520823 9800 9800 9800 2511754 9775 9950 9600 2701885 9825 10000 9650 267471

Average value 9690 9650 9730 256274

Reduction 5

1 9325 8800 9850 1809592 9600 9800 9400 1965633 9750 9750 9750 1967234 9800 9900 9700 2078295 9850 9950 9750 219703

Average value 9665 9640 9690 200355

Mathematical Problems in Engineering 15

Table 17 Results of VPRS-GA running 5 times when 1 minus β 1 ω1 1ω2 1ω3 0

Experimenttimes C_ reduction Reduction

lengthOptimal fitness

valueAttribute

dependency degree Time (s)

1 3 4 5 8 9 11 12 17 19 29 34 35 38 46 52 53 55 59 63 6672 75 77 78 79 87 92 27 minus 38867 09550 28981789

2 4 8 9 11 12 15 17 29 33 37 38 39 42 43 48 55 67 73 7881 83 84 88 89 90 25 minus 38167 09715 55783772

3 2 3 4 8 9 10 11 12 13 15 16 19 24 25 30 36 49 54 55 6064 67 68 70 74 77 83 85 86 91 30 minus 38807 09530 34831096

4 4 5 7 11 12 14 15 17 25 29 33 36 39 41 42 47 48 50 5556 58 62 67 69 72 74 77 84 86 90 91 31 minus 39430 09665 35742822

5 3 4 5 8 9 11 12 17 19 29 34 35 38 46 52 53 55 59 63 6672 75 77 78 79 87 92 27 minus 38867 09550 27919582

Average value 28 minus 38827 09602 36651812

ndash3

ndash35

ndash40 50 100 150

Generation stopping criteria

Fitn

ess v

alue

Best fitnessMean fitness

Best ndash394298 Mean ndash393327

Figure 11 +e variation of fitness function value in a running process for experiment 3-third group

Table 18 +e statistical results of the Second group for experiment 3 with the SVM classifier

Experiment times Accuracy () Sensitivity () Specificity () Time (s)

Reduction 1

1 9200 8700 9700 2187172 9750 9750 9750 2105503 9850 9850 9850 2032064 9800 9900 9700 2211645 9925 10000 9850 272536

Average value 9705 9640 9770 225235

Reduction 2

1 9400 8850 9950 2331232 9575 9750 9400 2433493 9750 9700 9800 2442024 9775 9900 9650 2566075 9900 9950 9850 259071

Average value 9680 9630 9730 247270

Reduction 3

1 9275 8650 9900 2525842 9625 9750 9500 2624123 9775 9800 9750 2601274 9775 9900 9650 2686705 9875 10000 9750 265387

Average value 9665 9620 9710 261836

Reduction 4

1 9150 8550 9750 2532312 9625 9750 9500 2649433 9750 9700 9800 2752834 9800 9950 9650 3229545 9825 9950 9700 277432

Average value 9630 9580 9680 278769

Reduction 5

1 9200 8800 9600 1951962 9700 9700 9700 2148893 9825 9800 9850 2036124 9850 10000 9700 2133615 9900 9900 9900 225526

Average value 9695 9640 9750 210517

16 Mathematical Problems in Engineering

(3) 3rd Group Experiment ω1 3 ω2 1 ω3 0 +e al-gorithm is run 5 times according to the group weights andthe results of the 5 groups are given in Table 17 including thereduction of the conditional attributes the length of re-duction the optimal fitness value the attribute dependencyand the time +e convergence of VPRS-GA under thevariation for fitness function value for one time is shown inFigure 11

Each reduction is classified by SVM classifier using themethod of 5-fold cross validation through changing thetraining samples and test samples the results of the fivegroups were obtained including accuracy sensitivityspecificity and time (training samples are constructed by800 malignant samples and 800 benign samples testingsamples are constructed by 200 malignant samples and 200benign samples the experiment is repeated 5 times bychanging training samples and testing samples) Finally theaverage values of these five groups are obtained as the finalresult of the reduction and shown in Table 18

+e experiment in the case of 1 minus β 06 unchangedincrease the weight of the ω1 ω1 3 ω2 1 ω3 0 InTable 18 the recognition accuracy of reduction 1 is over 97only +e average recognition accuracy of the experimentalgroup is 9675 and the accuracy is decreased by 028compared with that in the other second groups +e threegroups of experiment 3 the purpose is to verify whether theexperimental accuracy is influenced by increasing theweight +e experimental results show that the accuracy ofsecond group for experimental weight 2 1 0 comparedwith first group experiment when 1 1 0 is high but thethird groups of experimental weight was 3 1 0 and theaccuracy declined therefore the weight of 2 1 0 is the bestchoice for this experiment

4 Conclusions

Aiming at the deficiency of the traditional rough set modelthis paper proposes a new feature selection model based ongenetic algorithm and variable precision rough set by in-troducing the β value the rigid inclusion of the approxi-mation for the traditional rough set is relaxed and then wedesign the 3 kinds of experiments by constructing the de-cision information table of the PETCT feature for lungtumor ROI +e first type of experiment is the inclusion of1 minus β 06 and different values of ω made a total of threegroups of experiments the experimental results show thatthe better recognition accuracy can be obtained when theweight is 1 1 0 and the results show that the gene codingweight function has no effect on the fitness function For thesecond type of experiments ϖ1 1ω2 1 ω3 0according to the different values of β to do three groups ofexperiments the results show that the recognition accuracyof 1 minus β 06 is the best which shows that the larger the βvalue is the lower approximate cardinality will be largerthen the relative accuracy will increase For the third type ofexperiments 1 minus β 06 ω value is increased to achieve thebest fitness function in order to achieve the best results +eexperimental results show that the recognition accuracy isbetter than the others when the weight value is 2 1 0 so it

is better to solve the problem by increasing the proportion ofattribute dependency +rough the above experiments it isshown that the high-dimensional feature selection algorithmbased on genetic algorithm and variable precision rough setcan solve the multiobjective optimization problem wellHowever when the fitness function and its parameters areapplied in the specific application it is necessary to analyzethe specific problems

Data Availability

+e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

+e authors declare no conflicts of interest

Acknowledgments

+is work was supported by National Natural ScienceFoundation of China (Grant nos 61561040 and 61876121)First-Class Disciplines Foundation of Ningxia (NoNXYLXK2017B09)

References

[1] S Luo D Miao Z Zhang Y Zhang and S Hu ldquoA neigh-borhood rough set model with nominal metric embeddingrdquoInformation Sciences vol 520 pp 373ndash388 2020

[2] B Barman and S Patra ldquoVariable precision rough set basedunsupervised band selection technique for hyperspectralimage classificationrdquo Knowledge-Based Systems vol 1936Article ID 105414 2020

[3] Y Chenyi and L Jinjin ldquoApproximate attribute reductionunder variable precision rough set βrdquo Journal of ShandongUniversity vol 11 pp 17ndash21 2011

[4] S Xiaowei Research on Hierarchical Model of Attribute Re-duction in Variable Precision Rough Set Central SouthUniversity Changsha China 2013

[5] Z Jie and W Jiayang ldquoAnalysis of reduction feature ofvariable precision rough set modelrdquo Computer ApplicationResearch vol 7 pp 12ndash15 2007

[6] Z Pei and Z Qinghua ldquoFCM clustering algorithm based onvariable precision rough setrdquo Journal of Shanxi Universityvol 3 pp 342ndash348 2016

[7] C Hao and Y Junan ldquoAttribute kernel and minimum at-tribute reduction algorithm of variable precision rough setrdquoActa Sinica Sinica vol 5 pp 1011ndash1017 2012

[8] S Xu X Yang H Yu D-J Yu J Yang and E CC TsangldquoMulti-label learning with label-specific feature reductionrdquoKnowledge-Based Systems vol 104 pp 52ndash61 2016

[9] I Maryam and G Hassan ldquoFeature space discriminantanalysis for hyperspectral data feature reductionrdquo ISPRSJournal of Photogrammetry and Remote Sensing vol 102pp 1ndash13 2015

[10] S Q Wang C Y Gao C Luo G M Zheng and Y N ZhouldquoResearch on feature selectionattribute reduction methodbased on rough set theoryrdquo Procedia Computer Sciencevol 154 pp 194ndash198e 2019

[11] A W Omar M Azzam O Hadi and B Jamal ldquoCEAP SVM-based intelligent detection model for clustered vehicular ad

Mathematical Problems in Engineering 17

hoc networksrdquo Expert Systems with Applications vol 50pp 40ndash54 2016

[12] H Lee and Y-P P Chen ldquoImage based computer aideddiagnosis system for cancer detectionrdquo Expert Systems withApplications vol 42 no 12 pp 5356ndash5365 2015

[13] J A Guy and P L Harold ldquoAfter detection the improvedaccuracy of lung cancer assessment using radiologic com-puter-aided diagnosisrdquo Academic Radiology vol 23 no 2pp 186ndash191 2016

[14] E Kiyonori T Shodayu J Binghu et al ldquoPleural invasion byperipheral lung cancer prediction with three-dimensionalCTrdquo Academic Radiology vol 3 pp 310ndash319 2015

[15] B Koohestani ldquoA crossover operator for improving the ef-ficiency of permutation-based genetic algorithmsrdquo ExpertSystems with Applications vol 1511 Article ID 113381 2020

[16] N K Lee X Li and D Wang ldquoA comprehensive survey ongenetic algorithms for DNA motif predictionrdquo InformationSciences vol 466 pp 25ndash43 2018

[17] S Shibao and Y Leilei ldquoResearch on variable precision roughset model and its applicationrdquo Computer Engineering andApplication vol 07 pp 10ndash13 2009

[18] T Xiaolong Several Problems of Multi Granularity VariablePrecision Rough Set Guangxi University For NationalitiesNanning China 2015

[19] W Xueming Research on Several Rough Set Models andNeural Network University of Electronic Science and Tech-nology of China Chengdu China 2013

[20] T Sun J Wang X Li et al ldquoComparative evaluation ofsupport vector machines for computer aided diagnosis of lungcancer in CT based on a multi-dimensional data setrdquo Com-puter Methods and Programs in Biomedicine vol 111 no 2pp 519ndash524 2013

[21] Z Yang T Ouyang X Fu and X Peng ldquoA decision-makingalgorithm for online shopping using deep-learning-basedopinion pairs mining and q -rung orthopair fuzzy interactionHeronianmean operatorsrdquo International Journal of IntelligentSystems vol 35 no 5 pp 783ndash825 2020

[22] W Chen C Lin C Li et al ldquoTracing the evolution of 3Dprinting technology in China using LDA-based patent ab-stract miningrdquo IEEE Transactions on Engineering Manage-men vol 36 pp 1ndash11 2020

18 Mathematical Problems in Engineering

convergence of VPRS-GA under the variation for fitnessfunction value for one time is shown in Figure 8

Each reduction is classified by SVM classifier using themethod of 5-fold cross validation through changing thetraining samples and test samples the results of the five

groups were obtained including accuracy sensitivityspecificity and time (training samples are constructed by800 malignant samples and 800 benign samples testingsamples are constructed by 200 malignant samples and 200benign samples the experiment is repeated 5 times by

ndash08

ndash1

ndash12

ndash14

ndash16

Fitn

ess v

alue

Best ndash141919 Mean ndash128476

0 50 100 150Generation stopping criteria

Best fitnessMean fitness

Figure 7 +e variation of fitness function value in a running process for experiment 1-third group

Table 8 +e statistical results of the third group for experiment 1 with the SVM classifier

Experiment times Accuracy () Sensitivity () Specificity () Time (s)

Reduction 1

1 9275 8600 9950 924922 9725 9750 9700 1074613 9850 9850 9850 1138114 9775 9900 9650 1155605 9875 10000 9750 117022

Average value 9700 9620 9780 109269

Reduction 2

1 9350 8750 9950 1482452 9700 9650 9750 1615353 9775 9850 9700 1664524 9800 9850 9750 1754505 9875 9950 9800 172348

Average value 9700 9610 9790 164806

Reduction 3

1 9125 8300 9950 2019042 9650 9700 9600 2185353 9800 9800 9800 2196054 9625 9900 9350 2230915 9825 10000 9650 236896

Average value 9605 9540 9670 220006

Reduction 4

1 9300 8700 9900 1654542 9675 9600 9750 1724323 9875 9850 9900 1793014 9800 9900 9700 1895605 9900 9950 9850 185249

Average value 9710 9600 9820 178399

Reduction 5

1 9275 8600 9950 1411732 9725 9800 9650 1612953 9900 9950 9850 1589924 9775 9950 9600 1648765 9875 10000 9750 166070

Average value 9710 9660 9760 158481

Table 9 Fitness function weight proportion and β value

Experiment timesω1 1 ω2 1 ω3 0

1 minus β 06 1 minus β 08 1 minus β 1First group experiment Second group experiment +ird group experiment

Mathematical Problems in Engineering 11

changing training samples and testing samples) Finally theaverage values of these five groups are obtained as the finalresult of the reduction and shown in Table 11

In the case of constant weight ϖ and classification errorrate of β 02 (which contains 1 minus β 08) the classificationerror rate is changed on the basis of the attribute dependencyand the length of control reduction +e premature phe-nomena are shown in Figure 8 and evolution progress isterminated early such that the attribute dependency ofreduction 5 was 08405 appeared in attribute dependency onless than 09 compared with first groups of experiment 2attribute dependency declined +e average recognitionaccuracy of the experimental group was 9674 Comparedwith the classification error rate of 04 and inclusion degreeof 06 the accuracy was decreased by 024

(3) 3rd Group Experiment 1 minus β1 +e algorithm is run 5times according to the group weights and the results of the 5groups are shown in Table 12 including the reduction of theconditional attributes the length of reduction the optimalfitness value the attribute dependency and the time +econvergence of VPRS-GA under the variation for fitnessfunction value for one time is shown in Figure 9

Each reduction is classified by SVM classifier using themethod of 5-fold cross validation through changing thetraining samples and test samples the results of the fivegroups were obtained including accuracy sensitivityspecificity and time (training samples are constructed by800 malignant samples and 800 benign samples testingsamples are constructed by 200 malignant samples and 200

benign samples the experiment is repeated 5 times bychanging training samples and testing samples) Finally theaverage values of these five groups are obtained as the finalresult of the reduction and shown in Table 13

In the case of constant weight ϖ and classification errorrate of β= 0 (which contains 1 minus β= 1) the classificationerror rate is reduced and the inclusion degree is improved onthe basis of the attribute dependency and the length ofcontrol reduction +e premature phenomena are shown inFigure 9 and evolution progress is terminated early +eaverage recognition accuracy of the experimental group was9573 which was decreased by 006 compared with thatin the second group In experiment 2 the effect of changingthe classification error rate on the recognition accuracy wasverified by the 3 groups of experiments By continuallyreducing the classification error rate the final recognitionaccuracy has been declining when inclusion degree is 1β= 0 variable precision rough set becomes Pawlak rough setthe recognition accuracy of the recognition accuracy of isminimum which was verified the advantages of variableprecision rough set

343 Experiment 3mdashResearch on Increasing the WeightCoefficient under the Condition in the Same ClassificationError Rate According to experiment 1 and experiment 2we can know that when β 06 ω1 1 ω2 1 ω3 0 therecognition accuracy is the best therefore in the thirdexperiment by increasing the weight of ω 3 groups ofexperiments are performed fitness goals target 1 (attribute

Table 10 Results of VPRS-GA running 5 times when 1 minus β 08 ω1 1ω2 1ω3 0

Experimenttimes C_ reduction Reduction

lengthOptimal fitness

valueAttribute

dependency degree Time (s)

1 8 9 11 12 15 16 17 18 25 26 29 31 35 39 40 41 42 48 5865 67 68 70 83 84 91 26 minus 67816 09490 10002827

2 1 6 8 9 11 12 15 17 21 23 26 28 30 31 34 44 50 56 58 5962 63 64 68 71 75 77 82 89 92 30 minus 67797 09615 9477387

3 6 8 12 14 15 16 17 21 28 35 38 39 45 49 55 58 61 62 6465 77 82 85 23 minus 68694 09070 12866181

4 4 6 7 8 11 12 13 16 17 20 25 26 31 32 34 35 41 42 44 4950 55 58 68 72 74 76 78 79 85 89 92 32 minus 67225 09540 10510220

5 3 6 8 9 10 16 17 26 27 34 36 37 38 40 42 44 46 51 52 6266 67 84 86 87 25 minus 65892 08405 8469324

Average value 272 minus 67484 09224 10265188

ndash55

ndash6

ndash65

ndash7

Fitn

ess v

alue

Best ndash686942 Mean ndash653584

0 50 100 150Generation stopping criteria

Best fitnessMean fitness

Figure 8 +e variation of fitness function value in a running process for experiment 2-second group

12 Mathematical Problems in Engineering

Table 11 +e statistical results of the second group for experiment 2 with the SVM classifier

Experiment times Accuracy () Sensitivity () Specificity () Time (s)

Reduction 1

1 9300 8650 9950 2280072 9575 9700 9450 2376463 9700 9600 9800 2332504 9750 9850 9650 2444915 9925 10000 9850 244816

Average value 9650 9560 9740 237642

Reduction 2

1 9375 8800 9950 2524032 9625 9750 9500 2652893 9800 9700 9900 2655234 9800 9900 9700 2682125 9950 10000 9900 275880

Average value 9710 9630 9790 265461

Reduction 3

1 9275 8750 9800 1807802 9675 9750 9600 1929923 9700 9600 9800 1872434 9775 9950 9600 2084825 9875 10000 9750 203507

Average value 9660 9610 9710 194601

Reduction 4

1 9200 8650 9750 2572602 9700 9750 9650 2730243 9775 9650 9900 2723164 9750 9900 9600 2815545 9900 10000 9800 291471

Average value 9665 9590 9740 275125

Reduction 5

1 9275 8750 9800 1437152 9675 9600 9750 1526373 9750 9800 9700 1589294 9775 9900 9650 1629975 9950 10000 9900 166792

Average value 9685 9610 9760 157014

Table 12 Results of VPRS-GA running 5 times when 1 minus β 1 ω1 1ω2 1ω3 0

Experimenttimes C_ reduction Reduction

lengthOptimal fitness

valueAttribute dependency

degree Time (s)

1 15 44 68 73 79 84 6 minus 27313 07965 114499012 34 51 54 75 80 90 6 minus 27047 08460 96993913 2 34 49 70 71 72 76 81 8 minus 34057 07535 112334894 12 25 78 85 4 minus 22872 09285 11668133

5 6 7 12 13 42 44 55 57 65 66 69 77 81 8687 15 minus 33230 08665 13236077

Average value 78 minus 28903 08382 11457398

ndash1

ndash2

ndash3

ndash4

Fitn

ess v

alue

0 50 100 150Generation stopping criteria

Best fitnessMean fitness

Best ndash340567 Mean ndash330598

Figure 9 +e variation of fitness function value in a running process for experiment 2-third group

Mathematical Problems in Engineering 13

dependency) target 2 (the minimum number of attributesreduction) and target 3 (gene encoding weight function)the three objective functions play an important role in theevaluation of fitness function However the importance offitness function is reduced in these three objectives+erefore in this experiment when the other conditions areunchanged the weight coefficient of the target 1 is increasedto verify the influence of the change in the weight coefficienton the experimental results and they are shown in Table 14

(1) 1st Group Experiment ω1 1 ω2 1 ω3 0 +e al-gorithm are run 5 times according to this group weights theresults of the 5 groups are given in Table 5 including thereduction of the conditional attributes the length of reduc-tion the optimal fitness value the attribute dependency andthe time +e convergence of VPRS-GA under the variationfor fitness function value in one time is shown in Figure 6 (ienot repeated for the second group of experiment 1)

(2) 2nd Group Experiment ω1 2 ω2 1 ω3 0 +ealgorithm is run 5 times according to this group weights theresults of the 5 groups are given in Table 15 including thereduction of the conditional attributes the length of re-duction the optimal fitness value the attribute dependencyand the time +e convergence of VPRS-GA under thevariation for fitness function value in one time is shown inFigure 10

Each reduction is classified by SVM classifier using themethod of 5-fold cross validation through changing thetraining samples and test samples the results of the fivegroups were obtained including accuracy sensitivityspecificity and time (training samples are constructed by800 malignant samples and 800 benign samples testingsamples are constructed by 200 malignant samples and 200benign samples the experiment is repeated 5 times bychanging training samples and testing samples) Finally theaverage values of these five groups are obtained as the finalresult of the reduction and shown in Table 16

+e experimental group in the case of 1 minus β= 06 un-changed the weight of ω1 was increased +e attributedependency and the optimal fitness function are relativelyhigh the average precision of reduction 1 reduction 2 andreduction 3 in Table 16 is more than 97 and that of re-duction 2 is even up to 9725 +e average recognitionaccuracy of the experimental group is 9703 which ishigher than that of the first group

Table 13 +e statistical results of the third group for experiment 2 with the SVM classifier

Experiment times Accuracy () Sensitivity () Specificity () Time (s)

Reduction 1

1 9225 8450 10000 812712 9550 9700 9400 945833 9575 9400 9750 881984 9600 9800 9400 937545 9725 9900 9550 98691

Average value 9535 9450 9620 91299

Reduction 2

1 9200 8450 9950 648942 9625 9550 9700 801983 9525 9300 9750 773374 9600 9750 9450 760125 9800 10000 9600 82763

Average value 9550 9410 9690 76241

Reduction 3

1 9200 8450 9950 648942 9625 9550 9700 801983 9525 9300 9750 773374 9600 9750 9450 760125 9800 10000 9600 82763

Average value 9550 9410 9690 76241

Reduction 4

1 9275 8550 10000 672642 9675 9600 9750 784673 9600 9450 9750 730224 9575 9750 9400 794605 9800 10000 9600 84184

Average value 9585 9470 9700 76479

Reduction 5

1 9200 8450 9950 1147192 9625 9750 9500 1287053 9850 9900 9800 1320494 9775 9950 9600 1335135 9850 10000 9700 133144

Average value 9660 9610 9710 128426

Table 14 Fitness function weight proportion and β value

Experiment times1 minus β 06

ω1 ω2 ω3First group experiment 1 1 0Second group experiment 2 1 0+ird group experiment 3 1 0

14 Mathematical Problems in Engineering

ndash2

ndash25

ndash3

Fitn

ess v

alue

0 50 100 150Generation stopping criteria

Best fitnessMean fitness

Best ndash2915 Mean ndash291446

Figure 10 +e variation of fitness function value in a running process for experiment 3-second group

Table 15 Results of VPRS-GA running 5 times when 1 minus β 06 ω1 2ω2 1ω3 0

Experimenttimes C_ reduction Reduction

lengthOptimal fitness

valueAttribute dependency

degree Time (s)

1 2 3 4 5 11 13 16 18 24 30 34 37 39 41 42 51 55 64 7077 78 82 22 minus 34859 09060 21515464

2 8 9 11 12 14 15 23 25 26 29 30 33 37 42 43 45 46 5060 61 69 74 80 87 89 25 minus 30845 09390 42761634

3 8 11 12 13 16 18 19 24 29 36 37 43 64 65 68 71 86 9192 19 minus 35039 09150 26197164

4 2 3 4 8 10 11 12 13 15 16 19 23 25 30 48 55 64 65 6874 77 80 81 83 84 86 89 27 minus 29150 09575 44271631

5 5 8 911 121517 23 25 29 31 36 39 41 48 54 59 63 8083 86 89 22 minus 29920 09525 43161464

Average value 23 minus 31962 09340 35581471

Table 16 +e statistical results of the second group for experiment 3 with the SVM classifier

Experiment times Accuracy () Sensitivity () Specificity () Time (s)

Reduction 1

1 9275 8600 9950 1884972 9725 9800 9650 1571623 9850 9900 9800 1586914 9800 9900 9700 1646035 9950 10000 9900 161914

Average value 9720 9640 9800 166173

Reduction 2

1 9450 8950 9950 1908132 9675 9800 9550 2002513 9775 9800 9750 1970084 9850 9900 9800 2009245 9875 9900 9850 209245

Average value 9725 9670 9780 199648

Reduction 3

1 9400 8800 10000 1313692 9725 9800 9650 1447973 9800 9800 9800 1426624 9725 9850 9600 1471905 9925 10000 9850 148799

Average value 9715 9650 9780 142963

Reduction 4

1 9350 8750 9950 2404562 9700 9750 9650 2520823 9800 9800 9800 2511754 9775 9950 9600 2701885 9825 10000 9650 267471

Average value 9690 9650 9730 256274

Reduction 5

1 9325 8800 9850 1809592 9600 9800 9400 1965633 9750 9750 9750 1967234 9800 9900 9700 2078295 9850 9950 9750 219703

Average value 9665 9640 9690 200355

Mathematical Problems in Engineering 15

Table 17 Results of VPRS-GA running 5 times when 1 minus β 1 ω1 1ω2 1ω3 0

Experimenttimes C_ reduction Reduction

lengthOptimal fitness

valueAttribute

dependency degree Time (s)

1 3 4 5 8 9 11 12 17 19 29 34 35 38 46 52 53 55 59 63 6672 75 77 78 79 87 92 27 minus 38867 09550 28981789

2 4 8 9 11 12 15 17 29 33 37 38 39 42 43 48 55 67 73 7881 83 84 88 89 90 25 minus 38167 09715 55783772

3 2 3 4 8 9 10 11 12 13 15 16 19 24 25 30 36 49 54 55 6064 67 68 70 74 77 83 85 86 91 30 minus 38807 09530 34831096

4 4 5 7 11 12 14 15 17 25 29 33 36 39 41 42 47 48 50 5556 58 62 67 69 72 74 77 84 86 90 91 31 minus 39430 09665 35742822

5 3 4 5 8 9 11 12 17 19 29 34 35 38 46 52 53 55 59 63 6672 75 77 78 79 87 92 27 minus 38867 09550 27919582

Average value 28 minus 38827 09602 36651812

ndash3

ndash35

ndash40 50 100 150

Generation stopping criteria

Fitn

ess v

alue

Best fitnessMean fitness

Best ndash394298 Mean ndash393327

Figure 11 +e variation of fitness function value in a running process for experiment 3-third group

Table 18 +e statistical results of the Second group for experiment 3 with the SVM classifier

Experiment times Accuracy () Sensitivity () Specificity () Time (s)

Reduction 1

1 9200 8700 9700 2187172 9750 9750 9750 2105503 9850 9850 9850 2032064 9800 9900 9700 2211645 9925 10000 9850 272536

Average value 9705 9640 9770 225235

Reduction 2

1 9400 8850 9950 2331232 9575 9750 9400 2433493 9750 9700 9800 2442024 9775 9900 9650 2566075 9900 9950 9850 259071

Average value 9680 9630 9730 247270

Reduction 3

1 9275 8650 9900 2525842 9625 9750 9500 2624123 9775 9800 9750 2601274 9775 9900 9650 2686705 9875 10000 9750 265387

Average value 9665 9620 9710 261836

Reduction 4

1 9150 8550 9750 2532312 9625 9750 9500 2649433 9750 9700 9800 2752834 9800 9950 9650 3229545 9825 9950 9700 277432

Average value 9630 9580 9680 278769

Reduction 5

1 9200 8800 9600 1951962 9700 9700 9700 2148893 9825 9800 9850 2036124 9850 10000 9700 2133615 9900 9900 9900 225526

Average value 9695 9640 9750 210517

16 Mathematical Problems in Engineering

(3) 3rd Group Experiment ω1 3 ω2 1 ω3 0 +e al-gorithm is run 5 times according to the group weights andthe results of the 5 groups are given in Table 17 including thereduction of the conditional attributes the length of re-duction the optimal fitness value the attribute dependencyand the time +e convergence of VPRS-GA under thevariation for fitness function value for one time is shown inFigure 11

Each reduction is classified by SVM classifier using themethod of 5-fold cross validation through changing thetraining samples and test samples the results of the fivegroups were obtained including accuracy sensitivityspecificity and time (training samples are constructed by800 malignant samples and 800 benign samples testingsamples are constructed by 200 malignant samples and 200benign samples the experiment is repeated 5 times bychanging training samples and testing samples) Finally theaverage values of these five groups are obtained as the finalresult of the reduction and shown in Table 18

+e experiment in the case of 1 minus β 06 unchangedincrease the weight of the ω1 ω1 3 ω2 1 ω3 0 InTable 18 the recognition accuracy of reduction 1 is over 97only +e average recognition accuracy of the experimentalgroup is 9675 and the accuracy is decreased by 028compared with that in the other second groups +e threegroups of experiment 3 the purpose is to verify whether theexperimental accuracy is influenced by increasing theweight +e experimental results show that the accuracy ofsecond group for experimental weight 2 1 0 comparedwith first group experiment when 1 1 0 is high but thethird groups of experimental weight was 3 1 0 and theaccuracy declined therefore the weight of 2 1 0 is the bestchoice for this experiment

4 Conclusions

Aiming at the deficiency of the traditional rough set modelthis paper proposes a new feature selection model based ongenetic algorithm and variable precision rough set by in-troducing the β value the rigid inclusion of the approxi-mation for the traditional rough set is relaxed and then wedesign the 3 kinds of experiments by constructing the de-cision information table of the PETCT feature for lungtumor ROI +e first type of experiment is the inclusion of1 minus β 06 and different values of ω made a total of threegroups of experiments the experimental results show thatthe better recognition accuracy can be obtained when theweight is 1 1 0 and the results show that the gene codingweight function has no effect on the fitness function For thesecond type of experiments ϖ1 1ω2 1 ω3 0according to the different values of β to do three groups ofexperiments the results show that the recognition accuracyof 1 minus β 06 is the best which shows that the larger the βvalue is the lower approximate cardinality will be largerthen the relative accuracy will increase For the third type ofexperiments 1 minus β 06 ω value is increased to achieve thebest fitness function in order to achieve the best results +eexperimental results show that the recognition accuracy isbetter than the others when the weight value is 2 1 0 so it

is better to solve the problem by increasing the proportion ofattribute dependency +rough the above experiments it isshown that the high-dimensional feature selection algorithmbased on genetic algorithm and variable precision rough setcan solve the multiobjective optimization problem wellHowever when the fitness function and its parameters areapplied in the specific application it is necessary to analyzethe specific problems

Data Availability

+e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

+e authors declare no conflicts of interest

Acknowledgments

+is work was supported by National Natural ScienceFoundation of China (Grant nos 61561040 and 61876121)First-Class Disciplines Foundation of Ningxia (NoNXYLXK2017B09)

References

[1] S Luo D Miao Z Zhang Y Zhang and S Hu ldquoA neigh-borhood rough set model with nominal metric embeddingrdquoInformation Sciences vol 520 pp 373ndash388 2020

[2] B Barman and S Patra ldquoVariable precision rough set basedunsupervised band selection technique for hyperspectralimage classificationrdquo Knowledge-Based Systems vol 1936Article ID 105414 2020

[3] Y Chenyi and L Jinjin ldquoApproximate attribute reductionunder variable precision rough set βrdquo Journal of ShandongUniversity vol 11 pp 17ndash21 2011

[4] S Xiaowei Research on Hierarchical Model of Attribute Re-duction in Variable Precision Rough Set Central SouthUniversity Changsha China 2013

[5] Z Jie and W Jiayang ldquoAnalysis of reduction feature ofvariable precision rough set modelrdquo Computer ApplicationResearch vol 7 pp 12ndash15 2007

[6] Z Pei and Z Qinghua ldquoFCM clustering algorithm based onvariable precision rough setrdquo Journal of Shanxi Universityvol 3 pp 342ndash348 2016

[7] C Hao and Y Junan ldquoAttribute kernel and minimum at-tribute reduction algorithm of variable precision rough setrdquoActa Sinica Sinica vol 5 pp 1011ndash1017 2012

[8] S Xu X Yang H Yu D-J Yu J Yang and E CC TsangldquoMulti-label learning with label-specific feature reductionrdquoKnowledge-Based Systems vol 104 pp 52ndash61 2016

[9] I Maryam and G Hassan ldquoFeature space discriminantanalysis for hyperspectral data feature reductionrdquo ISPRSJournal of Photogrammetry and Remote Sensing vol 102pp 1ndash13 2015

[10] S Q Wang C Y Gao C Luo G M Zheng and Y N ZhouldquoResearch on feature selectionattribute reduction methodbased on rough set theoryrdquo Procedia Computer Sciencevol 154 pp 194ndash198e 2019

[11] A W Omar M Azzam O Hadi and B Jamal ldquoCEAP SVM-based intelligent detection model for clustered vehicular ad

Mathematical Problems in Engineering 17

hoc networksrdquo Expert Systems with Applications vol 50pp 40ndash54 2016

[12] H Lee and Y-P P Chen ldquoImage based computer aideddiagnosis system for cancer detectionrdquo Expert Systems withApplications vol 42 no 12 pp 5356ndash5365 2015

[13] J A Guy and P L Harold ldquoAfter detection the improvedaccuracy of lung cancer assessment using radiologic com-puter-aided diagnosisrdquo Academic Radiology vol 23 no 2pp 186ndash191 2016

[14] E Kiyonori T Shodayu J Binghu et al ldquoPleural invasion byperipheral lung cancer prediction with three-dimensionalCTrdquo Academic Radiology vol 3 pp 310ndash319 2015

[15] B Koohestani ldquoA crossover operator for improving the ef-ficiency of permutation-based genetic algorithmsrdquo ExpertSystems with Applications vol 1511 Article ID 113381 2020

[16] N K Lee X Li and D Wang ldquoA comprehensive survey ongenetic algorithms for DNA motif predictionrdquo InformationSciences vol 466 pp 25ndash43 2018

[17] S Shibao and Y Leilei ldquoResearch on variable precision roughset model and its applicationrdquo Computer Engineering andApplication vol 07 pp 10ndash13 2009

[18] T Xiaolong Several Problems of Multi Granularity VariablePrecision Rough Set Guangxi University For NationalitiesNanning China 2015

[19] W Xueming Research on Several Rough Set Models andNeural Network University of Electronic Science and Tech-nology of China Chengdu China 2013

[20] T Sun J Wang X Li et al ldquoComparative evaluation ofsupport vector machines for computer aided diagnosis of lungcancer in CT based on a multi-dimensional data setrdquo Com-puter Methods and Programs in Biomedicine vol 111 no 2pp 519ndash524 2013

[21] Z Yang T Ouyang X Fu and X Peng ldquoA decision-makingalgorithm for online shopping using deep-learning-basedopinion pairs mining and q -rung orthopair fuzzy interactionHeronianmean operatorsrdquo International Journal of IntelligentSystems vol 35 no 5 pp 783ndash825 2020

[22] W Chen C Lin C Li et al ldquoTracing the evolution of 3Dprinting technology in China using LDA-based patent ab-stract miningrdquo IEEE Transactions on Engineering Manage-men vol 36 pp 1ndash11 2020

18 Mathematical Problems in Engineering

changing training samples and testing samples) Finally theaverage values of these five groups are obtained as the finalresult of the reduction and shown in Table 11

In the case of constant weight ϖ and classification errorrate of β 02 (which contains 1 minus β 08) the classificationerror rate is changed on the basis of the attribute dependencyand the length of control reduction +e premature phe-nomena are shown in Figure 8 and evolution progress isterminated early such that the attribute dependency ofreduction 5 was 08405 appeared in attribute dependency onless than 09 compared with first groups of experiment 2attribute dependency declined +e average recognitionaccuracy of the experimental group was 9674 Comparedwith the classification error rate of 04 and inclusion degreeof 06 the accuracy was decreased by 024

(3) 3rd Group Experiment 1 minus β1 +e algorithm is run 5times according to the group weights and the results of the 5groups are shown in Table 12 including the reduction of theconditional attributes the length of reduction the optimalfitness value the attribute dependency and the time +econvergence of VPRS-GA under the variation for fitnessfunction value for one time is shown in Figure 9

Each reduction is classified by SVM classifier using themethod of 5-fold cross validation through changing thetraining samples and test samples the results of the fivegroups were obtained including accuracy sensitivityspecificity and time (training samples are constructed by800 malignant samples and 800 benign samples testingsamples are constructed by 200 malignant samples and 200

benign samples the experiment is repeated 5 times bychanging training samples and testing samples) Finally theaverage values of these five groups are obtained as the finalresult of the reduction and shown in Table 13

In the case of constant weight ϖ and classification errorrate of β= 0 (which contains 1 minus β= 1) the classificationerror rate is reduced and the inclusion degree is improved onthe basis of the attribute dependency and the length ofcontrol reduction +e premature phenomena are shown inFigure 9 and evolution progress is terminated early +eaverage recognition accuracy of the experimental group was9573 which was decreased by 006 compared with thatin the second group In experiment 2 the effect of changingthe classification error rate on the recognition accuracy wasverified by the 3 groups of experiments By continuallyreducing the classification error rate the final recognitionaccuracy has been declining when inclusion degree is 1β= 0 variable precision rough set becomes Pawlak rough setthe recognition accuracy of the recognition accuracy of isminimum which was verified the advantages of variableprecision rough set

343 Experiment 3mdashResearch on Increasing the WeightCoefficient under the Condition in the Same ClassificationError Rate According to experiment 1 and experiment 2we can know that when β 06 ω1 1 ω2 1 ω3 0 therecognition accuracy is the best therefore in the thirdexperiment by increasing the weight of ω 3 groups ofexperiments are performed fitness goals target 1 (attribute

Table 10 Results of VPRS-GA running 5 times when 1 minus β 08 ω1 1ω2 1ω3 0

Experimenttimes C_ reduction Reduction

lengthOptimal fitness

valueAttribute

dependency degree Time (s)

1 8 9 11 12 15 16 17 18 25 26 29 31 35 39 40 41 42 48 5865 67 68 70 83 84 91 26 minus 67816 09490 10002827

2 1 6 8 9 11 12 15 17 21 23 26 28 30 31 34 44 50 56 58 5962 63 64 68 71 75 77 82 89 92 30 minus 67797 09615 9477387

3 6 8 12 14 15 16 17 21 28 35 38 39 45 49 55 58 61 62 6465 77 82 85 23 minus 68694 09070 12866181

4 4 6 7 8 11 12 13 16 17 20 25 26 31 32 34 35 41 42 44 4950 55 58 68 72 74 76 78 79 85 89 92 32 minus 67225 09540 10510220

5 3 6 8 9 10 16 17 26 27 34 36 37 38 40 42 44 46 51 52 6266 67 84 86 87 25 minus 65892 08405 8469324

Average value 272 minus 67484 09224 10265188

ndash55

ndash6

ndash65

ndash7

Fitn

ess v

alue

Best ndash686942 Mean ndash653584

0 50 100 150Generation stopping criteria

Best fitnessMean fitness

Figure 8 +e variation of fitness function value in a running process for experiment 2-second group

12 Mathematical Problems in Engineering

Table 11 +e statistical results of the second group for experiment 2 with the SVM classifier

Experiment times Accuracy () Sensitivity () Specificity () Time (s)

Reduction 1

1 9300 8650 9950 2280072 9575 9700 9450 2376463 9700 9600 9800 2332504 9750 9850 9650 2444915 9925 10000 9850 244816

Average value 9650 9560 9740 237642

Reduction 2

1 9375 8800 9950 2524032 9625 9750 9500 2652893 9800 9700 9900 2655234 9800 9900 9700 2682125 9950 10000 9900 275880

Average value 9710 9630 9790 265461

Reduction 3

1 9275 8750 9800 1807802 9675 9750 9600 1929923 9700 9600 9800 1872434 9775 9950 9600 2084825 9875 10000 9750 203507

Average value 9660 9610 9710 194601

Reduction 4

1 9200 8650 9750 2572602 9700 9750 9650 2730243 9775 9650 9900 2723164 9750 9900 9600 2815545 9900 10000 9800 291471

Average value 9665 9590 9740 275125

Reduction 5

1 9275 8750 9800 1437152 9675 9600 9750 1526373 9750 9800 9700 1589294 9775 9900 9650 1629975 9950 10000 9900 166792

Average value 9685 9610 9760 157014

Table 12 Results of VPRS-GA running 5 times when 1 minus β 1 ω1 1ω2 1ω3 0

Experimenttimes C_ reduction Reduction

lengthOptimal fitness

valueAttribute dependency

degree Time (s)

1 15 44 68 73 79 84 6 minus 27313 07965 114499012 34 51 54 75 80 90 6 minus 27047 08460 96993913 2 34 49 70 71 72 76 81 8 minus 34057 07535 112334894 12 25 78 85 4 minus 22872 09285 11668133

5 6 7 12 13 42 44 55 57 65 66 69 77 81 8687 15 minus 33230 08665 13236077

Average value 78 minus 28903 08382 11457398

ndash1

ndash2

ndash3

ndash4

Fitn

ess v

alue

0 50 100 150Generation stopping criteria

Best fitnessMean fitness

Best ndash340567 Mean ndash330598

Figure 9 +e variation of fitness function value in a running process for experiment 2-third group

Mathematical Problems in Engineering 13

dependency) target 2 (the minimum number of attributesreduction) and target 3 (gene encoding weight function)the three objective functions play an important role in theevaluation of fitness function However the importance offitness function is reduced in these three objectives+erefore in this experiment when the other conditions areunchanged the weight coefficient of the target 1 is increasedto verify the influence of the change in the weight coefficienton the experimental results and they are shown in Table 14

(1) 1st Group Experiment ω1 1 ω2 1 ω3 0 +e al-gorithm are run 5 times according to this group weights theresults of the 5 groups are given in Table 5 including thereduction of the conditional attributes the length of reduc-tion the optimal fitness value the attribute dependency andthe time +e convergence of VPRS-GA under the variationfor fitness function value in one time is shown in Figure 6 (ienot repeated for the second group of experiment 1)

(2) 2nd Group Experiment ω1 2 ω2 1 ω3 0 +ealgorithm is run 5 times according to this group weights theresults of the 5 groups are given in Table 15 including thereduction of the conditional attributes the length of re-duction the optimal fitness value the attribute dependencyand the time +e convergence of VPRS-GA under thevariation for fitness function value in one time is shown inFigure 10

Each reduction is classified by SVM classifier using themethod of 5-fold cross validation through changing thetraining samples and test samples the results of the fivegroups were obtained including accuracy sensitivityspecificity and time (training samples are constructed by800 malignant samples and 800 benign samples testingsamples are constructed by 200 malignant samples and 200benign samples the experiment is repeated 5 times bychanging training samples and testing samples) Finally theaverage values of these five groups are obtained as the finalresult of the reduction and shown in Table 16

+e experimental group in the case of 1 minus β= 06 un-changed the weight of ω1 was increased +e attributedependency and the optimal fitness function are relativelyhigh the average precision of reduction 1 reduction 2 andreduction 3 in Table 16 is more than 97 and that of re-duction 2 is even up to 9725 +e average recognitionaccuracy of the experimental group is 9703 which ishigher than that of the first group

Table 13 +e statistical results of the third group for experiment 2 with the SVM classifier

Experiment times Accuracy () Sensitivity () Specificity () Time (s)

Reduction 1

1 9225 8450 10000 812712 9550 9700 9400 945833 9575 9400 9750 881984 9600 9800 9400 937545 9725 9900 9550 98691

Average value 9535 9450 9620 91299

Reduction 2

1 9200 8450 9950 648942 9625 9550 9700 801983 9525 9300 9750 773374 9600 9750 9450 760125 9800 10000 9600 82763

Average value 9550 9410 9690 76241

Reduction 3

1 9200 8450 9950 648942 9625 9550 9700 801983 9525 9300 9750 773374 9600 9750 9450 760125 9800 10000 9600 82763

Average value 9550 9410 9690 76241

Reduction 4

1 9275 8550 10000 672642 9675 9600 9750 784673 9600 9450 9750 730224 9575 9750 9400 794605 9800 10000 9600 84184

Average value 9585 9470 9700 76479

Reduction 5

1 9200 8450 9950 1147192 9625 9750 9500 1287053 9850 9900 9800 1320494 9775 9950 9600 1335135 9850 10000 9700 133144

Average value 9660 9610 9710 128426

Table 14 Fitness function weight proportion and β value

Experiment times1 minus β 06

ω1 ω2 ω3First group experiment 1 1 0Second group experiment 2 1 0+ird group experiment 3 1 0

14 Mathematical Problems in Engineering

ndash2

ndash25

ndash3

Fitn

ess v

alue

0 50 100 150Generation stopping criteria

Best fitnessMean fitness

Best ndash2915 Mean ndash291446

Figure 10 +e variation of fitness function value in a running process for experiment 3-second group

Table 15 Results of VPRS-GA running 5 times when 1 minus β 06 ω1 2ω2 1ω3 0

Experimenttimes C_ reduction Reduction

lengthOptimal fitness

valueAttribute dependency

degree Time (s)

1 2 3 4 5 11 13 16 18 24 30 34 37 39 41 42 51 55 64 7077 78 82 22 minus 34859 09060 21515464

2 8 9 11 12 14 15 23 25 26 29 30 33 37 42 43 45 46 5060 61 69 74 80 87 89 25 minus 30845 09390 42761634

3 8 11 12 13 16 18 19 24 29 36 37 43 64 65 68 71 86 9192 19 minus 35039 09150 26197164

4 2 3 4 8 10 11 12 13 15 16 19 23 25 30 48 55 64 65 6874 77 80 81 83 84 86 89 27 minus 29150 09575 44271631

5 5 8 911 121517 23 25 29 31 36 39 41 48 54 59 63 8083 86 89 22 minus 29920 09525 43161464

Average value 23 minus 31962 09340 35581471

Table 16 +e statistical results of the second group for experiment 3 with the SVM classifier

Experiment times Accuracy () Sensitivity () Specificity () Time (s)

Reduction 1

1 9275 8600 9950 1884972 9725 9800 9650 1571623 9850 9900 9800 1586914 9800 9900 9700 1646035 9950 10000 9900 161914

Average value 9720 9640 9800 166173

Reduction 2

1 9450 8950 9950 1908132 9675 9800 9550 2002513 9775 9800 9750 1970084 9850 9900 9800 2009245 9875 9900 9850 209245

Average value 9725 9670 9780 199648

Reduction 3

1 9400 8800 10000 1313692 9725 9800 9650 1447973 9800 9800 9800 1426624 9725 9850 9600 1471905 9925 10000 9850 148799

Average value 9715 9650 9780 142963

Reduction 4

1 9350 8750 9950 2404562 9700 9750 9650 2520823 9800 9800 9800 2511754 9775 9950 9600 2701885 9825 10000 9650 267471

Average value 9690 9650 9730 256274

Reduction 5

1 9325 8800 9850 1809592 9600 9800 9400 1965633 9750 9750 9750 1967234 9800 9900 9700 2078295 9850 9950 9750 219703

Average value 9665 9640 9690 200355

Mathematical Problems in Engineering 15

Table 17 Results of VPRS-GA running 5 times when 1 minus β 1 ω1 1ω2 1ω3 0

Experimenttimes C_ reduction Reduction

lengthOptimal fitness

valueAttribute

dependency degree Time (s)

1 3 4 5 8 9 11 12 17 19 29 34 35 38 46 52 53 55 59 63 6672 75 77 78 79 87 92 27 minus 38867 09550 28981789

2 4 8 9 11 12 15 17 29 33 37 38 39 42 43 48 55 67 73 7881 83 84 88 89 90 25 minus 38167 09715 55783772

3 2 3 4 8 9 10 11 12 13 15 16 19 24 25 30 36 49 54 55 6064 67 68 70 74 77 83 85 86 91 30 minus 38807 09530 34831096

4 4 5 7 11 12 14 15 17 25 29 33 36 39 41 42 47 48 50 5556 58 62 67 69 72 74 77 84 86 90 91 31 minus 39430 09665 35742822

5 3 4 5 8 9 11 12 17 19 29 34 35 38 46 52 53 55 59 63 6672 75 77 78 79 87 92 27 minus 38867 09550 27919582

Average value 28 minus 38827 09602 36651812

ndash3

ndash35

ndash40 50 100 150

Generation stopping criteria

Fitn

ess v

alue

Best fitnessMean fitness

Best ndash394298 Mean ndash393327

Figure 11 +e variation of fitness function value in a running process for experiment 3-third group

Table 18 +e statistical results of the Second group for experiment 3 with the SVM classifier

Experiment times Accuracy () Sensitivity () Specificity () Time (s)

Reduction 1

1 9200 8700 9700 2187172 9750 9750 9750 2105503 9850 9850 9850 2032064 9800 9900 9700 2211645 9925 10000 9850 272536

Average value 9705 9640 9770 225235

Reduction 2

1 9400 8850 9950 2331232 9575 9750 9400 2433493 9750 9700 9800 2442024 9775 9900 9650 2566075 9900 9950 9850 259071

Average value 9680 9630 9730 247270

Reduction 3

1 9275 8650 9900 2525842 9625 9750 9500 2624123 9775 9800 9750 2601274 9775 9900 9650 2686705 9875 10000 9750 265387

Average value 9665 9620 9710 261836

Reduction 4

1 9150 8550 9750 2532312 9625 9750 9500 2649433 9750 9700 9800 2752834 9800 9950 9650 3229545 9825 9950 9700 277432

Average value 9630 9580 9680 278769

Reduction 5

1 9200 8800 9600 1951962 9700 9700 9700 2148893 9825 9800 9850 2036124 9850 10000 9700 2133615 9900 9900 9900 225526

Average value 9695 9640 9750 210517

16 Mathematical Problems in Engineering

(3) 3rd Group Experiment ω1 3 ω2 1 ω3 0 +e al-gorithm is run 5 times according to the group weights andthe results of the 5 groups are given in Table 17 including thereduction of the conditional attributes the length of re-duction the optimal fitness value the attribute dependencyand the time +e convergence of VPRS-GA under thevariation for fitness function value for one time is shown inFigure 11

Each reduction is classified by SVM classifier using themethod of 5-fold cross validation through changing thetraining samples and test samples the results of the fivegroups were obtained including accuracy sensitivityspecificity and time (training samples are constructed by800 malignant samples and 800 benign samples testingsamples are constructed by 200 malignant samples and 200benign samples the experiment is repeated 5 times bychanging training samples and testing samples) Finally theaverage values of these five groups are obtained as the finalresult of the reduction and shown in Table 18

+e experiment in the case of 1 minus β 06 unchangedincrease the weight of the ω1 ω1 3 ω2 1 ω3 0 InTable 18 the recognition accuracy of reduction 1 is over 97only +e average recognition accuracy of the experimentalgroup is 9675 and the accuracy is decreased by 028compared with that in the other second groups +e threegroups of experiment 3 the purpose is to verify whether theexperimental accuracy is influenced by increasing theweight +e experimental results show that the accuracy ofsecond group for experimental weight 2 1 0 comparedwith first group experiment when 1 1 0 is high but thethird groups of experimental weight was 3 1 0 and theaccuracy declined therefore the weight of 2 1 0 is the bestchoice for this experiment

4 Conclusions

Aiming at the deficiency of the traditional rough set modelthis paper proposes a new feature selection model based ongenetic algorithm and variable precision rough set by in-troducing the β value the rigid inclusion of the approxi-mation for the traditional rough set is relaxed and then wedesign the 3 kinds of experiments by constructing the de-cision information table of the PETCT feature for lungtumor ROI +e first type of experiment is the inclusion of1 minus β 06 and different values of ω made a total of threegroups of experiments the experimental results show thatthe better recognition accuracy can be obtained when theweight is 1 1 0 and the results show that the gene codingweight function has no effect on the fitness function For thesecond type of experiments ϖ1 1ω2 1 ω3 0according to the different values of β to do three groups ofexperiments the results show that the recognition accuracyof 1 minus β 06 is the best which shows that the larger the βvalue is the lower approximate cardinality will be largerthen the relative accuracy will increase For the third type ofexperiments 1 minus β 06 ω value is increased to achieve thebest fitness function in order to achieve the best results +eexperimental results show that the recognition accuracy isbetter than the others when the weight value is 2 1 0 so it

is better to solve the problem by increasing the proportion ofattribute dependency +rough the above experiments it isshown that the high-dimensional feature selection algorithmbased on genetic algorithm and variable precision rough setcan solve the multiobjective optimization problem wellHowever when the fitness function and its parameters areapplied in the specific application it is necessary to analyzethe specific problems

Data Availability

+e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

+e authors declare no conflicts of interest

Acknowledgments

+is work was supported by National Natural ScienceFoundation of China (Grant nos 61561040 and 61876121)First-Class Disciplines Foundation of Ningxia (NoNXYLXK2017B09)

References

[1] S Luo D Miao Z Zhang Y Zhang and S Hu ldquoA neigh-borhood rough set model with nominal metric embeddingrdquoInformation Sciences vol 520 pp 373ndash388 2020

[2] B Barman and S Patra ldquoVariable precision rough set basedunsupervised band selection technique for hyperspectralimage classificationrdquo Knowledge-Based Systems vol 1936Article ID 105414 2020

[3] Y Chenyi and L Jinjin ldquoApproximate attribute reductionunder variable precision rough set βrdquo Journal of ShandongUniversity vol 11 pp 17ndash21 2011

[4] S Xiaowei Research on Hierarchical Model of Attribute Re-duction in Variable Precision Rough Set Central SouthUniversity Changsha China 2013

[5] Z Jie and W Jiayang ldquoAnalysis of reduction feature ofvariable precision rough set modelrdquo Computer ApplicationResearch vol 7 pp 12ndash15 2007

[6] Z Pei and Z Qinghua ldquoFCM clustering algorithm based onvariable precision rough setrdquo Journal of Shanxi Universityvol 3 pp 342ndash348 2016

[7] C Hao and Y Junan ldquoAttribute kernel and minimum at-tribute reduction algorithm of variable precision rough setrdquoActa Sinica Sinica vol 5 pp 1011ndash1017 2012

[8] S Xu X Yang H Yu D-J Yu J Yang and E CC TsangldquoMulti-label learning with label-specific feature reductionrdquoKnowledge-Based Systems vol 104 pp 52ndash61 2016

[9] I Maryam and G Hassan ldquoFeature space discriminantanalysis for hyperspectral data feature reductionrdquo ISPRSJournal of Photogrammetry and Remote Sensing vol 102pp 1ndash13 2015

[10] S Q Wang C Y Gao C Luo G M Zheng and Y N ZhouldquoResearch on feature selectionattribute reduction methodbased on rough set theoryrdquo Procedia Computer Sciencevol 154 pp 194ndash198e 2019

[11] A W Omar M Azzam O Hadi and B Jamal ldquoCEAP SVM-based intelligent detection model for clustered vehicular ad

Mathematical Problems in Engineering 17

hoc networksrdquo Expert Systems with Applications vol 50pp 40ndash54 2016

[12] H Lee and Y-P P Chen ldquoImage based computer aideddiagnosis system for cancer detectionrdquo Expert Systems withApplications vol 42 no 12 pp 5356ndash5365 2015

[13] J A Guy and P L Harold ldquoAfter detection the improvedaccuracy of lung cancer assessment using radiologic com-puter-aided diagnosisrdquo Academic Radiology vol 23 no 2pp 186ndash191 2016

[14] E Kiyonori T Shodayu J Binghu et al ldquoPleural invasion byperipheral lung cancer prediction with three-dimensionalCTrdquo Academic Radiology vol 3 pp 310ndash319 2015

[15] B Koohestani ldquoA crossover operator for improving the ef-ficiency of permutation-based genetic algorithmsrdquo ExpertSystems with Applications vol 1511 Article ID 113381 2020

[16] N K Lee X Li and D Wang ldquoA comprehensive survey ongenetic algorithms for DNA motif predictionrdquo InformationSciences vol 466 pp 25ndash43 2018

[17] S Shibao and Y Leilei ldquoResearch on variable precision roughset model and its applicationrdquo Computer Engineering andApplication vol 07 pp 10ndash13 2009

[18] T Xiaolong Several Problems of Multi Granularity VariablePrecision Rough Set Guangxi University For NationalitiesNanning China 2015

[19] W Xueming Research on Several Rough Set Models andNeural Network University of Electronic Science and Tech-nology of China Chengdu China 2013

[20] T Sun J Wang X Li et al ldquoComparative evaluation ofsupport vector machines for computer aided diagnosis of lungcancer in CT based on a multi-dimensional data setrdquo Com-puter Methods and Programs in Biomedicine vol 111 no 2pp 519ndash524 2013

[21] Z Yang T Ouyang X Fu and X Peng ldquoA decision-makingalgorithm for online shopping using deep-learning-basedopinion pairs mining and q -rung orthopair fuzzy interactionHeronianmean operatorsrdquo International Journal of IntelligentSystems vol 35 no 5 pp 783ndash825 2020

[22] W Chen C Lin C Li et al ldquoTracing the evolution of 3Dprinting technology in China using LDA-based patent ab-stract miningrdquo IEEE Transactions on Engineering Manage-men vol 36 pp 1ndash11 2020

18 Mathematical Problems in Engineering

Table 11 +e statistical results of the second group for experiment 2 with the SVM classifier

Experiment times Accuracy () Sensitivity () Specificity () Time (s)

Reduction 1

1 9300 8650 9950 2280072 9575 9700 9450 2376463 9700 9600 9800 2332504 9750 9850 9650 2444915 9925 10000 9850 244816

Average value 9650 9560 9740 237642

Reduction 2

1 9375 8800 9950 2524032 9625 9750 9500 2652893 9800 9700 9900 2655234 9800 9900 9700 2682125 9950 10000 9900 275880

Average value 9710 9630 9790 265461

Reduction 3

1 9275 8750 9800 1807802 9675 9750 9600 1929923 9700 9600 9800 1872434 9775 9950 9600 2084825 9875 10000 9750 203507

Average value 9660 9610 9710 194601

Reduction 4

1 9200 8650 9750 2572602 9700 9750 9650 2730243 9775 9650 9900 2723164 9750 9900 9600 2815545 9900 10000 9800 291471

Average value 9665 9590 9740 275125

Reduction 5

1 9275 8750 9800 1437152 9675 9600 9750 1526373 9750 9800 9700 1589294 9775 9900 9650 1629975 9950 10000 9900 166792

Average value 9685 9610 9760 157014

Table 12 Results of VPRS-GA running 5 times when 1 minus β 1 ω1 1ω2 1ω3 0

Experimenttimes C_ reduction Reduction

lengthOptimal fitness

valueAttribute dependency

degree Time (s)

1 15 44 68 73 79 84 6 minus 27313 07965 114499012 34 51 54 75 80 90 6 minus 27047 08460 96993913 2 34 49 70 71 72 76 81 8 minus 34057 07535 112334894 12 25 78 85 4 minus 22872 09285 11668133

5 6 7 12 13 42 44 55 57 65 66 69 77 81 8687 15 minus 33230 08665 13236077

Average value 78 minus 28903 08382 11457398

ndash1

ndash2

ndash3

ndash4

Fitn

ess v

alue

0 50 100 150Generation stopping criteria

Best fitnessMean fitness

Best ndash340567 Mean ndash330598

Figure 9 +e variation of fitness function value in a running process for experiment 2-third group

Mathematical Problems in Engineering 13

dependency) target 2 (the minimum number of attributesreduction) and target 3 (gene encoding weight function)the three objective functions play an important role in theevaluation of fitness function However the importance offitness function is reduced in these three objectives+erefore in this experiment when the other conditions areunchanged the weight coefficient of the target 1 is increasedto verify the influence of the change in the weight coefficienton the experimental results and they are shown in Table 14

(1) 1st Group Experiment ω1 1 ω2 1 ω3 0 +e al-gorithm are run 5 times according to this group weights theresults of the 5 groups are given in Table 5 including thereduction of the conditional attributes the length of reduc-tion the optimal fitness value the attribute dependency andthe time +e convergence of VPRS-GA under the variationfor fitness function value in one time is shown in Figure 6 (ienot repeated for the second group of experiment 1)

(2) 2nd Group Experiment ω1 2 ω2 1 ω3 0 +ealgorithm is run 5 times according to this group weights theresults of the 5 groups are given in Table 15 including thereduction of the conditional attributes the length of re-duction the optimal fitness value the attribute dependencyand the time +e convergence of VPRS-GA under thevariation for fitness function value in one time is shown inFigure 10

Each reduction is classified by SVM classifier using themethod of 5-fold cross validation through changing thetraining samples and test samples the results of the fivegroups were obtained including accuracy sensitivityspecificity and time (training samples are constructed by800 malignant samples and 800 benign samples testingsamples are constructed by 200 malignant samples and 200benign samples the experiment is repeated 5 times bychanging training samples and testing samples) Finally theaverage values of these five groups are obtained as the finalresult of the reduction and shown in Table 16

+e experimental group in the case of 1 minus β= 06 un-changed the weight of ω1 was increased +e attributedependency and the optimal fitness function are relativelyhigh the average precision of reduction 1 reduction 2 andreduction 3 in Table 16 is more than 97 and that of re-duction 2 is even up to 9725 +e average recognitionaccuracy of the experimental group is 9703 which ishigher than that of the first group

Table 13 +e statistical results of the third group for experiment 2 with the SVM classifier

Experiment times Accuracy () Sensitivity () Specificity () Time (s)

Reduction 1

1 9225 8450 10000 812712 9550 9700 9400 945833 9575 9400 9750 881984 9600 9800 9400 937545 9725 9900 9550 98691

Average value 9535 9450 9620 91299

Reduction 2

1 9200 8450 9950 648942 9625 9550 9700 801983 9525 9300 9750 773374 9600 9750 9450 760125 9800 10000 9600 82763

Average value 9550 9410 9690 76241

Reduction 3

1 9200 8450 9950 648942 9625 9550 9700 801983 9525 9300 9750 773374 9600 9750 9450 760125 9800 10000 9600 82763

Average value 9550 9410 9690 76241

Reduction 4

1 9275 8550 10000 672642 9675 9600 9750 784673 9600 9450 9750 730224 9575 9750 9400 794605 9800 10000 9600 84184

Average value 9585 9470 9700 76479

Reduction 5

1 9200 8450 9950 1147192 9625 9750 9500 1287053 9850 9900 9800 1320494 9775 9950 9600 1335135 9850 10000 9700 133144

Average value 9660 9610 9710 128426

Table 14 Fitness function weight proportion and β value

Experiment times1 minus β 06

ω1 ω2 ω3First group experiment 1 1 0Second group experiment 2 1 0+ird group experiment 3 1 0

14 Mathematical Problems in Engineering

ndash2

ndash25

ndash3

Fitn

ess v

alue

0 50 100 150Generation stopping criteria

Best fitnessMean fitness

Best ndash2915 Mean ndash291446

Figure 10 +e variation of fitness function value in a running process for experiment 3-second group

Table 15 Results of VPRS-GA running 5 times when 1 minus β 06 ω1 2ω2 1ω3 0

Experimenttimes C_ reduction Reduction

lengthOptimal fitness

valueAttribute dependency

degree Time (s)

1 2 3 4 5 11 13 16 18 24 30 34 37 39 41 42 51 55 64 7077 78 82 22 minus 34859 09060 21515464

2 8 9 11 12 14 15 23 25 26 29 30 33 37 42 43 45 46 5060 61 69 74 80 87 89 25 minus 30845 09390 42761634

3 8 11 12 13 16 18 19 24 29 36 37 43 64 65 68 71 86 9192 19 minus 35039 09150 26197164

4 2 3 4 8 10 11 12 13 15 16 19 23 25 30 48 55 64 65 6874 77 80 81 83 84 86 89 27 minus 29150 09575 44271631

5 5 8 911 121517 23 25 29 31 36 39 41 48 54 59 63 8083 86 89 22 minus 29920 09525 43161464

Average value 23 minus 31962 09340 35581471

Table 16 +e statistical results of the second group for experiment 3 with the SVM classifier

Experiment times Accuracy () Sensitivity () Specificity () Time (s)

Reduction 1

1 9275 8600 9950 1884972 9725 9800 9650 1571623 9850 9900 9800 1586914 9800 9900 9700 1646035 9950 10000 9900 161914

Average value 9720 9640 9800 166173

Reduction 2

1 9450 8950 9950 1908132 9675 9800 9550 2002513 9775 9800 9750 1970084 9850 9900 9800 2009245 9875 9900 9850 209245

Average value 9725 9670 9780 199648

Reduction 3

1 9400 8800 10000 1313692 9725 9800 9650 1447973 9800 9800 9800 1426624 9725 9850 9600 1471905 9925 10000 9850 148799

Average value 9715 9650 9780 142963

Reduction 4

1 9350 8750 9950 2404562 9700 9750 9650 2520823 9800 9800 9800 2511754 9775 9950 9600 2701885 9825 10000 9650 267471

Average value 9690 9650 9730 256274

Reduction 5

1 9325 8800 9850 1809592 9600 9800 9400 1965633 9750 9750 9750 1967234 9800 9900 9700 2078295 9850 9950 9750 219703

Average value 9665 9640 9690 200355

Mathematical Problems in Engineering 15

Table 17 Results of VPRS-GA running 5 times when 1 minus β 1 ω1 1ω2 1ω3 0

Experimenttimes C_ reduction Reduction

lengthOptimal fitness

valueAttribute

dependency degree Time (s)

1 3 4 5 8 9 11 12 17 19 29 34 35 38 46 52 53 55 59 63 6672 75 77 78 79 87 92 27 minus 38867 09550 28981789

2 4 8 9 11 12 15 17 29 33 37 38 39 42 43 48 55 67 73 7881 83 84 88 89 90 25 minus 38167 09715 55783772

3 2 3 4 8 9 10 11 12 13 15 16 19 24 25 30 36 49 54 55 6064 67 68 70 74 77 83 85 86 91 30 minus 38807 09530 34831096

4 4 5 7 11 12 14 15 17 25 29 33 36 39 41 42 47 48 50 5556 58 62 67 69 72 74 77 84 86 90 91 31 minus 39430 09665 35742822

5 3 4 5 8 9 11 12 17 19 29 34 35 38 46 52 53 55 59 63 6672 75 77 78 79 87 92 27 minus 38867 09550 27919582

Average value 28 minus 38827 09602 36651812

ndash3

ndash35

ndash40 50 100 150

Generation stopping criteria

Fitn

ess v

alue

Best fitnessMean fitness

Best ndash394298 Mean ndash393327

Figure 11 +e variation of fitness function value in a running process for experiment 3-third group

Table 18 +e statistical results of the Second group for experiment 3 with the SVM classifier

Experiment times Accuracy () Sensitivity () Specificity () Time (s)

Reduction 1

1 9200 8700 9700 2187172 9750 9750 9750 2105503 9850 9850 9850 2032064 9800 9900 9700 2211645 9925 10000 9850 272536

Average value 9705 9640 9770 225235

Reduction 2

1 9400 8850 9950 2331232 9575 9750 9400 2433493 9750 9700 9800 2442024 9775 9900 9650 2566075 9900 9950 9850 259071

Average value 9680 9630 9730 247270

Reduction 3

1 9275 8650 9900 2525842 9625 9750 9500 2624123 9775 9800 9750 2601274 9775 9900 9650 2686705 9875 10000 9750 265387

Average value 9665 9620 9710 261836

Reduction 4

1 9150 8550 9750 2532312 9625 9750 9500 2649433 9750 9700 9800 2752834 9800 9950 9650 3229545 9825 9950 9700 277432

Average value 9630 9580 9680 278769

Reduction 5

1 9200 8800 9600 1951962 9700 9700 9700 2148893 9825 9800 9850 2036124 9850 10000 9700 2133615 9900 9900 9900 225526

Average value 9695 9640 9750 210517

16 Mathematical Problems in Engineering

(3) 3rd Group Experiment ω1 3 ω2 1 ω3 0 +e al-gorithm is run 5 times according to the group weights andthe results of the 5 groups are given in Table 17 including thereduction of the conditional attributes the length of re-duction the optimal fitness value the attribute dependencyand the time +e convergence of VPRS-GA under thevariation for fitness function value for one time is shown inFigure 11

Each reduction is classified by SVM classifier using themethod of 5-fold cross validation through changing thetraining samples and test samples the results of the fivegroups were obtained including accuracy sensitivityspecificity and time (training samples are constructed by800 malignant samples and 800 benign samples testingsamples are constructed by 200 malignant samples and 200benign samples the experiment is repeated 5 times bychanging training samples and testing samples) Finally theaverage values of these five groups are obtained as the finalresult of the reduction and shown in Table 18

+e experiment in the case of 1 minus β 06 unchangedincrease the weight of the ω1 ω1 3 ω2 1 ω3 0 InTable 18 the recognition accuracy of reduction 1 is over 97only +e average recognition accuracy of the experimentalgroup is 9675 and the accuracy is decreased by 028compared with that in the other second groups +e threegroups of experiment 3 the purpose is to verify whether theexperimental accuracy is influenced by increasing theweight +e experimental results show that the accuracy ofsecond group for experimental weight 2 1 0 comparedwith first group experiment when 1 1 0 is high but thethird groups of experimental weight was 3 1 0 and theaccuracy declined therefore the weight of 2 1 0 is the bestchoice for this experiment

4 Conclusions

Aiming at the deficiency of the traditional rough set modelthis paper proposes a new feature selection model based ongenetic algorithm and variable precision rough set by in-troducing the β value the rigid inclusion of the approxi-mation for the traditional rough set is relaxed and then wedesign the 3 kinds of experiments by constructing the de-cision information table of the PETCT feature for lungtumor ROI +e first type of experiment is the inclusion of1 minus β 06 and different values of ω made a total of threegroups of experiments the experimental results show thatthe better recognition accuracy can be obtained when theweight is 1 1 0 and the results show that the gene codingweight function has no effect on the fitness function For thesecond type of experiments ϖ1 1ω2 1 ω3 0according to the different values of β to do three groups ofexperiments the results show that the recognition accuracyof 1 minus β 06 is the best which shows that the larger the βvalue is the lower approximate cardinality will be largerthen the relative accuracy will increase For the third type ofexperiments 1 minus β 06 ω value is increased to achieve thebest fitness function in order to achieve the best results +eexperimental results show that the recognition accuracy isbetter than the others when the weight value is 2 1 0 so it

is better to solve the problem by increasing the proportion ofattribute dependency +rough the above experiments it isshown that the high-dimensional feature selection algorithmbased on genetic algorithm and variable precision rough setcan solve the multiobjective optimization problem wellHowever when the fitness function and its parameters areapplied in the specific application it is necessary to analyzethe specific problems

Data Availability

+e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

+e authors declare no conflicts of interest

Acknowledgments

+is work was supported by National Natural ScienceFoundation of China (Grant nos 61561040 and 61876121)First-Class Disciplines Foundation of Ningxia (NoNXYLXK2017B09)

References

[1] S Luo D Miao Z Zhang Y Zhang and S Hu ldquoA neigh-borhood rough set model with nominal metric embeddingrdquoInformation Sciences vol 520 pp 373ndash388 2020

[2] B Barman and S Patra ldquoVariable precision rough set basedunsupervised band selection technique for hyperspectralimage classificationrdquo Knowledge-Based Systems vol 1936Article ID 105414 2020

[3] Y Chenyi and L Jinjin ldquoApproximate attribute reductionunder variable precision rough set βrdquo Journal of ShandongUniversity vol 11 pp 17ndash21 2011

[4] S Xiaowei Research on Hierarchical Model of Attribute Re-duction in Variable Precision Rough Set Central SouthUniversity Changsha China 2013

[5] Z Jie and W Jiayang ldquoAnalysis of reduction feature ofvariable precision rough set modelrdquo Computer ApplicationResearch vol 7 pp 12ndash15 2007

[6] Z Pei and Z Qinghua ldquoFCM clustering algorithm based onvariable precision rough setrdquo Journal of Shanxi Universityvol 3 pp 342ndash348 2016

[7] C Hao and Y Junan ldquoAttribute kernel and minimum at-tribute reduction algorithm of variable precision rough setrdquoActa Sinica Sinica vol 5 pp 1011ndash1017 2012

[8] S Xu X Yang H Yu D-J Yu J Yang and E CC TsangldquoMulti-label learning with label-specific feature reductionrdquoKnowledge-Based Systems vol 104 pp 52ndash61 2016

[9] I Maryam and G Hassan ldquoFeature space discriminantanalysis for hyperspectral data feature reductionrdquo ISPRSJournal of Photogrammetry and Remote Sensing vol 102pp 1ndash13 2015

[10] S Q Wang C Y Gao C Luo G M Zheng and Y N ZhouldquoResearch on feature selectionattribute reduction methodbased on rough set theoryrdquo Procedia Computer Sciencevol 154 pp 194ndash198e 2019

[11] A W Omar M Azzam O Hadi and B Jamal ldquoCEAP SVM-based intelligent detection model for clustered vehicular ad

Mathematical Problems in Engineering 17

hoc networksrdquo Expert Systems with Applications vol 50pp 40ndash54 2016

[12] H Lee and Y-P P Chen ldquoImage based computer aideddiagnosis system for cancer detectionrdquo Expert Systems withApplications vol 42 no 12 pp 5356ndash5365 2015

[13] J A Guy and P L Harold ldquoAfter detection the improvedaccuracy of lung cancer assessment using radiologic com-puter-aided diagnosisrdquo Academic Radiology vol 23 no 2pp 186ndash191 2016

[14] E Kiyonori T Shodayu J Binghu et al ldquoPleural invasion byperipheral lung cancer prediction with three-dimensionalCTrdquo Academic Radiology vol 3 pp 310ndash319 2015

[15] B Koohestani ldquoA crossover operator for improving the ef-ficiency of permutation-based genetic algorithmsrdquo ExpertSystems with Applications vol 1511 Article ID 113381 2020

[16] N K Lee X Li and D Wang ldquoA comprehensive survey ongenetic algorithms for DNA motif predictionrdquo InformationSciences vol 466 pp 25ndash43 2018

[17] S Shibao and Y Leilei ldquoResearch on variable precision roughset model and its applicationrdquo Computer Engineering andApplication vol 07 pp 10ndash13 2009

[18] T Xiaolong Several Problems of Multi Granularity VariablePrecision Rough Set Guangxi University For NationalitiesNanning China 2015

[19] W Xueming Research on Several Rough Set Models andNeural Network University of Electronic Science and Tech-nology of China Chengdu China 2013

[20] T Sun J Wang X Li et al ldquoComparative evaluation ofsupport vector machines for computer aided diagnosis of lungcancer in CT based on a multi-dimensional data setrdquo Com-puter Methods and Programs in Biomedicine vol 111 no 2pp 519ndash524 2013

[21] Z Yang T Ouyang X Fu and X Peng ldquoA decision-makingalgorithm for online shopping using deep-learning-basedopinion pairs mining and q -rung orthopair fuzzy interactionHeronianmean operatorsrdquo International Journal of IntelligentSystems vol 35 no 5 pp 783ndash825 2020

[22] W Chen C Lin C Li et al ldquoTracing the evolution of 3Dprinting technology in China using LDA-based patent ab-stract miningrdquo IEEE Transactions on Engineering Manage-men vol 36 pp 1ndash11 2020

18 Mathematical Problems in Engineering

dependency) target 2 (the minimum number of attributesreduction) and target 3 (gene encoding weight function)the three objective functions play an important role in theevaluation of fitness function However the importance offitness function is reduced in these three objectives+erefore in this experiment when the other conditions areunchanged the weight coefficient of the target 1 is increasedto verify the influence of the change in the weight coefficienton the experimental results and they are shown in Table 14

(1) 1st Group Experiment ω1 1 ω2 1 ω3 0 +e al-gorithm are run 5 times according to this group weights theresults of the 5 groups are given in Table 5 including thereduction of the conditional attributes the length of reduc-tion the optimal fitness value the attribute dependency andthe time +e convergence of VPRS-GA under the variationfor fitness function value in one time is shown in Figure 6 (ienot repeated for the second group of experiment 1)

(2) 2nd Group Experiment ω1 2 ω2 1 ω3 0 +ealgorithm is run 5 times according to this group weights theresults of the 5 groups are given in Table 15 including thereduction of the conditional attributes the length of re-duction the optimal fitness value the attribute dependencyand the time +e convergence of VPRS-GA under thevariation for fitness function value in one time is shown inFigure 10

Each reduction is classified by SVM classifier using themethod of 5-fold cross validation through changing thetraining samples and test samples the results of the fivegroups were obtained including accuracy sensitivityspecificity and time (training samples are constructed by800 malignant samples and 800 benign samples testingsamples are constructed by 200 malignant samples and 200benign samples the experiment is repeated 5 times bychanging training samples and testing samples) Finally theaverage values of these five groups are obtained as the finalresult of the reduction and shown in Table 16

+e experimental group in the case of 1 minus β= 06 un-changed the weight of ω1 was increased +e attributedependency and the optimal fitness function are relativelyhigh the average precision of reduction 1 reduction 2 andreduction 3 in Table 16 is more than 97 and that of re-duction 2 is even up to 9725 +e average recognitionaccuracy of the experimental group is 9703 which ishigher than that of the first group

Table 13 +e statistical results of the third group for experiment 2 with the SVM classifier

Experiment times Accuracy () Sensitivity () Specificity () Time (s)

Reduction 1

1 9225 8450 10000 812712 9550 9700 9400 945833 9575 9400 9750 881984 9600 9800 9400 937545 9725 9900 9550 98691

Average value 9535 9450 9620 91299

Reduction 2

1 9200 8450 9950 648942 9625 9550 9700 801983 9525 9300 9750 773374 9600 9750 9450 760125 9800 10000 9600 82763

Average value 9550 9410 9690 76241

Reduction 3

1 9200 8450 9950 648942 9625 9550 9700 801983 9525 9300 9750 773374 9600 9750 9450 760125 9800 10000 9600 82763

Average value 9550 9410 9690 76241

Reduction 4

1 9275 8550 10000 672642 9675 9600 9750 784673 9600 9450 9750 730224 9575 9750 9400 794605 9800 10000 9600 84184

Average value 9585 9470 9700 76479

Reduction 5

1 9200 8450 9950 1147192 9625 9750 9500 1287053 9850 9900 9800 1320494 9775 9950 9600 1335135 9850 10000 9700 133144

Average value 9660 9610 9710 128426

Table 14 Fitness function weight proportion and β value

Experiment times1 minus β 06

ω1 ω2 ω3First group experiment 1 1 0Second group experiment 2 1 0+ird group experiment 3 1 0

14 Mathematical Problems in Engineering

ndash2

ndash25

ndash3

Fitn

ess v

alue

0 50 100 150Generation stopping criteria

Best fitnessMean fitness

Best ndash2915 Mean ndash291446

Figure 10 +e variation of fitness function value in a running process for experiment 3-second group

Table 15 Results of VPRS-GA running 5 times when 1 minus β 06 ω1 2ω2 1ω3 0

Experimenttimes C_ reduction Reduction

lengthOptimal fitness

valueAttribute dependency

degree Time (s)

1 2 3 4 5 11 13 16 18 24 30 34 37 39 41 42 51 55 64 7077 78 82 22 minus 34859 09060 21515464

2 8 9 11 12 14 15 23 25 26 29 30 33 37 42 43 45 46 5060 61 69 74 80 87 89 25 minus 30845 09390 42761634

3 8 11 12 13 16 18 19 24 29 36 37 43 64 65 68 71 86 9192 19 minus 35039 09150 26197164

4 2 3 4 8 10 11 12 13 15 16 19 23 25 30 48 55 64 65 6874 77 80 81 83 84 86 89 27 minus 29150 09575 44271631

5 5 8 911 121517 23 25 29 31 36 39 41 48 54 59 63 8083 86 89 22 minus 29920 09525 43161464

Average value 23 minus 31962 09340 35581471

Table 16 +e statistical results of the second group for experiment 3 with the SVM classifier

Experiment times Accuracy () Sensitivity () Specificity () Time (s)

Reduction 1

1 9275 8600 9950 1884972 9725 9800 9650 1571623 9850 9900 9800 1586914 9800 9900 9700 1646035 9950 10000 9900 161914

Average value 9720 9640 9800 166173

Reduction 2

1 9450 8950 9950 1908132 9675 9800 9550 2002513 9775 9800 9750 1970084 9850 9900 9800 2009245 9875 9900 9850 209245

Average value 9725 9670 9780 199648

Reduction 3

1 9400 8800 10000 1313692 9725 9800 9650 1447973 9800 9800 9800 1426624 9725 9850 9600 1471905 9925 10000 9850 148799

Average value 9715 9650 9780 142963

Reduction 4

1 9350 8750 9950 2404562 9700 9750 9650 2520823 9800 9800 9800 2511754 9775 9950 9600 2701885 9825 10000 9650 267471

Average value 9690 9650 9730 256274

Reduction 5

1 9325 8800 9850 1809592 9600 9800 9400 1965633 9750 9750 9750 1967234 9800 9900 9700 2078295 9850 9950 9750 219703

Average value 9665 9640 9690 200355

Mathematical Problems in Engineering 15

Table 17 Results of VPRS-GA running 5 times when 1 minus β 1 ω1 1ω2 1ω3 0

Experimenttimes C_ reduction Reduction

lengthOptimal fitness

valueAttribute

dependency degree Time (s)

1 3 4 5 8 9 11 12 17 19 29 34 35 38 46 52 53 55 59 63 6672 75 77 78 79 87 92 27 minus 38867 09550 28981789

2 4 8 9 11 12 15 17 29 33 37 38 39 42 43 48 55 67 73 7881 83 84 88 89 90 25 minus 38167 09715 55783772

3 2 3 4 8 9 10 11 12 13 15 16 19 24 25 30 36 49 54 55 6064 67 68 70 74 77 83 85 86 91 30 minus 38807 09530 34831096

4 4 5 7 11 12 14 15 17 25 29 33 36 39 41 42 47 48 50 5556 58 62 67 69 72 74 77 84 86 90 91 31 minus 39430 09665 35742822

5 3 4 5 8 9 11 12 17 19 29 34 35 38 46 52 53 55 59 63 6672 75 77 78 79 87 92 27 minus 38867 09550 27919582

Average value 28 minus 38827 09602 36651812

ndash3

ndash35

ndash40 50 100 150

Generation stopping criteria

Fitn

ess v

alue

Best fitnessMean fitness

Best ndash394298 Mean ndash393327

Figure 11 +e variation of fitness function value in a running process for experiment 3-third group

Table 18 +e statistical results of the Second group for experiment 3 with the SVM classifier

Experiment times Accuracy () Sensitivity () Specificity () Time (s)

Reduction 1

1 9200 8700 9700 2187172 9750 9750 9750 2105503 9850 9850 9850 2032064 9800 9900 9700 2211645 9925 10000 9850 272536

Average value 9705 9640 9770 225235

Reduction 2

1 9400 8850 9950 2331232 9575 9750 9400 2433493 9750 9700 9800 2442024 9775 9900 9650 2566075 9900 9950 9850 259071

Average value 9680 9630 9730 247270

Reduction 3

1 9275 8650 9900 2525842 9625 9750 9500 2624123 9775 9800 9750 2601274 9775 9900 9650 2686705 9875 10000 9750 265387

Average value 9665 9620 9710 261836

Reduction 4

1 9150 8550 9750 2532312 9625 9750 9500 2649433 9750 9700 9800 2752834 9800 9950 9650 3229545 9825 9950 9700 277432

Average value 9630 9580 9680 278769

Reduction 5

1 9200 8800 9600 1951962 9700 9700 9700 2148893 9825 9800 9850 2036124 9850 10000 9700 2133615 9900 9900 9900 225526

Average value 9695 9640 9750 210517

16 Mathematical Problems in Engineering

(3) 3rd Group Experiment ω1 3 ω2 1 ω3 0 +e al-gorithm is run 5 times according to the group weights andthe results of the 5 groups are given in Table 17 including thereduction of the conditional attributes the length of re-duction the optimal fitness value the attribute dependencyand the time +e convergence of VPRS-GA under thevariation for fitness function value for one time is shown inFigure 11

Each reduction is classified by SVM classifier using themethod of 5-fold cross validation through changing thetraining samples and test samples the results of the fivegroups were obtained including accuracy sensitivityspecificity and time (training samples are constructed by800 malignant samples and 800 benign samples testingsamples are constructed by 200 malignant samples and 200benign samples the experiment is repeated 5 times bychanging training samples and testing samples) Finally theaverage values of these five groups are obtained as the finalresult of the reduction and shown in Table 18

+e experiment in the case of 1 minus β 06 unchangedincrease the weight of the ω1 ω1 3 ω2 1 ω3 0 InTable 18 the recognition accuracy of reduction 1 is over 97only +e average recognition accuracy of the experimentalgroup is 9675 and the accuracy is decreased by 028compared with that in the other second groups +e threegroups of experiment 3 the purpose is to verify whether theexperimental accuracy is influenced by increasing theweight +e experimental results show that the accuracy ofsecond group for experimental weight 2 1 0 comparedwith first group experiment when 1 1 0 is high but thethird groups of experimental weight was 3 1 0 and theaccuracy declined therefore the weight of 2 1 0 is the bestchoice for this experiment

4 Conclusions

Aiming at the deficiency of the traditional rough set modelthis paper proposes a new feature selection model based ongenetic algorithm and variable precision rough set by in-troducing the β value the rigid inclusion of the approxi-mation for the traditional rough set is relaxed and then wedesign the 3 kinds of experiments by constructing the de-cision information table of the PETCT feature for lungtumor ROI +e first type of experiment is the inclusion of1 minus β 06 and different values of ω made a total of threegroups of experiments the experimental results show thatthe better recognition accuracy can be obtained when theweight is 1 1 0 and the results show that the gene codingweight function has no effect on the fitness function For thesecond type of experiments ϖ1 1ω2 1 ω3 0according to the different values of β to do three groups ofexperiments the results show that the recognition accuracyof 1 minus β 06 is the best which shows that the larger the βvalue is the lower approximate cardinality will be largerthen the relative accuracy will increase For the third type ofexperiments 1 minus β 06 ω value is increased to achieve thebest fitness function in order to achieve the best results +eexperimental results show that the recognition accuracy isbetter than the others when the weight value is 2 1 0 so it

is better to solve the problem by increasing the proportion ofattribute dependency +rough the above experiments it isshown that the high-dimensional feature selection algorithmbased on genetic algorithm and variable precision rough setcan solve the multiobjective optimization problem wellHowever when the fitness function and its parameters areapplied in the specific application it is necessary to analyzethe specific problems

Data Availability

+e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

+e authors declare no conflicts of interest

Acknowledgments

+is work was supported by National Natural ScienceFoundation of China (Grant nos 61561040 and 61876121)First-Class Disciplines Foundation of Ningxia (NoNXYLXK2017B09)

References

[1] S Luo D Miao Z Zhang Y Zhang and S Hu ldquoA neigh-borhood rough set model with nominal metric embeddingrdquoInformation Sciences vol 520 pp 373ndash388 2020

[2] B Barman and S Patra ldquoVariable precision rough set basedunsupervised band selection technique for hyperspectralimage classificationrdquo Knowledge-Based Systems vol 1936Article ID 105414 2020

[3] Y Chenyi and L Jinjin ldquoApproximate attribute reductionunder variable precision rough set βrdquo Journal of ShandongUniversity vol 11 pp 17ndash21 2011

[4] S Xiaowei Research on Hierarchical Model of Attribute Re-duction in Variable Precision Rough Set Central SouthUniversity Changsha China 2013

[5] Z Jie and W Jiayang ldquoAnalysis of reduction feature ofvariable precision rough set modelrdquo Computer ApplicationResearch vol 7 pp 12ndash15 2007

[6] Z Pei and Z Qinghua ldquoFCM clustering algorithm based onvariable precision rough setrdquo Journal of Shanxi Universityvol 3 pp 342ndash348 2016

[7] C Hao and Y Junan ldquoAttribute kernel and minimum at-tribute reduction algorithm of variable precision rough setrdquoActa Sinica Sinica vol 5 pp 1011ndash1017 2012

[8] S Xu X Yang H Yu D-J Yu J Yang and E CC TsangldquoMulti-label learning with label-specific feature reductionrdquoKnowledge-Based Systems vol 104 pp 52ndash61 2016

[9] I Maryam and G Hassan ldquoFeature space discriminantanalysis for hyperspectral data feature reductionrdquo ISPRSJournal of Photogrammetry and Remote Sensing vol 102pp 1ndash13 2015

[10] S Q Wang C Y Gao C Luo G M Zheng and Y N ZhouldquoResearch on feature selectionattribute reduction methodbased on rough set theoryrdquo Procedia Computer Sciencevol 154 pp 194ndash198e 2019

[11] A W Omar M Azzam O Hadi and B Jamal ldquoCEAP SVM-based intelligent detection model for clustered vehicular ad

Mathematical Problems in Engineering 17

hoc networksrdquo Expert Systems with Applications vol 50pp 40ndash54 2016

[12] H Lee and Y-P P Chen ldquoImage based computer aideddiagnosis system for cancer detectionrdquo Expert Systems withApplications vol 42 no 12 pp 5356ndash5365 2015

[13] J A Guy and P L Harold ldquoAfter detection the improvedaccuracy of lung cancer assessment using radiologic com-puter-aided diagnosisrdquo Academic Radiology vol 23 no 2pp 186ndash191 2016

[14] E Kiyonori T Shodayu J Binghu et al ldquoPleural invasion byperipheral lung cancer prediction with three-dimensionalCTrdquo Academic Radiology vol 3 pp 310ndash319 2015

[15] B Koohestani ldquoA crossover operator for improving the ef-ficiency of permutation-based genetic algorithmsrdquo ExpertSystems with Applications vol 1511 Article ID 113381 2020

[16] N K Lee X Li and D Wang ldquoA comprehensive survey ongenetic algorithms for DNA motif predictionrdquo InformationSciences vol 466 pp 25ndash43 2018

[17] S Shibao and Y Leilei ldquoResearch on variable precision roughset model and its applicationrdquo Computer Engineering andApplication vol 07 pp 10ndash13 2009

[18] T Xiaolong Several Problems of Multi Granularity VariablePrecision Rough Set Guangxi University For NationalitiesNanning China 2015

[19] W Xueming Research on Several Rough Set Models andNeural Network University of Electronic Science and Tech-nology of China Chengdu China 2013

[20] T Sun J Wang X Li et al ldquoComparative evaluation ofsupport vector machines for computer aided diagnosis of lungcancer in CT based on a multi-dimensional data setrdquo Com-puter Methods and Programs in Biomedicine vol 111 no 2pp 519ndash524 2013

[21] Z Yang T Ouyang X Fu and X Peng ldquoA decision-makingalgorithm for online shopping using deep-learning-basedopinion pairs mining and q -rung orthopair fuzzy interactionHeronianmean operatorsrdquo International Journal of IntelligentSystems vol 35 no 5 pp 783ndash825 2020

[22] W Chen C Lin C Li et al ldquoTracing the evolution of 3Dprinting technology in China using LDA-based patent ab-stract miningrdquo IEEE Transactions on Engineering Manage-men vol 36 pp 1ndash11 2020

18 Mathematical Problems in Engineering

ndash2

ndash25

ndash3

Fitn

ess v

alue

0 50 100 150Generation stopping criteria

Best fitnessMean fitness

Best ndash2915 Mean ndash291446

Figure 10 +e variation of fitness function value in a running process for experiment 3-second group

Table 15 Results of VPRS-GA running 5 times when 1 minus β 06 ω1 2ω2 1ω3 0

Experimenttimes C_ reduction Reduction

lengthOptimal fitness

valueAttribute dependency

degree Time (s)

1 2 3 4 5 11 13 16 18 24 30 34 37 39 41 42 51 55 64 7077 78 82 22 minus 34859 09060 21515464

2 8 9 11 12 14 15 23 25 26 29 30 33 37 42 43 45 46 5060 61 69 74 80 87 89 25 minus 30845 09390 42761634

3 8 11 12 13 16 18 19 24 29 36 37 43 64 65 68 71 86 9192 19 minus 35039 09150 26197164

4 2 3 4 8 10 11 12 13 15 16 19 23 25 30 48 55 64 65 6874 77 80 81 83 84 86 89 27 minus 29150 09575 44271631

5 5 8 911 121517 23 25 29 31 36 39 41 48 54 59 63 8083 86 89 22 minus 29920 09525 43161464

Average value 23 minus 31962 09340 35581471

Table 16 +e statistical results of the second group for experiment 3 with the SVM classifier

Experiment times Accuracy () Sensitivity () Specificity () Time (s)

Reduction 1

1 9275 8600 9950 1884972 9725 9800 9650 1571623 9850 9900 9800 1586914 9800 9900 9700 1646035 9950 10000 9900 161914

Average value 9720 9640 9800 166173

Reduction 2

1 9450 8950 9950 1908132 9675 9800 9550 2002513 9775 9800 9750 1970084 9850 9900 9800 2009245 9875 9900 9850 209245

Average value 9725 9670 9780 199648

Reduction 3

1 9400 8800 10000 1313692 9725 9800 9650 1447973 9800 9800 9800 1426624 9725 9850 9600 1471905 9925 10000 9850 148799

Average value 9715 9650 9780 142963

Reduction 4

1 9350 8750 9950 2404562 9700 9750 9650 2520823 9800 9800 9800 2511754 9775 9950 9600 2701885 9825 10000 9650 267471

Average value 9690 9650 9730 256274

Reduction 5

1 9325 8800 9850 1809592 9600 9800 9400 1965633 9750 9750 9750 1967234 9800 9900 9700 2078295 9850 9950 9750 219703

Average value 9665 9640 9690 200355

Mathematical Problems in Engineering 15

Table 17 Results of VPRS-GA running 5 times when 1 minus β 1 ω1 1ω2 1ω3 0

Experimenttimes C_ reduction Reduction

lengthOptimal fitness

valueAttribute

dependency degree Time (s)

1 3 4 5 8 9 11 12 17 19 29 34 35 38 46 52 53 55 59 63 6672 75 77 78 79 87 92 27 minus 38867 09550 28981789

2 4 8 9 11 12 15 17 29 33 37 38 39 42 43 48 55 67 73 7881 83 84 88 89 90 25 minus 38167 09715 55783772

3 2 3 4 8 9 10 11 12 13 15 16 19 24 25 30 36 49 54 55 6064 67 68 70 74 77 83 85 86 91 30 minus 38807 09530 34831096

4 4 5 7 11 12 14 15 17 25 29 33 36 39 41 42 47 48 50 5556 58 62 67 69 72 74 77 84 86 90 91 31 minus 39430 09665 35742822

5 3 4 5 8 9 11 12 17 19 29 34 35 38 46 52 53 55 59 63 6672 75 77 78 79 87 92 27 minus 38867 09550 27919582

Average value 28 minus 38827 09602 36651812

ndash3

ndash35

ndash40 50 100 150

Generation stopping criteria

Fitn

ess v

alue

Best fitnessMean fitness

Best ndash394298 Mean ndash393327

Figure 11 +e variation of fitness function value in a running process for experiment 3-third group

Table 18 +e statistical results of the Second group for experiment 3 with the SVM classifier

Experiment times Accuracy () Sensitivity () Specificity () Time (s)

Reduction 1

1 9200 8700 9700 2187172 9750 9750 9750 2105503 9850 9850 9850 2032064 9800 9900 9700 2211645 9925 10000 9850 272536

Average value 9705 9640 9770 225235

Reduction 2

1 9400 8850 9950 2331232 9575 9750 9400 2433493 9750 9700 9800 2442024 9775 9900 9650 2566075 9900 9950 9850 259071

Average value 9680 9630 9730 247270

Reduction 3

1 9275 8650 9900 2525842 9625 9750 9500 2624123 9775 9800 9750 2601274 9775 9900 9650 2686705 9875 10000 9750 265387

Average value 9665 9620 9710 261836

Reduction 4

1 9150 8550 9750 2532312 9625 9750 9500 2649433 9750 9700 9800 2752834 9800 9950 9650 3229545 9825 9950 9700 277432

Average value 9630 9580 9680 278769

Reduction 5

1 9200 8800 9600 1951962 9700 9700 9700 2148893 9825 9800 9850 2036124 9850 10000 9700 2133615 9900 9900 9900 225526

Average value 9695 9640 9750 210517

16 Mathematical Problems in Engineering

(3) 3rd Group Experiment ω1 3 ω2 1 ω3 0 +e al-gorithm is run 5 times according to the group weights andthe results of the 5 groups are given in Table 17 including thereduction of the conditional attributes the length of re-duction the optimal fitness value the attribute dependencyand the time +e convergence of VPRS-GA under thevariation for fitness function value for one time is shown inFigure 11

Each reduction is classified by SVM classifier using themethod of 5-fold cross validation through changing thetraining samples and test samples the results of the fivegroups were obtained including accuracy sensitivityspecificity and time (training samples are constructed by800 malignant samples and 800 benign samples testingsamples are constructed by 200 malignant samples and 200benign samples the experiment is repeated 5 times bychanging training samples and testing samples) Finally theaverage values of these five groups are obtained as the finalresult of the reduction and shown in Table 18

+e experiment in the case of 1 minus β 06 unchangedincrease the weight of the ω1 ω1 3 ω2 1 ω3 0 InTable 18 the recognition accuracy of reduction 1 is over 97only +e average recognition accuracy of the experimentalgroup is 9675 and the accuracy is decreased by 028compared with that in the other second groups +e threegroups of experiment 3 the purpose is to verify whether theexperimental accuracy is influenced by increasing theweight +e experimental results show that the accuracy ofsecond group for experimental weight 2 1 0 comparedwith first group experiment when 1 1 0 is high but thethird groups of experimental weight was 3 1 0 and theaccuracy declined therefore the weight of 2 1 0 is the bestchoice for this experiment

4 Conclusions

Aiming at the deficiency of the traditional rough set modelthis paper proposes a new feature selection model based ongenetic algorithm and variable precision rough set by in-troducing the β value the rigid inclusion of the approxi-mation for the traditional rough set is relaxed and then wedesign the 3 kinds of experiments by constructing the de-cision information table of the PETCT feature for lungtumor ROI +e first type of experiment is the inclusion of1 minus β 06 and different values of ω made a total of threegroups of experiments the experimental results show thatthe better recognition accuracy can be obtained when theweight is 1 1 0 and the results show that the gene codingweight function has no effect on the fitness function For thesecond type of experiments ϖ1 1ω2 1 ω3 0according to the different values of β to do three groups ofexperiments the results show that the recognition accuracyof 1 minus β 06 is the best which shows that the larger the βvalue is the lower approximate cardinality will be largerthen the relative accuracy will increase For the third type ofexperiments 1 minus β 06 ω value is increased to achieve thebest fitness function in order to achieve the best results +eexperimental results show that the recognition accuracy isbetter than the others when the weight value is 2 1 0 so it

is better to solve the problem by increasing the proportion ofattribute dependency +rough the above experiments it isshown that the high-dimensional feature selection algorithmbased on genetic algorithm and variable precision rough setcan solve the multiobjective optimization problem wellHowever when the fitness function and its parameters areapplied in the specific application it is necessary to analyzethe specific problems

Data Availability

+e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

+e authors declare no conflicts of interest

Acknowledgments

+is work was supported by National Natural ScienceFoundation of China (Grant nos 61561040 and 61876121)First-Class Disciplines Foundation of Ningxia (NoNXYLXK2017B09)

References

[1] S Luo D Miao Z Zhang Y Zhang and S Hu ldquoA neigh-borhood rough set model with nominal metric embeddingrdquoInformation Sciences vol 520 pp 373ndash388 2020

[2] B Barman and S Patra ldquoVariable precision rough set basedunsupervised band selection technique for hyperspectralimage classificationrdquo Knowledge-Based Systems vol 1936Article ID 105414 2020

[3] Y Chenyi and L Jinjin ldquoApproximate attribute reductionunder variable precision rough set βrdquo Journal of ShandongUniversity vol 11 pp 17ndash21 2011

[4] S Xiaowei Research on Hierarchical Model of Attribute Re-duction in Variable Precision Rough Set Central SouthUniversity Changsha China 2013

[5] Z Jie and W Jiayang ldquoAnalysis of reduction feature ofvariable precision rough set modelrdquo Computer ApplicationResearch vol 7 pp 12ndash15 2007

[6] Z Pei and Z Qinghua ldquoFCM clustering algorithm based onvariable precision rough setrdquo Journal of Shanxi Universityvol 3 pp 342ndash348 2016

[7] C Hao and Y Junan ldquoAttribute kernel and minimum at-tribute reduction algorithm of variable precision rough setrdquoActa Sinica Sinica vol 5 pp 1011ndash1017 2012

[8] S Xu X Yang H Yu D-J Yu J Yang and E CC TsangldquoMulti-label learning with label-specific feature reductionrdquoKnowledge-Based Systems vol 104 pp 52ndash61 2016

[9] I Maryam and G Hassan ldquoFeature space discriminantanalysis for hyperspectral data feature reductionrdquo ISPRSJournal of Photogrammetry and Remote Sensing vol 102pp 1ndash13 2015

[10] S Q Wang C Y Gao C Luo G M Zheng and Y N ZhouldquoResearch on feature selectionattribute reduction methodbased on rough set theoryrdquo Procedia Computer Sciencevol 154 pp 194ndash198e 2019

[11] A W Omar M Azzam O Hadi and B Jamal ldquoCEAP SVM-based intelligent detection model for clustered vehicular ad

Mathematical Problems in Engineering 17

hoc networksrdquo Expert Systems with Applications vol 50pp 40ndash54 2016

[12] H Lee and Y-P P Chen ldquoImage based computer aideddiagnosis system for cancer detectionrdquo Expert Systems withApplications vol 42 no 12 pp 5356ndash5365 2015

[13] J A Guy and P L Harold ldquoAfter detection the improvedaccuracy of lung cancer assessment using radiologic com-puter-aided diagnosisrdquo Academic Radiology vol 23 no 2pp 186ndash191 2016

[14] E Kiyonori T Shodayu J Binghu et al ldquoPleural invasion byperipheral lung cancer prediction with three-dimensionalCTrdquo Academic Radiology vol 3 pp 310ndash319 2015

[15] B Koohestani ldquoA crossover operator for improving the ef-ficiency of permutation-based genetic algorithmsrdquo ExpertSystems with Applications vol 1511 Article ID 113381 2020

[16] N K Lee X Li and D Wang ldquoA comprehensive survey ongenetic algorithms for DNA motif predictionrdquo InformationSciences vol 466 pp 25ndash43 2018

[17] S Shibao and Y Leilei ldquoResearch on variable precision roughset model and its applicationrdquo Computer Engineering andApplication vol 07 pp 10ndash13 2009

[18] T Xiaolong Several Problems of Multi Granularity VariablePrecision Rough Set Guangxi University For NationalitiesNanning China 2015

[19] W Xueming Research on Several Rough Set Models andNeural Network University of Electronic Science and Tech-nology of China Chengdu China 2013

[20] T Sun J Wang X Li et al ldquoComparative evaluation ofsupport vector machines for computer aided diagnosis of lungcancer in CT based on a multi-dimensional data setrdquo Com-puter Methods and Programs in Biomedicine vol 111 no 2pp 519ndash524 2013

[21] Z Yang T Ouyang X Fu and X Peng ldquoA decision-makingalgorithm for online shopping using deep-learning-basedopinion pairs mining and q -rung orthopair fuzzy interactionHeronianmean operatorsrdquo International Journal of IntelligentSystems vol 35 no 5 pp 783ndash825 2020

[22] W Chen C Lin C Li et al ldquoTracing the evolution of 3Dprinting technology in China using LDA-based patent ab-stract miningrdquo IEEE Transactions on Engineering Manage-men vol 36 pp 1ndash11 2020

18 Mathematical Problems in Engineering

Table 17 Results of VPRS-GA running 5 times when 1 minus β 1 ω1 1ω2 1ω3 0

Experimenttimes C_ reduction Reduction

lengthOptimal fitness

valueAttribute

dependency degree Time (s)

1 3 4 5 8 9 11 12 17 19 29 34 35 38 46 52 53 55 59 63 6672 75 77 78 79 87 92 27 minus 38867 09550 28981789

2 4 8 9 11 12 15 17 29 33 37 38 39 42 43 48 55 67 73 7881 83 84 88 89 90 25 minus 38167 09715 55783772

3 2 3 4 8 9 10 11 12 13 15 16 19 24 25 30 36 49 54 55 6064 67 68 70 74 77 83 85 86 91 30 minus 38807 09530 34831096

4 4 5 7 11 12 14 15 17 25 29 33 36 39 41 42 47 48 50 5556 58 62 67 69 72 74 77 84 86 90 91 31 minus 39430 09665 35742822

5 3 4 5 8 9 11 12 17 19 29 34 35 38 46 52 53 55 59 63 6672 75 77 78 79 87 92 27 minus 38867 09550 27919582

Average value 28 minus 38827 09602 36651812

ndash3

ndash35

ndash40 50 100 150

Generation stopping criteria

Fitn

ess v

alue

Best fitnessMean fitness

Best ndash394298 Mean ndash393327

Figure 11 +e variation of fitness function value in a running process for experiment 3-third group

Table 18 +e statistical results of the Second group for experiment 3 with the SVM classifier

Experiment times Accuracy () Sensitivity () Specificity () Time (s)

Reduction 1

1 9200 8700 9700 2187172 9750 9750 9750 2105503 9850 9850 9850 2032064 9800 9900 9700 2211645 9925 10000 9850 272536

Average value 9705 9640 9770 225235

Reduction 2

1 9400 8850 9950 2331232 9575 9750 9400 2433493 9750 9700 9800 2442024 9775 9900 9650 2566075 9900 9950 9850 259071

Average value 9680 9630 9730 247270

Reduction 3

1 9275 8650 9900 2525842 9625 9750 9500 2624123 9775 9800 9750 2601274 9775 9900 9650 2686705 9875 10000 9750 265387

Average value 9665 9620 9710 261836

Reduction 4

1 9150 8550 9750 2532312 9625 9750 9500 2649433 9750 9700 9800 2752834 9800 9950 9650 3229545 9825 9950 9700 277432

Average value 9630 9580 9680 278769

Reduction 5

1 9200 8800 9600 1951962 9700 9700 9700 2148893 9825 9800 9850 2036124 9850 10000 9700 2133615 9900 9900 9900 225526

Average value 9695 9640 9750 210517

16 Mathematical Problems in Engineering

(3) 3rd Group Experiment ω1 3 ω2 1 ω3 0 +e al-gorithm is run 5 times according to the group weights andthe results of the 5 groups are given in Table 17 including thereduction of the conditional attributes the length of re-duction the optimal fitness value the attribute dependencyand the time +e convergence of VPRS-GA under thevariation for fitness function value for one time is shown inFigure 11

Each reduction is classified by SVM classifier using themethod of 5-fold cross validation through changing thetraining samples and test samples the results of the fivegroups were obtained including accuracy sensitivityspecificity and time (training samples are constructed by800 malignant samples and 800 benign samples testingsamples are constructed by 200 malignant samples and 200benign samples the experiment is repeated 5 times bychanging training samples and testing samples) Finally theaverage values of these five groups are obtained as the finalresult of the reduction and shown in Table 18

+e experiment in the case of 1 minus β 06 unchangedincrease the weight of the ω1 ω1 3 ω2 1 ω3 0 InTable 18 the recognition accuracy of reduction 1 is over 97only +e average recognition accuracy of the experimentalgroup is 9675 and the accuracy is decreased by 028compared with that in the other second groups +e threegroups of experiment 3 the purpose is to verify whether theexperimental accuracy is influenced by increasing theweight +e experimental results show that the accuracy ofsecond group for experimental weight 2 1 0 comparedwith first group experiment when 1 1 0 is high but thethird groups of experimental weight was 3 1 0 and theaccuracy declined therefore the weight of 2 1 0 is the bestchoice for this experiment

4 Conclusions

Aiming at the deficiency of the traditional rough set modelthis paper proposes a new feature selection model based ongenetic algorithm and variable precision rough set by in-troducing the β value the rigid inclusion of the approxi-mation for the traditional rough set is relaxed and then wedesign the 3 kinds of experiments by constructing the de-cision information table of the PETCT feature for lungtumor ROI +e first type of experiment is the inclusion of1 minus β 06 and different values of ω made a total of threegroups of experiments the experimental results show thatthe better recognition accuracy can be obtained when theweight is 1 1 0 and the results show that the gene codingweight function has no effect on the fitness function For thesecond type of experiments ϖ1 1ω2 1 ω3 0according to the different values of β to do three groups ofexperiments the results show that the recognition accuracyof 1 minus β 06 is the best which shows that the larger the βvalue is the lower approximate cardinality will be largerthen the relative accuracy will increase For the third type ofexperiments 1 minus β 06 ω value is increased to achieve thebest fitness function in order to achieve the best results +eexperimental results show that the recognition accuracy isbetter than the others when the weight value is 2 1 0 so it

is better to solve the problem by increasing the proportion ofattribute dependency +rough the above experiments it isshown that the high-dimensional feature selection algorithmbased on genetic algorithm and variable precision rough setcan solve the multiobjective optimization problem wellHowever when the fitness function and its parameters areapplied in the specific application it is necessary to analyzethe specific problems

Data Availability

+e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

+e authors declare no conflicts of interest

Acknowledgments

+is work was supported by National Natural ScienceFoundation of China (Grant nos 61561040 and 61876121)First-Class Disciplines Foundation of Ningxia (NoNXYLXK2017B09)

References

[1] S Luo D Miao Z Zhang Y Zhang and S Hu ldquoA neigh-borhood rough set model with nominal metric embeddingrdquoInformation Sciences vol 520 pp 373ndash388 2020

[2] B Barman and S Patra ldquoVariable precision rough set basedunsupervised band selection technique for hyperspectralimage classificationrdquo Knowledge-Based Systems vol 1936Article ID 105414 2020

[3] Y Chenyi and L Jinjin ldquoApproximate attribute reductionunder variable precision rough set βrdquo Journal of ShandongUniversity vol 11 pp 17ndash21 2011

[4] S Xiaowei Research on Hierarchical Model of Attribute Re-duction in Variable Precision Rough Set Central SouthUniversity Changsha China 2013

[5] Z Jie and W Jiayang ldquoAnalysis of reduction feature ofvariable precision rough set modelrdquo Computer ApplicationResearch vol 7 pp 12ndash15 2007

[6] Z Pei and Z Qinghua ldquoFCM clustering algorithm based onvariable precision rough setrdquo Journal of Shanxi Universityvol 3 pp 342ndash348 2016

[7] C Hao and Y Junan ldquoAttribute kernel and minimum at-tribute reduction algorithm of variable precision rough setrdquoActa Sinica Sinica vol 5 pp 1011ndash1017 2012

[8] S Xu X Yang H Yu D-J Yu J Yang and E CC TsangldquoMulti-label learning with label-specific feature reductionrdquoKnowledge-Based Systems vol 104 pp 52ndash61 2016

[9] I Maryam and G Hassan ldquoFeature space discriminantanalysis for hyperspectral data feature reductionrdquo ISPRSJournal of Photogrammetry and Remote Sensing vol 102pp 1ndash13 2015

[10] S Q Wang C Y Gao C Luo G M Zheng and Y N ZhouldquoResearch on feature selectionattribute reduction methodbased on rough set theoryrdquo Procedia Computer Sciencevol 154 pp 194ndash198e 2019

[11] A W Omar M Azzam O Hadi and B Jamal ldquoCEAP SVM-based intelligent detection model for clustered vehicular ad

Mathematical Problems in Engineering 17

hoc networksrdquo Expert Systems with Applications vol 50pp 40ndash54 2016

[12] H Lee and Y-P P Chen ldquoImage based computer aideddiagnosis system for cancer detectionrdquo Expert Systems withApplications vol 42 no 12 pp 5356ndash5365 2015

[13] J A Guy and P L Harold ldquoAfter detection the improvedaccuracy of lung cancer assessment using radiologic com-puter-aided diagnosisrdquo Academic Radiology vol 23 no 2pp 186ndash191 2016

[14] E Kiyonori T Shodayu J Binghu et al ldquoPleural invasion byperipheral lung cancer prediction with three-dimensionalCTrdquo Academic Radiology vol 3 pp 310ndash319 2015

[15] B Koohestani ldquoA crossover operator for improving the ef-ficiency of permutation-based genetic algorithmsrdquo ExpertSystems with Applications vol 1511 Article ID 113381 2020

[16] N K Lee X Li and D Wang ldquoA comprehensive survey ongenetic algorithms for DNA motif predictionrdquo InformationSciences vol 466 pp 25ndash43 2018

[17] S Shibao and Y Leilei ldquoResearch on variable precision roughset model and its applicationrdquo Computer Engineering andApplication vol 07 pp 10ndash13 2009

[18] T Xiaolong Several Problems of Multi Granularity VariablePrecision Rough Set Guangxi University For NationalitiesNanning China 2015

[19] W Xueming Research on Several Rough Set Models andNeural Network University of Electronic Science and Tech-nology of China Chengdu China 2013

[20] T Sun J Wang X Li et al ldquoComparative evaluation ofsupport vector machines for computer aided diagnosis of lungcancer in CT based on a multi-dimensional data setrdquo Com-puter Methods and Programs in Biomedicine vol 111 no 2pp 519ndash524 2013

[21] Z Yang T Ouyang X Fu and X Peng ldquoA decision-makingalgorithm for online shopping using deep-learning-basedopinion pairs mining and q -rung orthopair fuzzy interactionHeronianmean operatorsrdquo International Journal of IntelligentSystems vol 35 no 5 pp 783ndash825 2020

[22] W Chen C Lin C Li et al ldquoTracing the evolution of 3Dprinting technology in China using LDA-based patent ab-stract miningrdquo IEEE Transactions on Engineering Manage-men vol 36 pp 1ndash11 2020

18 Mathematical Problems in Engineering

(3) 3rd Group Experiment ω1 3 ω2 1 ω3 0 +e al-gorithm is run 5 times according to the group weights andthe results of the 5 groups are given in Table 17 including thereduction of the conditional attributes the length of re-duction the optimal fitness value the attribute dependencyand the time +e convergence of VPRS-GA under thevariation for fitness function value for one time is shown inFigure 11

Each reduction is classified by SVM classifier using themethod of 5-fold cross validation through changing thetraining samples and test samples the results of the fivegroups were obtained including accuracy sensitivityspecificity and time (training samples are constructed by800 malignant samples and 800 benign samples testingsamples are constructed by 200 malignant samples and 200benign samples the experiment is repeated 5 times bychanging training samples and testing samples) Finally theaverage values of these five groups are obtained as the finalresult of the reduction and shown in Table 18

+e experiment in the case of 1 minus β 06 unchangedincrease the weight of the ω1 ω1 3 ω2 1 ω3 0 InTable 18 the recognition accuracy of reduction 1 is over 97only +e average recognition accuracy of the experimentalgroup is 9675 and the accuracy is decreased by 028compared with that in the other second groups +e threegroups of experiment 3 the purpose is to verify whether theexperimental accuracy is influenced by increasing theweight +e experimental results show that the accuracy ofsecond group for experimental weight 2 1 0 comparedwith first group experiment when 1 1 0 is high but thethird groups of experimental weight was 3 1 0 and theaccuracy declined therefore the weight of 2 1 0 is the bestchoice for this experiment

4 Conclusions

Aiming at the deficiency of the traditional rough set modelthis paper proposes a new feature selection model based ongenetic algorithm and variable precision rough set by in-troducing the β value the rigid inclusion of the approxi-mation for the traditional rough set is relaxed and then wedesign the 3 kinds of experiments by constructing the de-cision information table of the PETCT feature for lungtumor ROI +e first type of experiment is the inclusion of1 minus β 06 and different values of ω made a total of threegroups of experiments the experimental results show thatthe better recognition accuracy can be obtained when theweight is 1 1 0 and the results show that the gene codingweight function has no effect on the fitness function For thesecond type of experiments ϖ1 1ω2 1 ω3 0according to the different values of β to do three groups ofexperiments the results show that the recognition accuracyof 1 minus β 06 is the best which shows that the larger the βvalue is the lower approximate cardinality will be largerthen the relative accuracy will increase For the third type ofexperiments 1 minus β 06 ω value is increased to achieve thebest fitness function in order to achieve the best results +eexperimental results show that the recognition accuracy isbetter than the others when the weight value is 2 1 0 so it

is better to solve the problem by increasing the proportion ofattribute dependency +rough the above experiments it isshown that the high-dimensional feature selection algorithmbased on genetic algorithm and variable precision rough setcan solve the multiobjective optimization problem wellHowever when the fitness function and its parameters areapplied in the specific application it is necessary to analyzethe specific problems

Data Availability

+e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

+e authors declare no conflicts of interest

Acknowledgments

+is work was supported by National Natural ScienceFoundation of China (Grant nos 61561040 and 61876121)First-Class Disciplines Foundation of Ningxia (NoNXYLXK2017B09)

References

[1] S Luo D Miao Z Zhang Y Zhang and S Hu ldquoA neigh-borhood rough set model with nominal metric embeddingrdquoInformation Sciences vol 520 pp 373ndash388 2020

[2] B Barman and S Patra ldquoVariable precision rough set basedunsupervised band selection technique for hyperspectralimage classificationrdquo Knowledge-Based Systems vol 1936Article ID 105414 2020

[3] Y Chenyi and L Jinjin ldquoApproximate attribute reductionunder variable precision rough set βrdquo Journal of ShandongUniversity vol 11 pp 17ndash21 2011

[4] S Xiaowei Research on Hierarchical Model of Attribute Re-duction in Variable Precision Rough Set Central SouthUniversity Changsha China 2013

[5] Z Jie and W Jiayang ldquoAnalysis of reduction feature ofvariable precision rough set modelrdquo Computer ApplicationResearch vol 7 pp 12ndash15 2007

[6] Z Pei and Z Qinghua ldquoFCM clustering algorithm based onvariable precision rough setrdquo Journal of Shanxi Universityvol 3 pp 342ndash348 2016

[7] C Hao and Y Junan ldquoAttribute kernel and minimum at-tribute reduction algorithm of variable precision rough setrdquoActa Sinica Sinica vol 5 pp 1011ndash1017 2012

[8] S Xu X Yang H Yu D-J Yu J Yang and E CC TsangldquoMulti-label learning with label-specific feature reductionrdquoKnowledge-Based Systems vol 104 pp 52ndash61 2016

[9] I Maryam and G Hassan ldquoFeature space discriminantanalysis for hyperspectral data feature reductionrdquo ISPRSJournal of Photogrammetry and Remote Sensing vol 102pp 1ndash13 2015

[10] S Q Wang C Y Gao C Luo G M Zheng and Y N ZhouldquoResearch on feature selectionattribute reduction methodbased on rough set theoryrdquo Procedia Computer Sciencevol 154 pp 194ndash198e 2019

[11] A W Omar M Azzam O Hadi and B Jamal ldquoCEAP SVM-based intelligent detection model for clustered vehicular ad

Mathematical Problems in Engineering 17

hoc networksrdquo Expert Systems with Applications vol 50pp 40ndash54 2016

[12] H Lee and Y-P P Chen ldquoImage based computer aideddiagnosis system for cancer detectionrdquo Expert Systems withApplications vol 42 no 12 pp 5356ndash5365 2015

[13] J A Guy and P L Harold ldquoAfter detection the improvedaccuracy of lung cancer assessment using radiologic com-puter-aided diagnosisrdquo Academic Radiology vol 23 no 2pp 186ndash191 2016

[14] E Kiyonori T Shodayu J Binghu et al ldquoPleural invasion byperipheral lung cancer prediction with three-dimensionalCTrdquo Academic Radiology vol 3 pp 310ndash319 2015

[15] B Koohestani ldquoA crossover operator for improving the ef-ficiency of permutation-based genetic algorithmsrdquo ExpertSystems with Applications vol 1511 Article ID 113381 2020

[16] N K Lee X Li and D Wang ldquoA comprehensive survey ongenetic algorithms for DNA motif predictionrdquo InformationSciences vol 466 pp 25ndash43 2018

[17] S Shibao and Y Leilei ldquoResearch on variable precision roughset model and its applicationrdquo Computer Engineering andApplication vol 07 pp 10ndash13 2009

[18] T Xiaolong Several Problems of Multi Granularity VariablePrecision Rough Set Guangxi University For NationalitiesNanning China 2015

[19] W Xueming Research on Several Rough Set Models andNeural Network University of Electronic Science and Tech-nology of China Chengdu China 2013

[20] T Sun J Wang X Li et al ldquoComparative evaluation ofsupport vector machines for computer aided diagnosis of lungcancer in CT based on a multi-dimensional data setrdquo Com-puter Methods and Programs in Biomedicine vol 111 no 2pp 519ndash524 2013

[21] Z Yang T Ouyang X Fu and X Peng ldquoA decision-makingalgorithm for online shopping using deep-learning-basedopinion pairs mining and q -rung orthopair fuzzy interactionHeronianmean operatorsrdquo International Journal of IntelligentSystems vol 35 no 5 pp 783ndash825 2020

[22] W Chen C Lin C Li et al ldquoTracing the evolution of 3Dprinting technology in China using LDA-based patent ab-stract miningrdquo IEEE Transactions on Engineering Manage-men vol 36 pp 1ndash11 2020

18 Mathematical Problems in Engineering

hoc networksrdquo Expert Systems with Applications vol 50pp 40ndash54 2016

[12] H Lee and Y-P P Chen ldquoImage based computer aideddiagnosis system for cancer detectionrdquo Expert Systems withApplications vol 42 no 12 pp 5356ndash5365 2015

[13] J A Guy and P L Harold ldquoAfter detection the improvedaccuracy of lung cancer assessment using radiologic com-puter-aided diagnosisrdquo Academic Radiology vol 23 no 2pp 186ndash191 2016

[14] E Kiyonori T Shodayu J Binghu et al ldquoPleural invasion byperipheral lung cancer prediction with three-dimensionalCTrdquo Academic Radiology vol 3 pp 310ndash319 2015

[15] B Koohestani ldquoA crossover operator for improving the ef-ficiency of permutation-based genetic algorithmsrdquo ExpertSystems with Applications vol 1511 Article ID 113381 2020

[16] N K Lee X Li and D Wang ldquoA comprehensive survey ongenetic algorithms for DNA motif predictionrdquo InformationSciences vol 466 pp 25ndash43 2018

[17] S Shibao and Y Leilei ldquoResearch on variable precision roughset model and its applicationrdquo Computer Engineering andApplication vol 07 pp 10ndash13 2009

[18] T Xiaolong Several Problems of Multi Granularity VariablePrecision Rough Set Guangxi University For NationalitiesNanning China 2015

[19] W Xueming Research on Several Rough Set Models andNeural Network University of Electronic Science and Tech-nology of China Chengdu China 2013

[20] T Sun J Wang X Li et al ldquoComparative evaluation ofsupport vector machines for computer aided diagnosis of lungcancer in CT based on a multi-dimensional data setrdquo Com-puter Methods and Programs in Biomedicine vol 111 no 2pp 519ndash524 2013

[21] Z Yang T Ouyang X Fu and X Peng ldquoA decision-makingalgorithm for online shopping using deep-learning-basedopinion pairs mining and q -rung orthopair fuzzy interactionHeronianmean operatorsrdquo International Journal of IntelligentSystems vol 35 no 5 pp 783ndash825 2020

[22] W Chen C Lin C Li et al ldquoTracing the evolution of 3Dprinting technology in China using LDA-based patent ab-stract miningrdquo IEEE Transactions on Engineering Manage-men vol 36 pp 1ndash11 2020

18 Mathematical Problems in Engineering