APPLICATIONS OF FUZZY LOGIC

SONEY SOMACHAN

MSc. Mathematics

PREFACE

Over the years this books has earned a name for itself because of its

completeness of coverage and simplicity of presentation. Fuzzy logic plays an

important role in mathematics. The book is intended to familiarize the reader with the

fuzzy logic in medicine, in domestic goods, and in engineering. Chapter 1 contains the

fuzzy logic in medicine, and bioinformatics. Chapter 2 contains fuzzy logic in

domestic goods. Chapter 3 contains fuzzy logic in engineering and other applications.

CONTENT

Chapter Title Page No.

Chapter 1 Fuzzy logic in medicine and bioinformatics 1

Chapter 2 Fuzzy logic in domestic goods 5

Chapter 3 Fuzzy logic in engineering &other applications 11

CHAPTER - 1

FUZZY LOGIC IN MEDICINE AND BIOINFORMATICS

1.1 Fuzzy logic in Medicine

The diagnosis of disease involves several levels of uncertainty and imprecision

and it is inherent to medicine. A single disease may manifest itself quite differently,

depending on the patient, and with different intensities. A single symptom may

correspond to different diseases. On the other hand, several diseases present in a

patient may interact and interfere with the usual description of any of the diseases. On

the other hand, several diseases present in a patient may interact and interfere with the

usual description of any of the diseases the best and most precise description of

disease entities uses linguistic terms that are also imprecise and vague. Moreover, the

classical concept of health and disease are mutually exclusive and opposite. However,

same recent approaches consider both concepts as complementary processes in the

same continuum. To read with imprecision and uncertainty, we have at our disposal

fuzzy logic. Fuzzy logic interduces partial truth values, between true and false.

According to Aristotelian logic, for a given proposition or state we only have

two logical values; true-false, black-white, 1-10. Thus, in many practical situations, it

is convenient to consider intermediate logical values. Let us show this with a very

simple medical example. Consider the statement “you are healthy”. It is true if you

have only a broken nail? Is it false if you have terminal cancer? Everybody is healthy

to some degree h and i11 to some degree i. if you are totally healthy, then of course

h=1, i=). Usually everybody has some minor health problems and h<1, but h+i=1.

Since uncertainty is inherent in fields such as medicine and massive data in

bioinformatics, fuzzy logic takes into account such uncertainty, fuzzy set theory can

be considered as a suitable formalism to deal with the imprecision intensic to many

biomedical and bioinformatics problems. Fuzzy logic is a method to center precise

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what is imprecise in the world of medicine. Several examples and illustrations are

made mentioned below.

The complexity of medical practice makes traditional quantitative approaches

of analysis inappropriate. In medicine the lack of information’s and its imprecision

and many times contradictory nature are facts. The sources of uncertainty can be

classified as follows.

1. Information about the patient.

2. Medical history of the patient, which is usually supplied by the patient, which

is usually, supplied by the patient and /or his/her family. This is usually highly

subjective and imprecise.

3. Physical examination- The physician usually obtains objective data, but in

some case the boundary between normal and pathological status is not sharp.

4. Result of laboratory and other diagnostic tests, but they are also subject to

some mistakes and even to improper behavior of the patient prior to the

examination.

5. The patient may include stimulated, exaggerated under stated symptoms, or

may even fail to mention some of them.

6. We stress the paradox of the growing number of mental disorders versus the

absence of a natural classification. The classification is critical (i.e.,

borderline) cases is difficult, particularly when a categorical system of

diagnosis is Fuzzy logic plays an important role in medicine. Some examples

showing that fuzzy logic crosses many disease groups are following.

1. To predict the response to treatment with citalopram in alcohol dependence.

2. To analyze diabetic neuropathy and to detect early diabetic retinopathy.

3. To determine appropriate lithium dosage.

4. To calculate volumes of brain tissue from magnetic resonance imagining and

to analyze MRI data.

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5. To characterize stroke subtypes and co-existing causes of ischemic stroke.

6. To prove decision-making in eradication therapy.

7. To control hypertension during anesthesia.

8. To determine flexor-tendon repair techniques.

9. To delete breast cancer, lung cancer or prostate cancer.

10. To assist the diagnosis of central nervous systems tumors (astrocytic tumors).

11. To visualize nerve fibers in the human brain.

12. To represent quantitative estimates of drug use.

13. Many other areas of application, to mention a few are

a. To study fuzzy epidemics

b. To make decision in nursing.

1.2 Fuzzy logic in Bioinformatics

Bioinformatics derives knowledge from computer analysis of biological data.

This data can consist of the information stored in the genetic code, and also

experimental result (and hence imprecision) from various sources, patient statistics,

and scientific literature. Bioinformatics combines computer science, biology, physical

and chemical principles, and tools for analysis end modeling of large sets of

biological data the managing of chronic diseases, the study of molecular computing,

cloning and the development of training tools of bio computing system.

Bioinformatics is a very active and attractive research field with a high impact in new

technological development.

Fuzzy logic and fuzzy technology are now frequently used in bioinformatics.

The following are some examples.

1. To increase the flexibility of protein motifs.

2. To study differences between polynucleotide’s.

3. To analysis experimental expression data using fuzzy adaptive resonance

theory.

4. DNA sequencing using genetic fuzzy systems.

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5. To cluster genes from microarray data.

6. To predict proteins sub cellular locations from their dipeptide composition

using fuzzy k-nearest neighbors algorithm.

7. To stimulate complex traits influenced by genes with fuzzy valued effects in

pedigreed populations

8. To attribute cluster membership values to genes applying a fuzzy partitioning

method, fuzzy C-means.

9. To map specific sequence patterns to putative functional classes. Since

evolutionary comparison leads to efficient functional characterization of

hypothetical proteins.

10. To analyze gene expression data.

11. To unravel functional and ancestral relationships between proteins via fuzzy

alignment methods, or using a generalized radial basics functional neural

network architecture that generates fuzzy classification rules.

12. To analyze the relationships between genes and decipher a genetic network.

13. To process complementary deoxyribonucleic acid (CDNA) microarray

images. The procedure should be automated due to the large number of spots

and it is achieved using a fuzzy vector filtering framework.

14. To classify amino acid sequence in to different super amities.

1.3 Fuzzy logic in predicting genetic traits

Genetic traits are a fuzzy situation for more than one reason. There is the fact

that many traits can not be linked to a single gene. So only specific combinations of

genes will create a given trait. Secondly, the dominant and recessive genes that are

frequently illustrated with pun net squares are sets in fuzzy logic. The degree of

membership in those sets is measured by the occurrence of a genetic trait. In clear,

cases of dominant and recessive genes, the possible degree in the sets are pretty strict.

Take, for instant eye color. Two brown eyed parents produce three blue-eyed

children. Brown is dominant, so each parent must have the recessive gene within

them. Their membership in the blue eye set, so that trait actually comes through.

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According to the punnet square, 25% of their children should have blue eyes, with the

other 75% having brown.

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CHAPTER-2

FUZZY LOGIC IN DOMESTIC GOODS

2.1 Fuzzy logic in washing machine

Washing machines are a common feature today in Indian household. The most

important utility a customer can drive from a washing machine is that it saves the

effort to put in brushing, agitating and washing the cloth. Most of the people could not

have noticed that different type of cloth need different amount of washing time which

depends directly on the type of dirt, cloth quality etc. The washing machine that are

used. Today serves all the purpose of washing, but which cloths needs what amount of

agitation time is a business which has not been dealt with properly. In most of the

case either the user is compelled to give all the cloth same agitation or is provided

with a restricted amount of control. The thing is that the washing machines used are

not as automatic as they should be and can be.

When one uses a washing machine, the person generally select the length of

wash time based on the amount of clothes wish to wash and type and degree of dirt

cloths have to automate this process, we use sensors to detect these parameters

volume of clothes, degree and type of dirt. The wash time is then determined from

this data. Unfortunately, there is no easy to formulate a precise mathematical

relationship between volume of clothes and dirt and length of wash time required.

Consequently, this problem has remined unsolved until very recently. Conventionally,

people simply set wash times by hand and form personal trial and error experience.

Washing machines were not as automatic as they could be. The sensor system

provides external input signal into the machine from which decision can be made. It is

the controller’s responsibility to make the decision and to signal the outside world by

some form of output. Because the input/output relationship is not clear, the design of a

washing machine controller has not in the past lent itself to traditional methods of

control designs. We address this design problem using fuzzy logic. Fuzzy logic has

been used because a fuzzy logic controlled washing machine controller gives the

correct wash time even though a precise model of the input/output relationship is not

available.

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The two inputs are : 1. Degree of dirt

2. Type of dirt

FUZZY CONTROLLER

Linguistic Input

Output

Type of dirt

Wash time

Dirtiness of clothes

Figure 1. Basic Block Diagram of the process

Figure 1 shows the basic approach to the problem. The fuzzy controller takes

two inputs, process the information and output a wash time. How to get these two

inputs can be left to the sensoes. The working of the sensoes is not a matter of concern

in this paper. We assume that we have these input at our hand. Any way the two

stated points need a bit of introduction which follows. The degree of dirt is

determined by transparency of the wash water. The dirtier the clothes, less transparent

the water being analyzed by the sensoes is. On the other hand, type of dirt is

Fuzzy arithematic &

Applying criterion

Defuzzyfication

Fuzzificztion

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determined by the time of saturation, the time it takes to reach saturation. Saturation is

a point, at which there is no more appreciable change in the color of the water. Degree

of dirt determines the quality of dirt. Greasy cloths, for example, take longer for water

transparency because grease is less soluble in water than other forms of dirt. Thus a

fairly straight forward sensoe system can provide us the necessary input for our fuzzy

controller.

The decision which the fuzzy controller makes is derived from the rules which

are stored in the data base. These are stored in a set of rules. Basically the rules are if-

then statements that are intuitive and easy to understand, since they are nothing but

common English statements. Rules used in this paper are derived from common

sense, data taken from typical home use, and experimentation in a controlled

environment.

Before the details of the fuzzy controller are dealt with, the range of possible

values for the input and input variables are determined. These (in language of fuzzy

sets theory) are values to the fuzzy values, so that the operations can be applied on

them. Values of the input variables degree of dirt and type of dirt are normalized over

the domain of optional sensor.

The sets of rules used here to derive the output are

1. IF dirtiness of clothes is large and type of dirt is Greasy then wash time is very

long.

2. IF dirtiness of clothes is medium and type of dirt is Greasy then wash time is

long.

3. IF dirtiness of clothes is small and type of dirt is Greasy then wash time is

long.

4. IF dirtiness of clothes is large and type of dirt is Medium then wash time is

long.

5. IF dirtiness of clothes is medium and type of dirt is medium then wash time is

medium.

6. IF dirtiness of clothes is small and type of dirt is Medium then wash time is

medium.

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7. IF dirtiness of clothes is large and type of dirt is not greasy then wash time is

medium.

8. IF dirtiness of clothes is medium and type of dirt is not greasy is short.

9. IF dirtiness of clothes is small and type of dirt is not greasy then wash time is

very short.

The rules too have been defined in imprecise sense and hence they too are not

crisp but fuzzy values. The two input parameters often being road from the sensors

are fuzzified as per the membership function of the respective variables. These in a

additions with the membership function curve are utilized to come to a solution (using

some criteria). At last the crisp value of the wash time is obtained as an answer.

The sensors sense the input valued and using the above model the inputs are

fuzzified and then by using simple fuzzy set operation the output fuzzy function is

obtained and using the criteria the output value for wash time is obtained.

By the use of fuzzy logic control we have been able to obtain a wash time for

different type of dirt and different degree of dirt. The conventional method required

the human intereption to decide upon what should be the wash time for different

cloths. In other words this situation analysis ability has been incorporated in the

machine which makes the machine much more automatic and represents the decision

taking power of the new arrangement.

2.2 Air Conditioner

The task of dehumidification and temperature decrease goes hand in hand in

case of conventional Ac.once target temperature is reached Ac seizes to function like

a dehumidifier. Also complex interactions between user preference, actual room

temperature and humidity level are very difficult to model mathematically. But in this

work this limitation has been taken in to cogitation and overcome to a great extent

using fuzzy logic to represent the intricate influences of all these parameters. The

optimal limits of control zone, typically marked at the temperature of 250 and dew

point 110 C, are used as the target. Conventional AC system control humidity unlike

in its on way without giving the users any scope for changing the set point for the

target humidity unlike the scope it offers to change the set point for the target

temperature through a thermostat. This causes significant level of flexibility as well as

efficiency loss especially in hot and humid countries like India. For instants of higher

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humidity level (say at dew point 180 C) an occupant may perceive same comfort level

at 220

C as he would perceive at 260 C at dew point 15

0 C. this translates to huge

energy and monitory saving in terms of reduced compressor/fan duty cycle. In the

developed scheme, the censor captured temperature, user temperature preference and

humidity reading are fuzzified. These are used to decide fuzzy qualifier, which is

decoded into a crisp value that in turn control different aspect of the AC in the

problem dew point(Td) temperature is used to measure humidity instead of relative

humidity (RH), this is because RH function of both temperature and moisture-content

while Td is a function of moisture content only. Hence it become very easy to model

comfort level on the basis of Td.

Slight modification air circulation method around beat exchanges allow a

conventional AC. To function anywhere between normal AC mode and dehumidifier

only mode. In dehumidifier only mode chilled air is totally passed through hot side of

heat exchange so that AC dehumidifies without any change input in output

temperature. The problem takes three variables into consideration.

1. User temperature preference (180

C ~300 C continues control)

2. Actual room temperature

3. Room dew point temperature

User temperature is subtracted from actual room temperature before being sent

for fuzzyfication. Fuzzy arithmetic and criterion is applied on these variables and final

result is defuzzfied to get following crisp results.

1. Compressors

2. Fan speed

3. Mode of operation

4. Fin direction

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User temperature

setting

Actual Room

Temperature

Room Dewpoint perati

Temperature

Basic block diagram of controller

2.3 Vacuum cleaner

Characteristics of floor and the amount of dust are sensed by an in feared

sensor, and the microprocessor selects the appropriate power by fuzzy control

according to these characteristics. The floor characteristics include the type

[hardwood, cement, tile, carpet, softness carpet, thickness etc]. the changing pattern of

the amount of dust padding through the in feared sensor is established the appropriate

setting of the vacuum head and the power of the motor, using a fuzzy control scheme.

Red and green lamps of the vacuum cleaner shoe the amount of dust left on the floor.

F

uzzificztio

n

Fu

zzy a

rithem

atic &

Apply

ing criterio

n

Defu

zzificztion

Compressor

Speed

Fan Speed

Operation

mode

Fin Direction

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CHAPTER – 3

FUZZY LOGIC IN ENGINEERING AND OTHER APPLICATION

3.1 Fuzzy logic in civil engineering

Civil engineering, when compaired with other engineering displines is

fundamentally different. This is because each civil engineering project id, by and

large; unique, hence there is almost never a enhance to test a prototype, as in other

engineering displines.

The most fundamental knowledge of the civil engineer concerns the material

employed. How they are made, shaped and assembled; how consistent they are to

stress, weather & use; & how they may fail. Before scientific knowledge regarding

these aspects of materials was available, civil engineering was a craft. Design

decisions were made by subjective judgments based on experience of the designs of

“rules of thumb” derived by accumulating design experience over the continues. In

spite of the scientific knowledge now available, great uncertainty concerning the

application of the knowledge to actual design problems still remains, primarily due to

the uniqueness of each design problem in civil engineering of the use of subjective

judgments and relevant “rules of thumb” is unavoidable. This seems to explain why

civil engineers so quickly found a strong affinity with fuzzy set theory. One important

category of problem in civil engineering for which fuzzy set theory has already

proven useful consists of problems of assigning or evaluating existing constructions.

Typically examples of these problem are the assessment of quality of highway

pavements, and the assessment of damage in building after an earthquake.

Let Ci, Wi denote respectively, the fuzzy no. expressing the structural

significance of component i of let n denote the no of components assessed. Then the

fuzzy set expressing the overall evolution A, is defined by the formula.

1

n

t

wici=

∑

1

p

n

t

w=

∑

A=

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Several applied areas of fuzzy set theory are found to be in civil engineering.

They include fuzzy decision making, approximate reasoning and fuzzy control e.g.

(to the control of traffic in cities).

3.2 Fuzzy logic in Mathematical Engineering

Classical mathematics is not equipped to deal with imprecise descriptions. As

a consequence, it has been difficult to provide the designer with computational tools

for the early stages of the design process. It was realized account the mid-19.80,

primarily in the context mechanical engineering design that fuzzy set theory is

eminently suited to facilitate the whole design process, including the early stages. The

basic idea is that fuzzy sets allow. The designer to describe the designed artifact as

approximately as desired at the early stage of the design process. The designer may

express the various dimensions of the design artifact by approximate fuzzy numbers

representing linguistic description such as about 15cm or smaller than but close

to50ky. Triangular fuzzy numbers seem most convenient for this purpose. Assume

that there is a restitution on the dimension to be greater than 10 cm and that the design

wants to keep the dimendion under 22cm. then Fi=<15, 5, 7> id the corresponding

triangular fuzzy number expressed by the triple <s, l, r>

For example, of wide range of materials might be used of the membership

function expressed in terms corrosion, thermal expansion, or some other measurable

material property. A combination of several properties, including the cost of different

materials, may also be used. An example of a membership function constructed from

the cost data for certain steel alloys. It is based on the designer’s preference for

minimum cost.

3.3 Fuzzy logic in computer engineering

Since the mid-1980s, when the utility of fuzzy controllers can became

increasingly visible, the need for computer hardware to implement the various

operations involved in fuzzy logic of approximate reasoning has been recognized.

Initial attempts to develop hardware for fuzzy computing, data from 1985. The

principal reason for using specialized hardware for fuzzy computing is to increase

operational speed via parallel processing. In general, computer hardware for fuzzy

logic is implemented in either digital mode or analog mode. In digital mode, fuzzy

sets are represented as vectors of numbers in [o, i]. operations on vectors. In analog

mode, fuzzy sets are represented in term of continuous electric circuits. The circuits

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play a role similar to function generators in classical analog computers. Either of the

two modes of fuzzy computer hardware has some favorable features. Digital fuzzy

hardware is characterized by flexible program ability of good compatibility with

existing computers, which are predominantly complex schemes of multi stage fuzzy

inference. Analog fuzzy hardware is characterized by high speed and good

compatibility with sensors, it is thus particularly suitable for complex on line fuzzy

controllers.

3.4 Fuzzy logic in Robotics

Robotics is a cross-disciplinary subject area at is concerned with the design

and construction of machines that are capable of human-like behavior. Such machines

are referred to as robots. Intelligent robot must be equipped with atleast three types of

functions: appropriate perceptual functions facilitated by visual auditory and other

sensor to allow the robot to perceive its environment; intelligent information

processing functions that allow the robot to process the incoming information with

respect to a given task; and mechanical functions with appropriate control to allow the

robot to more and act as desired. To achieve human-like behavior an intelligent robot

must have same key capability’s that distinguish human beings from classical non-

intelligent machines. They include the capability of common-sense reasoning in

natural language, that is based on incoming information as well as background

knowledge, high level capability of making decisions in the face of bounded

uncertainly. It is clear that the use of fuzzy set theory is essential for all these

capabilities.

The main subject of fuzzy set theory that are relevant robotics, include

approximate reasoning. Fuzzy controllers, other kind of fuzzy systems, image

processing fuzzy decision making etc… In robotics all these subjects are utilized in

the over all architecture of intelligent robot.

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3.5 Other applications

1. Camcorder (Panasonic, Sanyo, fisher, canon) :- The video camera determines

the best focus and lightening, particularly when several objects are in the

picture. Also it has a digital image stabilizer to remove hand jitter. Fuzzy

decision-making is used in these actions. For example, the following scheme

is used for image stabilization. The present image frame is compared with the

previous frame from memory. A typical stationary object (e.g. house) is

identified and its shift coordinates are computed. This shift is subtracted from

the image to compensate for the hand jitter. A fuzzy algorithm provides a

smooth control/compensation action.

2. Automatic transmission system :- In a conventional automatic transmission

system, electronic sensor measure the vehicle speed and throttle opening, and

gears are shifted based on the predetermined values of these variables.

According to Nissan, this type of system is incapable of uniformly providing

satisfactory control performance to a driver because it provides only about

three different shift patterns. The fuzzy control transmission senses several

variables including vehicle speed and acceleration, throttle opening, the rate of

change of throttle opening, engine load and driving style. Each sensed value is

given a weight, and a fuzzy aggregate is calculated to decide whether to shift

gears. This controller is said to be more flexible, smooth, and efficient,

providing better performance. Also, an integrated system developed by

Mitcubishi uses fuzzy logic for active control of the suspension system, four-

wheeler-derive (traction) streening, and air conditioning.

3. Auto focus on camera :- Auto focus cameras are a great revolution for those

who spent years struggling with “old fashioned” cameras. These cameras

some how figure out, based on multitudes of inputs what is meant to be the

main object of the photo. It takes fuzzy logic to make these assumptions.

Perhaps the standard is to focus on the object closest to the center of the

viewer. May be it focuses on the object closest to the camera. It is not a

precise science, and cameras error periodically. This margin of error is

acceptable for the average cameras owner whose main usage is for snapshots.

However, the “old fashioned” manual focus cameras are preferred by most

professional photographers. For any errors in those photos cannot be attributed

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to a mechanical glitch. The decision making in focusing a manual camera id

fuzzy as well, but it is mot controlled by a machine.

4. Predicting travel time:- This is especially difficult for driving, since there are

plenty of traffic situations that can occur to slow down travel.

As with bus time tabling, predicting. ETA’s is a great exercise in fuzzy

logic. That’s why it is called an estimated time of arrival. A major player in

predicting travel time is fuzzy logic. Weather, traffic construction, accidents

should all be added in to the fuzzy equation to delive a true estimate.

5. Elevator control (Fujitec, Toshiha) :- A fuzzy scheme evaluates passenger

traffic and the elevator variables (load, speed etc) to determine car

announcement and stopping time. This reduce waiting time and improves the

efficiency and reliability of operation

Hand held computer (Sony):- A fuzzy logic scheme reads the hand written input and

interprets the characters for data entry.

Television (Sony):- A fuzzy logic scheme uses sensed variables such as ambient

lightening, time of day, and users profile and adjust such parameters as screen

brightness, colour contrast, and sound.

Antilock bracking system (Nessan):- The system senses wheel speed, round

comditions and driving patter and fuzzy ABS determine the braking action with skid

control.

Subway train (Sendai):- A fuzzy decision scheme is used by the subway trains in

sendae, Japan to determine the speed and stopping routline. Ride comfort and safety

are used as performance requirements.

6. Other applications of fuzzy logic include a hotwater heater (Matsusbita) a rice

cooker (Hitachi) and a ciment Klin (Denmark). A fuzzy stock- trading

program can manage stock portfolios. A fuzzy golf diagnostic system is able

to select the best golf club based on size, characterstics, and siving of a golfer.

A fuzzy mug search system helps in criminal investigations by analyzing mug

shots (photos of suspects) along with other input data (say, stamets such as

“short, heavy-set, and young-looking…” from witness) to determine the most

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likely criminal. Gift-wrapped chocolates with fuzzy statements available for

valentine’s Day. Even a Yamaha “fuzzy” scooter was spotted in Taipci.

REFERENCE

1. George J Klir / Bo Yuan – Fuzzy sets and Fuzzy logic (Theory and

Application) Published by Asoke K Ghosh, prentice- Hall of India Private

Limited- 1995

2. A. Torres and J.J. Nieto – Biomedicine and Biotechnology published online

2006 March 26

3. L.A Zodeh –Fuzzy Algorithms -1968

4. http://www.mathworks.com

5. http://in .wikipedia.org

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