meaning of “fuzzy”, definition of fuzzy logic
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Lecture 7
Introduction to Neural Networksand Fuzzy Logic
President University Erwin Sitompul NNFL 7/1
Dr.-Ing. Erwin SitompulPresident University
http://zitompul.wordpress.com
2 0 1 4
President University Erwin Sitompul NNFL 7/2
Meaning of “fuzzy”, Definition of Fuzzy LogicIntroductionFuzzy Logic
Covered with fuzz;Of or resembling fuzz;Not clear; indistinct
A fuzzy recollection of past events.Not coherent; confused
A fuzzy plan of action.Unclear, blurred, or distorted
Some fuzzy pictures from a Russian radar probe.
Fuzzy logic: a form of knowledge representation suitable for notions that cannot be defined precisely, but depend upon their contexts, it deals with reasoning that is approximate rather than fixed and exact.
President University Erwin Sitompul NNFL 7/3
Origins of Fuzzy LogicIntroductionFuzzy Logic
The earliest record can be traced back as far as to the ancient Greece period
Lotfi Zadeh (1965) The first to publish ideas of fuzzy logic
Toshire Terano (1972) The first to organize a working group of fuzzy system
F. L. Smidth et. al. The first to market fuzzy expert system
President University Erwin Sitompul NNFL 7/4
4 Seasons
0
0.5
1
Time of the year
Mem
bers
hip
Spring Summer Autumn Winter
IntroductionFuzzy Logic
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Tall Persons
0 : A person is not tall
1 : A person is tall
IntroductionFuzzy Logic
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Incorporation of human’s perception
0 : room is not warm1 : room is warm
IntroductionFuzzy Logic
Room Temperature
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Characteristic function:
young
1, age( ) 20( )
0, age( ) 20
xx
x
young = { x P | age(x) ≤ 20 }
Set DefinitionFuzzy Logic
Classical Sets
A=“young”1
0
A ( )x
yearsx20x
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Classical Logic
Element x belongs to set Awith a certain “degree of membership”:
(x)[0,1]
Element x whether belongs to set A or not at all:
(x){0,1}
Fuzzy Logic
A=“young”1
0
A ( )x
yearsx21x
A=“young”1
0
21x
A ( )x
yearsx
Set DefinitionFuzzy Logic
Fuzzy Sets
President University Erwin Sitompul NNFL 7/9
yearsx
A=“young”1
0
21x
A ( )x
0.4A
Fuzzy Set A = {(x,A(x)) | x X, A(x) [0,1]}is defined by a universe of discourse x where0 ≤ x ≤ 100 and a membership function A where A(x) [0,1]
Definition:
Fuzzy SetsSet DefinitionFuzzy Logic
President University Erwin Sitompul NNFL 7/10
x
(x)
1
0
Set DefinitionFuzzy Logic
Some DefinitionsSupport of a fuzzy set A
supp(A) = { x X | A(x) > 0 }Core of a fuzzy set A
core(A) = { x X | A(x) = 1 }α-cut of a fuzzy set A
Aα = { x X | A(x) α}
α = 0.6
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Fuzzy Logic Control (FLC)Fuzzy Logic ControlFuzzy Logic
Fuzzy Logic Control (FLC) may be viewed as a branch of intelligent control which serves as an emulator of human decision-making behaviour which is approximate rather than exact.
FLC uses the IF-THEN rules, similar to binary control (Programmable Logic Controller, PLC).
Rule Format:Ri: IF x is Aj AND y is Bk THEN z is Cl
Ri: IF x is Aj OR y is Bk THEN z is Cl
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Logic Operators
A B A B A B
Fuzzy Logic OperatorsFuzzy Logic
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p q p q 0 0 0 0 1 1 1 0 1 1 1 1
p q p q 0 0 0 0 0.4 0.4 0 1 1
0.4 0 0.4 0.4 0.4 0.4 0.4 1 1 1 0 1 1 0.4 1 1 1 1
Boolean OR Fuzzy OR
Fuzzy Logic OperatorsFuzzy Logic
Boolean OR and Fuzzy OR
President University Erwin Sitompul NNFL 7/14
p q p^q 0 0 0 0 1 0 1 0 0 1 1 1
p q p^q 0 0 0 0 0.4 0 0 1 0
0.4 0 0 0.4 0.4 0.16 0.4 1 0.4 1 0 0 1 0.4 0.4 1 1 1
Boolean AND Fuzzy AND
Boolean AND and Fuzzy ANDFuzzy Logic OperatorsFuzzy Logic
President University Erwin Sitompul NNFL 7/15
Example: Air Fan Control (Single Input)Fuzzy Logic ControlFuzzy Logic
Conventional (On-Off) Control:IF temperature > X °C, THEN run fan,ELSE stop fan.
Fuzzy Control: IF temperature is hot, THEN run fan at full speed;
IF temperature is warm, THEN run fan at moderate speed;
IF temperature is comfortable, THEN maintain fan speed;
IF temperature is cool, THEN slow fan;
IF temperature is cold, THEN stop fan.
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Humidity
Temperature
Fan Wattage
Example: Heater Fan Control (Two Inputs)Fuzzy Logic ControlFuzzy Logic
Problem: Change the speed of the fan, based on the room temperature and humidity.
The temperature is classified into four conditions: Cold, Cool, Warm, and Hot.
The humidity can be defined by: Low, Medium, and High.
The available wattage settings of the heater fan are Zero, Low, Medium, and High.
President University Erwin Sitompul NNFL 7/17
Example: Stopping A Car
13600 N 0 N1500 kg
(0) 25 m(0) 10 m s
Fm
yy
Break force
Mass of the car
Initial position
Initial velocity
FF my y
m
Fuzzy Logic ControlFuzzy Logic
President University Erwin Sitompul NNFL 7/18
Example: Stopping A Car
( )p dK e T ey
m
pF K e
, 0e w y w
p pK e K yy
m m
With Kp = –240, the car will stop at the traffic light after 10 s.
P-Control PD-Control
2
p
p d p
K my
w s K mT s K m
Choosing ζ = 1, Td = 1, Kp = 6000, the car will stop at the traffic light after 5 s.
Fuzzy Logic ControlFuzzy Logic
2
2 22n
n ns s
President University Erwin Sitompul NNFL 7/19
Example: Stopping A CarFuzzy Logic ControlFuzzy Logic
Fuzzy Logic Control: IF distance is long AND approach is fast,
THEN brake zero; IF distance is long AND approach is slow,
THEN brake zero; IF distance is short AND approach is fast,
THEN brake hard; IF distance is short AND approach is slow,
THEN brake zero.
President University Erwin Sitompul NNFL 7/20
Example: Stopping A CarFuzzy Logic ControlFuzzy Logic
Fuzzy Membership Functions
25 m 100 %0 m 0 %
10 m/s 100 %0 m/s 0 %
Negative to emphasize that the value is decreasing
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Example: Stopping A CarFuzzy Logic ControlFuzzy Logic
Time Response
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Preparation AssignmentIntroductionNeural Networks
Ensure yourself to install Matlab 7 in your computer, along with Matlab Simulink, Control System Toolbox, and Fuzzy Logic Toolbox.
The Fuzzy Logic Toolbox can be opened by typing “fuzzy” on the command window.
Read the Fuzzy Toolbox Manual that can be found in the directory where Matlab is installed. One version of the manual can be found on the lecture website.
President University Erwin Sitompul NNFL 7/23
Homework 6AIntroductionNeural Networks
Make 3 groups. Conduct a literature research and prepare a short PowerPoint
presentation about the applications and implementations of fuzzy logics in:
1. Consumer electronics.2. Defense and security.3. Business decision making.
Each group will be given 15 minutes time for presentation on Wednesday, 18.02.2014.
Result of Homework 1A: Vincent, Zakaria : 120 Adrian, Johnson, Kristiantho : 100 Anthony, Fikri, Rayhan : 90
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