meaning of “fuzzy”, definition of fuzzy logic

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


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.


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


4 Seasons

0

0.5

1

Time of the year

Mem

bers

hip

Spring Summer Autumn Winter

IntroductionFuzzy Logic


Tall Persons

0 : A person is not tall

1 : A person is tall



Incorporation of human’s perception

0 : room is not warm1 : room is warm


Room Temperature


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


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


Fuzzy Sets


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


x

(x)

1

0


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


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


Logic Operators

A B A B A B

Fuzzy Logic OperatorsFuzzy Logic


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


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


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.


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.


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


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


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.



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



Time Response


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.


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

meaning of “fuzzy”, definition of fuzzy logic

Documents

ax x x

x x ax

young10 fuzzy set

fuzzy logica

fuzzy set asuppa

fuzzy set acorea

fuzzy set aa

distortedsome fuzzy