7/21/2019 Fuzzy Logic

1/39

FUZZY

LOGIC

SYSTEM

7/21/2019 Fuzzy Logic

2/39

FUZZY

not clear, distinct, or precise;blurred

7/21/2019 Fuzzy Logic

3/39

FUZZY LOGIC

A form of knowledge representationsuitable for notions that cannot bedened precisely, but which depend

upon their contexts.

7/21/2019 Fuzzy Logic

4/39

Fuy logic is a form of many"#aluedlogic in which the truth #alues of #ariables

may be any real number between $ and %.&y contrast, in &oolean logic, the truth#alues of #ariables may only be $ or %.

Fuy logic has been extended to handlethe concept of partial truth, where thetruth #alue may range betweencompletely true and completely false.

Furthermore, when linguistic #ariables areused, these degrees may be managed byspecic functions

7/21/2019 Fuzzy Logic

5/39

INTRODUCTION

Fuy logic is used in today's processcontrol systems. Fuy logic addressessuch applications perfectly as it resembleshuman decision making with an ability to

generate precise solution from uncertain orapproximate information. (t lls animportant gap in engineering designmethods left by mathematical and logic"based approaches while other approachesre)uire accurate e)uations to model real"world beha#iours.

7/21/2019 Fuzzy Logic

6/39

*he idea of fuy logic was rst

ad#anced by +r. ot -adeh of theni#ersity of /alifornia at &erkeley inthe mid %01$s. +r. -adeh was

working on the problem of computerunderstanding of natural language.2atural language 3like most otheracti#ities in life and indeed the

uni#erse4 is not easily translated intothe absolute terms of $ and %.

7/21/2019 Fuzzy Logic

7/39

*he 5apanese were the rst to utiliefuy logic for practical applications. *he

rst notable application was on the high"speed train in 6endai, in which fuy logicwas able to impro#e the economy,comfort, and precision of the ride. *his

control of the 2anboku line used a fuycontroller to run the train all day long.

7/21/2019 Fuzzy Logic

8/39

Traditional Logic (Boolean) andFuzzy Logic

7/21/2019 Fuzzy Logic

9/39

7/21/2019 Fuzzy Logic

10/39

!"T IS FUZZY LOGIC

SYSTEM (FLS) #

7/21/2019 Fuzzy Logic

11/39

(t is a type of logic that recognies more than

simple true and false #alues. 7ith fuy logic,

propositions can be represented with degrees

of truthfulness and falsehood.

For example, let a %$$ml glass contain 8$mlof water. (t can be dened that the glass is9$: empty or 8$: full.

7/21/2019 Fuzzy Logic

12/39

7/21/2019 Fuzzy Logic

13/39

*>?(6

7/21/2019 Fuzzy Logic

14/39

FUZZIFIC"TIO$

*he fuication comprises theprocess of transforming crisp #alues

into grades of membershipfor linguistic terms of fuy sets.*he membership function is used toassociate a grade to each linguistic

term.

7/21/2019 Fuzzy Logic

15/39

FUZZY I$FE%E$CE

Fuy inference is the process offormulating the mapping from a

gi#en input to an output using fuylogic. *he mapping then pro#ides abasis from which decisions can bemade, or patterns discerned.

7/21/2019 Fuzzy Logic

16/39

7/21/2019 Fuzzy Logic

17/39

7/21/2019 Fuzzy Logic

18/39

C%IS' "LUES

(t is the term used for the

input and output #alues infuy logic system.

7/21/2019 Fuzzy Logic

19/39

MEMBE%S!I'FU$CTIO$ (MF)

is a cur#e that denes how each point inthe input space is mapped toa membership #alue 3or degreeof membership4 between $ and %. *heinput space is sometimes referred to asthe uni#erse of discourse, a fancy name

for a simple concept.

7/21/2019 Fuzzy Logic

20/39

T!%EE STE'S I$ FUZZYLOGIC

7/21/2019 Fuzzy Logic

21/39

STE' *FUZZIFIC"TIO$

(t is identifying the degree ofmembership of the crisp input.

=any methods can be used such astriangular, trapeoidal and ?aussianmembership function.

7/21/2019 Fuzzy Logic

22/39

FUZZIFICATION

7/21/2019 Fuzzy Logic

23/39

STE' +*I$FE%E$CE

>nce the degrees of membership areidentied, the fuy rules will be appliedto fulll the if"then conditions

(F @>* (F2>+

*@2

@(?@

*@2=A(2*

A(2

*@2>7

7/21/2019 Fuzzy Logic

24/39

STE' ,*&EFUZZIFIC"TIO$

*he crisp output is computed based onthe crisp inputs and the fuy rules.

>**

-

7/21/2019 Fuzzy Logic

25/39

E-"M'LE I&EO

YUNG ITLOG

7/21/2019 Fuzzy Logic

26/39

7/21/2019 Fuzzy Logic

27/39

"&"$T"GES

/onceptually easy to understand Flexible *olerant of imprecise data /an model nonlinear function of

arbitrary complexity &lended with con#entional control

techni)ues &ased on natural language ery robust ery )uick and cheaper to implement

7/21/2019 Fuzzy Logic

28/39

7/21/2019 Fuzzy Logic

29/39

7/21/2019 Fuzzy Logic

30/39

7/21/2019 Fuzzy Logic

31/39

7/21/2019 Fuzzy Logic

32/39

STE' ,

&ased on gure 9 the crisp input is 9$: smalland 8$: large. sing a table we can identifythe total output re)uired in the problem.

7/21/2019 Fuzzy Logic

33/39

*he input +>= is multiplied to the outputset #alue to identify the output

component, after sol#ing for the outputcomponents nd their sum and thatwould be the crisp output.

7/21/2019 Fuzzy Logic

34/39

7/21/2019 Fuzzy Logic

35/39

THEREFORE

S.e need/ ,012inute/ or +,3

/econd/ to 4oil t.eegg 5er6ectly0

7/21/2019 Fuzzy Logic

36/39

&IS"&"$T"GES

=any parameter

/omputational /ost

+ening the rules

7/21/2019 Fuzzy Logic

37/39

7/21/2019 Fuzzy Logic

38/39

7/21/2019 Fuzzy Logic

39/39

TRAFFIC LIGHT