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FUZZY
LOGIC
SYSTEM
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FUZZY
not clear, distinct, or precise;blurred
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FUZZY LOGIC
A form of knowledge representationsuitable for notions that cannot bedened precisely, but which depend
upon their contexts.
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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
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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.
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*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 %.
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*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.
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Traditional Logic (Boolean) andFuzzy Logic
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!"T IS FUZZY LOGIC
SYSTEM (FLS) #
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(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$: full.
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*>?(6
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FUZZIFIC"TIO$
*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.
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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.
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C%IS' "LUES
(t is the term used for the
input and output #alues infuy logic system.
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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.
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T!%EE STE'S I$ FUZZYLOGIC
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STE' *FUZZIFIC"TIO$
(t is identifying the degree ofmembership of the crisp input.
=any methods can be used such astriangular, trapeoidal and ?aussianmembership function.
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FUZZIFICATION
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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
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STE' ,*&EFUZZIFIC"TIO$
*he crisp output is computed based onthe crisp inputs and the fuy rules.
>**
-
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E-"M'LE I&EO
YUNG ITLOG
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"&"$T"GES
/onceptually easy to understand Flexible *olerant of imprecise data /an model nonlinear function of
arbitrary complexity &lended with con#entional control
techni)ues &ased on natural language ery robust ery )uick and cheaper to implement
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STE' ,
&ased on gure 9 the crisp input is 9$: smalland 8$: large. sing a table we can identifythe total output re)uired in the problem.
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*he input +>= is multiplied to the outputset #alue to identify the output
component, after sol#ing for the outputcomponents nd their sum and thatwould be the crisp output.
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THEREFORE
S.e need/ ,012inute/ or +,3
/econd/ to 4oil t.eegg 5er6ectly0
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&IS"&"$T"GES
=any parameter
/omputational /ost
+ening the rules
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TRAFFIC LIGHT