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Chapter 5Fuzzy Logic(Knowledge-Based Systems; R Akerkar, P Sajja)

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Fuzzy Log!

Fle"#le ma!$ne learnng te!$n%ue

&m!kng t$e log! o' $uman t$oug$t

Log! may $ae two alues and reresents

two oss#le solutonsFuzzy log! s a mult alued log! and allows

ntermedate alues to #e de*ned

Prodes an n'eren!e me!$ansm w$!$ !annterret and e"e!ute !ommands

Fuzzy systems are suta#le 'or un!ertan oraro"mate reasonng

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Fuzzy Log! s Balued Log!

Balued log! !an $ae only two oss#lealues as ./, yes.no, rg$t.wrong et!

Fuzzy log! !an #e mult alued0 1t !an $ae

relate alues lke yes, not, not so mu!$, alttle #t et!0

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2$ara!terst!s o' Fuzzy Log!

3"a!t reasonng s ewed as a lmtng !ase o'aro"mate reasonng

3eryt$ng s a matter o' degree

Knowledge s nterreted as a !olle!ton o'elast! or e%ualently 'uzzy !onstrants on a!olle!ton o' ara#les

1n'eren!e s ewed as a ro!ess o'

roagatng elast! !onstrantsAny log!al system !an #e 'uzz*ed

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Fuzzy Set

Let 4 #e a non emty set, A 'uzzy set A n 4 s!$ara!terzed #y ts mem#ers$ 'un!ton 5A+4 -6 7,/8, w$ere 5A(") s t$e degree o'

mem#ers$ o' element " n 'uzzy set A 'orea!$ " 9 4

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&em#ers$ Fun!ton

&as elements o' a 'uzzy set to realnum#ered alues n t$e nteral to /0

:$e !ure reresentng t$e mat$emat!al

'un!ton s a mem#ers$ 'un!ton t$atdetermnes t$e degree o' #elongng o'mem#er " to t$e 'uzzy set :0

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Fuzz*!aton:$e ro!ess o' trans'ormng !rs(#alued)

nut alues nto lngust! alues s !alled'uzz*!aton

Stes o' Fuzz*!aton+

Ste /+ 1nut alues are translated ntolngust! !on!ets, w$!$ are reresented #y'uzzy set0

Ste + &em#ers$ 'un!tons are aled to t$emeasurements, and t$e degree o'mem#ers$ s determned

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=eratons on Fuzzy setIntersection of Fuzzy et

:$e nterse!ton o' A and B s de*ned as (A > B)(") ? mn@A("), B(") ? A(")>B("), " 9 4, asdemonstrated n *gure

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=eratons on Fuzzy set!nion of Fuzzy et

:$e unon o' A and B s de*ned as (A C B)(") ?ma"@A("), B(") ? A(")CB("), " 9 4, asdemonstrated n *gure

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=eratons on Fuzzy setComp"ement of Fuzzy et

:$e !omlement o' a 'uzzy set A s de*ned as(D A)(") ? / - A(") as demonstrated n *gure

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:yes o' Fuzzy Fun!ton%uasi-Fuzzy Membership Functions:

:$e mem#ers$ 'un!ton 'ollows a %uas!ure0 A %uas !ure s a real lne wt$ anormal 'uzzy !one" and a !ontnuous

mem#ers$ 'un!ton sats'yng t$e lmt!ondtons as #elow+

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:yes o' Fuzzy Fun!ton&riangu"ar Fuzzy Membership

Functions:

:$e mem#ers$ !ure 'ollows a trangulars$ae t$en t s trangular mem#ers$

'un!ton0 Fuzzy 'un!ton A s !alledtrangular 'uzzy 'un!ton(A?a,,G) wt$eak a, le't wdt$ 6 and rg$t wdt$ G6

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:yes o' Fuzzy Fun!ton&rapezoida" Fuzzy Membership

Functions:

:$e mem#ers$ !ure 'ollows a traezodals$ae0 Fuzzy 'un!ton A s !alled trangular

'uzzy 'un!ton(A?a,,G) wt$ toleran!enteral 7a, #8, le't wdt$ and rg$t wdt$G

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Lngust! ara#leA ara#le w$ose alues are words or senten!es n

natural language0 3"amle+ :emerature slngust! ara#le ' t takes alues $ot, !ool,warm, !om'orta#le et!0

:$e 'ramework o' lngust! ara#le s gen as (4,

L", H, I") w$ere

4 denotes t$e sym#ol! name o' lngust! ara#le

L" s a set o' lngust! alues t$at 4 !an take

H s t$e $ys!al doman t$at de'nes !rs alues

I" s a 'uzzy 'un!ton t$at mas lngust! termso' ara#les to t$e e%ualent !rs alues

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Fuzzy ProostonsA 'uzzy rooston s a statement t$at dres a'uzzy trut$ alue0

Fuzzy Connectives: Fuzzy !onne!tes areused to jon smle 'uzzy roostons to make

!omound roostons0 3"amles o' 'uzzy!onne!tes are+

Jegaton

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Fuzzy Rules

:$e ower and e"#lty o' smle 1'-:$en-3lselog! rules s en$an!ed #y addng lngust!arameter0

Fuzzy rules are e"ressed n t$e 'orm+

1F ara#le 1S set :3J a!ton

#xamp"es:

1F temerature s ery !old :3J sto ar!ondtoner

1F temerature s normal :3J adjust ar!ondtoner

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Fuzzy 2ontrol System

A 'uzzy !ontrol system s #ased on Fuzzy Log!0:$e ro!ess o' desgnng 'uzzy !ontrol system!an #e des!r#ed usng 'ollowng stes

tep ': 1dent'y t$e rn!al nut, outut and

ro!ess taskstep (: 1dent'y lngust! ara#les used and

de*ne 'uzzy sets and mem#ers$s a!!ordngly

tep ): Mse t$ese 'uzzy sets and lngust!

ara#les to 'orm ro!edural rulestep *:

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Fuzzy 2ontrol System

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&odelng Fuzzy Systems

Fuzzy system modelng !an #e ursued usng t$e'ollowng stes

tep ': 2$oose t$e relate nut and oututara#les

tep (:

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Lmtatons o' Fuzzy Systems

Fuzzy systems la!k t$e !aa#lty o' ma!$nelearnng as-well-as neural network tye atternre!ognton

er*!aton and aldaton o' a 'uzzyknowledge-#ased system re%ure e"tensetestng wt$ $ardware

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Al!atons o' Fuzzy Log!

Automat! !ontrol system

Pred!ton, dagnost! and adsory systems

Mser nter'a!e and neural language

ro!essng