13.11.7 fylladio

Er6rrcfg r6l6tqteg (Special properties). Kdnoru enr)"oyr1 ano ng no,pa,zcdvrrlevCI,)"l.CI,Ktrrc6g teprrcdg pnopei vu, odqyrloei oe FIE ps ooyKrKprp6veg r6r6cireq,or onoieg 0s etvar enr0upr"1dg.

Fuzzy Models -Fuzzy Inference EnginesIlapri6stypuRr : ifx is ,A.1 and y is 81 then z is CrRz : ifx is A.2 and y is B2 then z is C2

$*lfeesmf part sf fb* ruleFuz:r,,fication

Conseqe*enf psrf *f r,fue ru,rie

lrnpiicaticrrr

tT;r",rrt* ,3

J = - :r i , i % .

Isrrkamsfn'sr"r;efJr*r,t

A.p,plicati*.nal -T n,Brm,nro$*el,g,f fi?iit

Dif'* I ,T;*'5-re 3

b

{tll't nr f ;

Serite," nfs.rsyiflr

1o f'*iurj n'rts

I;,rgr* 4

ri = friJx,yj= g.H+btf+g

3;,=, f1fp.,'5r]=: pts+q'}r+r

kl,ieiS'hledffi.r#t gilg

Defueeification

,F r - ,i r

'rf :r*-1,*-"-ir,": :::: l l l

t{d; i

l 1l:l lnPutsU

*ilfl

l i\,:

*: l f, ' , *r [:{I ""J''.l;'". "i*li. 1.

* . r

lZ

I*$earr affilffIii?l$

! : - + r - ! : l-

-

' ' : - : "- : - :4 - -

1 r : - l r l

Typel: mirVproduct - product - maxType}: min/product - min - maxType3: mir/product - Tsukamoto's methodType4: min/product - TSK methodAnl,oruorqp6vq p60o6oq COA/COG: Xpqotporuororitrre 6vo 8eiypo oqpeirov yrouno)"opop6 rot o,Opoiopatoq.

r "t r 'L . .F

" ,I i \ , rI r r t t s 't i , .*- . : i " .

l /t - rEr

f.r' '- - - -$ \

A,\yopr0po g otronoiq oq S crocr goDs Fqxqv{ S oupuep aoFqros1o prlpo: Aoogonoirloq2" prlpa: Egoppoyq roD qoogoog tetreonl (*ir,4 product) oro qirrq rcDV KcrvovcDv3" pqpo: Ecpcppoyq rlls ooqgoDs ouverrsyc,ry4g (Mamdani, Larsen, Tsukamoto, TSK)4" pqpc: XovoOpotoe ug e{o6oo5 rc,:v KctvovcDv oe Frq ouvotrrxrl e{o6o (oovotrrxoqoqges oovo.Lo)

Erpcppoyrl rou al,yopt0poD orr FIE: Mamdani, Larsen, Tsukamoto, TSKA. Yl,onoirlorl FrlIqvrls qoqgor>q ouFnepqoFqtoc pe mix-man (Mamdani)

Iu.l,l,oytopo9 Fe l.ertoupyi.cr min-max

Kavovca i: Ecrv x eivqt A,,, KcIt y ei"vor 8,,, Tote z eivc{tC,,I

A. Yl,onoirloq prl.lavrlc qoqqous oDFnepqoFstoc (TSK)

= 1tn (x) ^ ttu,(y) onou a, o pa0pos evepYoroirlorls-uc.llv qt-ri'cov roo i rccrvovrr

A1) Zero-order TSK

Or e(o6ot rc,rv Kqvova:v 4 eivat oroOepoi optOpoi"

QJi + a)b + '-.+ aMrML = -

a\ + a2* . . .4u

A2) First-order TSK

Or eqo6or" rov Kcrvovov eivqr notrucbvupo npcbtrlg roqrlS rrls Fopqrls

f , ( * , y )= P ,x *Q i ! * r i

a , f , (xn,Yr)+ o l f r7o, i l+ " ' * o ,z - -

a t+a2* . . . au

flpcrcttrrl Aorcrloq 1@ec,lpoupe evcl qo(I(peg ooorqpq 6Do etoo6cov Kfl Ftcts e$o6oo nou 6opei--rorqno roDS ilqpqKqrc,r 6uo tcovoveg:

Kavovcg l: Eqv x ei-vqr A, xaty eivor A, T6t'e z eivatA,

Kcrvovog 2: Eqv x eivqt A, xaty ei'vor' '4' Tote z eivatA,

onoo At icqr Az eivcrt qooqq ouvotrq pe oDvqPrrloets oDFFeroxrls

[ t - l t - l l edv 0

l l

nrlreru e elvqr ruirnt ne eivct ruJtotE u elvqt Pt t t

RzIEAN e elvo.t N jKAl Ae etvat PjTO,T_E.U eivcr, PR3iEAN e etvat z jrnt ne ei.vor rultorE u etvqr Zn+irnru e etvar zkat ae eivar P horr u etvq.t Z

! I - tRSIEAN e etvar PIKAI Ae ei.vo.t NITOTE u etvqt NR6IEAN e etvqt PIKAI Ae etvct efrorE u etvor N

t t l

Aornon (Me rtirbtra)

Atverarto ar6trou0o o0vol,o xavdvov (qoa$nS d\y6pr0poq el,6y1ou):

Onou or ouvo.pt{oetq oupproxiq rulv cocSti.rv pretcpl,qrdrv e rqt de 61ouv rrlq eriq :Eloo6og 1 (e) :

H Z a

'*'tr.o -16

Etoodoq 2: , '...-" ],'

,ft

^ t 7 . S

(de) :

A) Na ppeOel n o6oq u !ro. e=L6 kai de=-2 Xpnoq]onordlvrcg 14 p60o6o mamdani.Xprlo4ronoretore rr1 p60o6o cnoooagonotrlo4g COA yta rov npoo6toprop6 rqge66ou.

B) Na enaval,qQOei n corqoq lprlotpronotdlwoq rov rov6vq Larsen.

A6on ue rtir6wq oro MATLAB :

r ' o -8 ' " -$ "41