Design of Interval Type-2 T-S Fuzzy Logic Control Systems

Transcription

1 Scfc Jou of Coo Egg Ocob 04, Vou 4, Issu 5, PP.-37 Dsg of Iv Typ- T-S Fuzzy Logc Coo Syss L L #, Yu Du, Y L. Schoo of Copu Scc Tcouco Egg, Jgsu Uvsy, Zhg Jgsu 03, Ch. Fcuy of Scc, Jgsu Uvsy, Zhg Jgsu 03, Ch # E: y@us.du.c Absc I hs pp, v yp- T-S fuzzy ogc coo syss (ITT-S FLCS) s dsgd. Th poposd ITT-S FLCS s cobo of IT fuzzy ogc sys (FLS) d T-S FLCS, d so hs h bfs of hs o hods. Fuho, Ksovs s hod s uzd o sfy h suffc codo fo h sypoc sby of ITT-S FLCS, hch us h ccuo of h Jcob. Fy, h suo sus sho h h ITT-S FLCS chvs h bs cg pfoc copso h h yp- (T) T-S FLCS d h poposd hod c hd updcd dsubc d d ucs. Kyods: Typ- Fuzzy Ss; Sby; Jcob ITRODUCTIO Sc Tg d Sugo [] poposd h T-S fuzzy od 985, h T-S fuzzy sys hs gd s o of h os cv d fufu s of fuzzy coo. Th T-S FLS [, ] s poposd ffo o dvop sysc ppoch o g fuzzy us fo gv pu-oupu d s. Ths od cosss of us h fuzzy cds d hc fuco h cosu p. By usg hs odg ppoch, cop o- sys c b psd by s of fuzzy us of hch h cosu ps s uos. Th cop o- p c h b dscbd s ghd su of hs s uos. Ths T-S fuzzy od s dy ccpd s pofu odg oo. Th ppcos o vous ds of o- syss c b foud [3-5].Qu of, h odg usd o cosuc us T-S FLS s uc. Ths ucy ds o us hvg uc cds d/o cosus, hch u ss o uc cd d/o cosu bshp fucos. Wh h sud d s ss d h od s c, c us Typ- fuzzy ss[6]. Such yp- fuzzy ss hos bshp gds hsvs yp- fuzzy ss; hy vy usfu ccuscs h s dffcu o d c bshp fuco fo fuzzy s, hy usfu fo copog gusc ucs. Th yp- FLS hs b succssfuy ppd o sdg-od coo dsgs, fu o syss dsg, obus dpv v yp- fuzzy cg coo of uvb o syss d pusv coo of o syss[7-0].a dc dpv v yp- fuzzy coo s poposd [,]. oov,dc d dc dpv v yp- fuzzy coos dvopd[3,4] fo u-pu/u-oupu(io) o sys. Typ - fuzzy syss hv sho g po vous odg s s coo ppco [5]. A. Abbd[6] popos v yp- fuzzy coo h hs h by o hc h s sby d chv vog guo suousy fo uch po syss. Th dsg of hs coo vovs h dc fdbc zo chu. Hc, hs pp, sudy h dsg of h ITT-S FLCS.Th poposd ITT-S FLCS s cobo of IT FLS d T-S FLCS, d so hs h bfs of hs o hods. I s bvd h ITT-S FLS hv h po o b usd coo d oh s h TT-S od y b ub o pfo. Ths pp s ogzd s foos: I Sco, dsg pocdu of h ITT-S FLCS s ddssd d. I Sco 3, h poposd Ksovs s hod s uzd o sfy h suffc codo fo h sypoc sby - - hp://.s-c.og

2 of ITT-S FLCS. I Sco 4, dvopd pssos obd dvg h ITT-S fuzzy sys od h gd o vy cood of h s spc. I Sco 5, dvopd pssos h pvous sco usd o p goh. I Sco 6, h poposd hodoogy s usd by p. Th cocusos d Sco 7. AALYSIS AD DESIG OF IT FUZZY COTROLLER O T-S ODEL A sy y o copy h h ou pp fog us s o us hs docu s p d spy yp you o.. RULE BASE R : If s A d s A d s A d u s B d u s B d u s Th (, ) g X U 0 b u b u () Wh,, s h ub of us, A h IT fuzzy ss dfd uvs of dscous fo h s vb,,, d s h fs-od dff uo, B s h IT fuzzy s dfd uvs of dscous fo h h coo sg u,,,, d b ps h spcv cos coffcs fo h s vb d fo h h sg of coo of h dff uo h pss h pocss. Th poposd ITT-S FLCS fo h cs h cds IT d cosus csp ubs.. FUZZY IFERECE EGIE Th fc g cobs h fd us d gvs o- ppg fo h pu IT fuzzy ss o h oupu IT fuzzy ss. Ipu X (,,, ) T R dos h s vco, d U ( u, u,, u) R dos h pu coo vco. Ths u pss IT o b h pu spc X XU U, d h oupu spc X, of h IT FLS. Th fg sgh of h h u s ( X ) ( ) X A X X A ( u ) u ( u ) u u U U B u U U B H focus o o spfco of () s su of sgo fuzzfco, hc h fuzzy s X o U s such h s hs bshp gd cospodg o X X o U U d hs zo bshp gd fo oh pus; hfo, () ducs o hp://.s-c.og B u u u (3) A A B B A B h (,, ) d u (,, ) do h oco of h sgo. R s dscbd by h bshp fuco ( ) R h o ch X s csp vu Th oupu fuzzy s ( ) fo IT FLS s R ( ) u, so (4) ducs o R X A B ( ) u R A B (5) h dos h poduc opo. ( R ) ( ) R u A B L COG ( ( )) d COG ( ( )) do h cod of h o bshp fuco (LF) d upp R R () (4) (6)

3 bshp fuco (UF), spcvy, of R( ). Th, c df h oupu of IT FLS, s = COG ( ( ))+(-) COG( ( )) (7) R h gh [0, ] c b ud dug dsg pocdu [7]. So h oupu of ITT-S FLCS s sho s ( ) g ( X, U) g ( X, U) A B R hp://.s-c.og ( ) ( u ) (9) A B ( ) ( u )) (9b) A B ( ) ( u ), (0) Wh c b ud dug dsg pocdu. ( ) A d ( u ) B h bshp fucos dfd h cospodg uvs of dscous X d U. T h cosu of h u () o (8), hch c b s Ths s Wh 0, d 0 b u bu bu b u bu bu + 0 b u b u b u 0 0 b u (8) () () b vb coffcs copud s b b b (3),, (3b),, (4) Up o h, h IT fuzzy p od s obd fo h dvop of h hodoogy., dvop h IT fuzzy coo od. Th pocss of h fuzzy coo dsg h sbzs h p s cosdd dpdy fo h pocss of h p dfco. Thfo, dos o u h od p d h coo hv h s ub of us. Cosdg hos od bov, h chv of h IT fuzzy p od pocds s y. Th IT fuzzy coo c b psd by h foog goup of us: R : If s C d s C d s C Th u c0 c c (5) Wh C pss h IT fuzzy ss of,, s vbs, h,, coo cos d,, us.

4 Coo sgs c b pssd s foos s y sho (8)-(): O, o spfd y: u c c c + 0 c0 c c (6) u c0 c c c = c 0 c (7) h h vb coffcs gv by c 0 c 0 0 c c c c d h o d upp chg dg of h u of h coo, spcvy by hp://.s-c.og (8),, (8b) ( ) (9) C C ( ) (9b) Rpcg psso (7) o (), h foog ITT-S cosd oop oupu fuco c b s: 0 0 b c b c,,,, d,, (0) Epsso (0) s uv hc cosd oop od of ITT-S FLCS. I od o spfy E. (0), h s vco b dd cood, h s T 0,, X Rpcg h dd s vco o (0) h spfd foog psso s obd 0,,, ( ) 0 b c 3 STABILITY VERIFICATIO OF THE ITT-S FLCS (),,, d,, () Th sby of o syss hs o b vsgd hou g ppochs. I od o do hs, sv ppochs c b dopd bsd o Lypuov s scod hod, fo sc, Ksovs s ho [7, 9]. Ksovs s ho fo gob sypoc sby offs suffc codos fo o syss. A ubu s of o sys c b sb v h h codos spcfd hs ho o ssfd; hov, h syhss of syss h cop hs ho ssus h hy sypocy sb goby. Ksovs s ho doss h gv sys X = ( X ), f h sys s Jcob J( X ) J( X ) T s gv df go oud h ubu s X, hs s sypocy sb s pos. T oov, f ( X) ( X) h X, h sypoc sby s gob. Th Lypuov fuco fo hs sys s ( X ) T ( X ). I sco 4, ps g goh o copu h Jcob of cosd oop ITT-S FLCS. Th goh hs b povd by spfco of h uos bsd o h s vco so. Th goh s dpd of h yp of bshp fuco usd fo budg h ods of h p d h coo. Dff yps of bshp fucos h s od c so b cobd h poposd goh.

5 4 COPUTATIO OF THE JACOBIA ATRIX OF A CLOSED LOOP ITT-S FLCS L h ITT-S coo sys odd by E. (), hch c b psd h foog gc y: (,,, ) (,,, )... (,,, ) (3) T L X (,,, ) b ubu s of sys (0). Whs h fuco s couous ov h g, Tyo ss pso bou h po X y b usd: d d (,,, ) X hp://.s-c.og (,,, ) + + X + R( X ) (4) Wh h o R ( X ) fufs (5), bg K suffcy s cos, h h Jcob of h sys ds h pops of sby of h ubu s X : R X K Th Jcob s ccud ppyg h foog pssos: ( ) (,,, ) (,,, ) X X J ( X) (6) X (,,, ) (,,, ) X X I h pvous psso s dd o ccu h p dvv fo E. () h gd o ch o of h s vbs. Ths uo c b dvdd o ddds: = bc (7) ( ) 0 b c 0 0 Th p dvvs b obd gc fo fo h,, s vbs d h,, fs dg dffs uos. 4. DERIVATIVE OF THE FIRST ADDED Th fs p dvv o ccu s fo h fs ddg of E. (7): Bg d (3b): (5) (8) Ccu h fs ddg of E. (9): h (9) (30) (3)

6 Rpcg o h pvous o pssos (30) d spfyg, sus p p p ( ) ccu h scod ddg of E. (9) s s o ccu h fs ddg of E. (9): p p p ( ) d Rpcg (33), (34) pssos (9), sus Fy, E. (8) c b s hp://.s-c.og (3) 0 p p p p p p ( ) ( ) p p p p p p 0 oc h o vu psso (36) s cssy o ccu pvousy h dvv of h chg dg of h us of h p, gv fo E. (9), (9b). Ths po s sovd Sco DERIVATIVE OF THE SECOD ADDED To ccu h dvv of h scod ddd, h foog psso us b sovd: b 0 c b c b c 0 Wh (33) (34) (35) (36) (37) bc b c c b (38) Gv h sy of h pssos fo h ccuo of d b, s sy o dduc h p p p p p b b p b b b ( ) ( ) Th dvv of h cospodg o h fuzzy coo b: c c c c c (39) (40)

7 ccu h fs ddg of E. (40): c c h d c c c Rpcg o h pvous o pssos (4) d spfyg, sus (4) (4) (43) c s s s c c ( ) ccu h scod ddg of E. (40) s s o ccu h fs ddg of E. (40): Fy, E. (40) c b s ( ) ( ) c s s s c c ( ) c s s s s c c c c s s ( ) ( ) oc h o vu psso (46) s cssy o ccu pvousy h dvv of h chg dg of h us of h coo, gv fo E. (9), (9b). Ths po s sovd Sco 4.3. As soo s d pssos (39) d (46) ccud, hy c b pcd (38): bc p p p p p b b p b b c ( ) ( ) s s s s c c s s c c b ( ) ( ) Thus, h dvv of h scod ddd gv by E. (37) s (44) (45) (46) (47) hp://.s-c.og

8 b 0 c p p p p p b b p b b c 0 ( ) ( ) b b c s s s s c c c s s c ( ) ( ) (48) 4.3 DERIVATIVE OF THE ATCHIG DEGREE OF THE RULES OF THE COTROLLER Gv psso (9) h dfs h o chg dg of h us of h coo, h p dvv of hs psso gdg o vy s vb s obd fo Bg d h E. (49) c b s ( ) ( ) C C ( ) ( ) ( ) C C C f( ) 0 (49) (50) ( ) C ( ) C S of h psso fo h ccuo, s sy o dduc h ( ) C ( ) C (5) (5b) 4.4 DERIVATIVE OF THE ATCHIG DEGREE OF THE RULES OF THE PLAT Gv psso (9) h dfs h o chg dg of h us of h p, h p dvv of hs psso h gd o vy s vb s obd fo h h o, bg d (50): hp://.s-c.og ( ) u u A B u ( ( ), u A B ( u ) ) u ( u ) ( u ) ( ) ( ) ( ) B u B u u B B ( ) v Bv v v u B (5) (53) ( u ) ( u ) (54) B

9 ( ) ( ) ( ) A A A Rpcg Es. (54) d (55) (5): ( ) ( u ) v A Bv ( u ) ( ) ( ) ( ) B A A u v (56) B v Sy of h psso fo h ccuo, s sy o dduc h ( ) ( u ) A B v v ( u ) ( ) ( ) ( ) B A A u v (56b) B v u Fy, h ccuo of ps h dvv of h coo vco. Wg g E. (7) h h dd s vco shod (): c Rpcg o fo (46): u c 0 Th u u c hp://.s-c.og (55) (57) c 0 c c 0 (58) s s s s c c s s c c c 0 ( ) ( ) 4.5 JACOBIA ATRIX Evy of h Jcob, E. (6), s gv by h dvv of h psso (7). To ddds of hs psso hv b ccud Scos 4. d 4., d hy gv by Es. (36) d (48), hfo J ( ) b c p p p p p p 0 ( ) ( ) p p p p p b b p b b c ( ) ( ) s s s s c c s s c c b ( ) ( ) (59) (60)

10 oc h Es. (5), (5b)d (56), (56b)d hfo E. (60), dpd o h yp of bshp fuco h s chos o fuf h fuzzy p d coo ods, so, s possb o vu h Jcob fo y bshp fuco. oov, s possb o cob dff bshp fucos s od. 5 ALGORITHS L ITT-S FLCS dfd by () d (5), hos fuzzy uv, cosdg ITT-S cosu hch s gv by (), d h coo, cosdg uy ITT-S cosu hch s gv by (7); h ITT-S fuzzy cosd oop od s gv by (). A ubu s s gv fo h pogg of hs od. Gv coc s sho s foos:,, T X, h sps o copu h Jcob of h cosd oop sys (). Ccu h chg dg of h us of h fuzzy coo by (9), (9b). (). Copu h vb coffcs of h fuzzy coo by (8b), 0,,,. (3). Fd h vu of ch of h sgs gd by h fuzzy coo by (7). (4). Ccu h chg dg of h us of h fuzzy p od by (9), (9b). (5). Fo h h uo of h pocss d h h s vb: 5.. Ccu h vb coffc of h p od by (8b) d by (4) h 0,,,. 5.. Copu h scod ddd of E. (60) Ccu h p dvv of h chg dg of h us of h fuzzy coo od by (5), (5b) Ccu h p dvv of h chg dg of h us of h fuzzy pocss od by (56), (56b). E. (59) s usd o cop hs dvv Copu hd ddd of (60) Ccu h cospodg J of h Jcob. (6). Rp sp 5 u s of h Jcob vud h s X copud. (s Fg.) As ch hs po, g hod s vb fo h ccuo of h Jcob po of fuzzy coo sys dfd o pu/oupu d bss. 6 SIULATIO AD EXAPLE L h foog p gv by s pso b: u u Ths p hs ubu po h og of h s spc. Lzg h o od gv by (6) oud hs po, h foog sys s obd: u u hos dyc s A 0 Egvus of h A : d dc h h sys (6) s usb, d h ogs of h s spc c s sdd po fo hs sys. Fo h po of hs p, h p dycs s supposd o b uo, so h E.(6) s oy usd hp://.s-c.og (6) (6)

11 o ob pu/oupu d of h p. TT-S od of h p hs b obd by h hodoogy bsd o dscdg gd dvopd [7-8]. (s Appd) Th pu/oupu d of h p hs b obd by, 0,0 [7]. do ub go h v FIG.. ALGORITH TO COPUTE EQ. (60) o, oc h p dycs s o, s possb o dsg TT-S od of coo h sbzs h sys oud h ubu po h og of h s spc. (s Appd) W us h ITT-S FLS by dg h TT-S FLS. Assu h ucs s h cds of ch u, d d h TT-S FLS o ITT-S FLS by spdg cd F sd dvo vus ±% (s Appd). Th Jcob of h ITT-S fuzzy sys vud h ubu s by h FuzJc fuco s hp://.s-c.og

12 J To d h coo sys sby by h ppco of Ksovs s ho, s obvous h J( X ) J( X ) T s gv df vo of h ubu s. Fg. d Fg.3 sho h copso of h ss fo h T d IT T-S fuzzy sys. Th fuzzy cosd oop coo syss sypocy sb h og of h s spc. Fuho, hy sho h h IT T-S fuzzy sys s b h h T T-S fuzzy sys, spcvy. FIG.. THE COPARISO OF FOR THE T AD IT T-S FUZZY SYSTE FIG.3. THE COPARISO OF FOR THE T AD IT FUZZY T-S SYSTE I od o sho h h IT T-S fuzzy sys c hd h su ucs, g d s coupd by do os. Fo Fg.4 o Fg.7, fgus sho h sposs h dsubc = 0.06 fo h T d IT fuzzy T-S sys, spcvy. Wh h IT T-S fuzzy sys s fucd by do dsubc, h ffc s vy s, d h oupu cos of d hv s pud h h cos hou do dsubc. Th suo sus sho h h IT T-S fuzzy sys c hd updcd dsubc d d ucs vy. FIG.4. THE WITH DISTURBACE FOR THE T FUZZY T-S SYSTE hp://.s-c.og

13 FIG.5. THE WITH DISTURBACE FOR THE IT FUZZY T-S SYSTE FIG.6. THE WITH DISTURBACE FOR THE T FUZZY T-S SYSTE 7 COCLUSIOS FIG.7. THE WITH DISTURBACE FOR THE IT FUZZY T-S SYSTE I hs pp, ps dsg of ITT-S FLCS ds. Fuho, Ksovs s hod s oducd o sfy h suffc codo fo h sypoc sby of ITT-S FLCS. L, h Jcob of cosd oop fuzzy sys s copud d goh o sov h Jcob s poposd. Fy, h suo sus sho h h ITT-S FLCS chvs h bs cg pfoc copso h h TT-S FLCS. oov, h ITT-S FLCS c hd updcd dsubc d d ucs. ACKOWLEDGET Th o s suppod by h o u Scc Foudo of Ch (07090). Th o s suppod by h Opg Poc of Gug Ky Lbooy of Auoob Copos d Vhc Tchoogy, Gug Uvsy of Scc d Tchoogy (0KFS) hp://.s-c.og

14 REFERECES [] T. Tg,. Sugo. Fuzzy Idfco of Syss d Is Appcos o odg d Coo. IEEE Tsco o Syss,, d Cybcs, 985, 5(): 6-3 []. Sugo, G. Kg. Sucu Idfco of Fuzzy od. Fuzzy Ss d Syss, 988; 8(): 5-33 [3] K. T,. So. A obus sbzo pob of fuzzy coo syss d s ppco o bcg up coo of uc. IEEE Tsco o Fuzzy Syss, 994, (): 9-34 [4] K. T, T. Id, H.O. Wg. Robus sbzo of css of uc o syss v fuzzy coo: udc sbzby h coo hoy d us. IEEE Tsco o Fuzzy Syss, 996, 4():-3 [5] H.O. Wg, K. T,.F. Gff. A ppoch o fuzzy coo of o syss: sby d dsg ssus, IEEE Tsco o Fuzzy Syss, 996; 4(): 4-3 [6] J.. d. O sg h uso Wh do I s od o sov pob vovg v yp- fuzzy ss? Ifoo Sccs, 009; 79(9): [7] g-yg Hso, Tzuu-Hsg S. L, J.-Z. L, c, Dsg of v yp- fuzzy sdg-od coo, Ifoo Sccs, 008, 78(6): [8] Od Ld, os c, Iv Typ- fuzzy vo dsg fo fu o syss,ifoo Sccs, 0, 8(4): [9] Tsug-Chh L, Obsv-bsd obus dpv v yp- fuzzy cg coo of uvb o syss, Egg Appcos of Afc Igc, 00, 3(3): [0] Y L, Yu Du, Idc dpv fuzzy obsv d coo dsg bsd o v yp- T-S fuzzy od,appd hc odg, 0, 36(4): [] Khdd, C., L, S., ou, G., Kh, B., 007. Idc dpv v yp- fuzzy coo fo o syss. Io Jou of odg, Idfco d Coo, 06-9 [] Y- L, Yu-Yu Su, Typ- T-S fuzzy pusv coo of o syss,ppd hc odg, 0, 36(6): [3] L, T.C., Lu, H.L., Kuo,.J.,Dc dpv v yp- fuzzy coo of uvb o syss. Egg Appcos of Afc Igc, 009., [4] Tsug-Chh L, Obsv-bsd obus dpv v yp- fuzzy cg coo of uvb o syss, Egg Appcos of Afc Igc, 00, 3(3): [5] J..d. Advc yp- fuzzy s d syss. Ifoo sccs, 007, 77(): 84-0 [6] A. Abbd, L. z, D. Bouh, A o vog coo bsd o v yp fuzzy ogc coo sys fo uch po syss,io Jou of Ecc Po & Egy Syss, 03, 45(): [7] José. Adú, Aoo J. Bgá, A hodoogy o dsg sb o fuzzy coo syss, Fuzzy Ss d Syss, 005, 54: 57-8 [8] J.. Adú, J.. Bvo. uvb fuzzy coo ppd o h physc-chc fcy of cuos fcoy. Fuzzy Ss d Syss, 005, 50(3): [9] J.. Adú, J.. Bvo, A. Pgí. Sby yss d syhss of u vb fuzzy syss usg v hc. Fuzzy Ss d Syss, 004, 48(3): APPEDIX Th TT-S fuzzy od of h p: s GAUSSF( 3.9,6.5) d s GAUSSF( 3.5,5.) d u s GAUSSF( 3.6,5.4) d u s GAUSSF( 3.,5.3) THE u 0.35u s GAUSSF( 6.0,5.) d s GAUSSF( 5.03,4.) d u s GAUSSF( 6.85,5.03) d u s GAUSSF( 5.4,5) THE u.3u s GAUSSF(0.68,4.) d s GAUSSF(.67,4.5) d u s GAUSSF(.6,4.7) d u s GAUSSF(.59,4.9) THE u 0.498u s GAUSSF(8.54,5.5) d s GAUSSF(9.69,5.4) d u s GAUSSF(9.4,5.) d u s GAUSSF(8.7,5.3) THE u 0.894u hp://.s-c.og

15 s GAUSSF( 8.5,4.9) d s GAUSSF( 5.4,3.3) d u s GAUSSF( 6.7,5.4) d u s GAUSSF( 9.8,4.8) THE u 44u s GAUSSF( 6.8,6.9) d s GAUSSF( 9.74,4.) d u s GAUSSF( 6.48,5.) d u s GAUSSF( 6.78,5.6) THE u 0.3u s GAUSSF(.8,6.) d s GAUSSF(3.07,5.) d u s GAUSSF(.37,5.6) d u s GAUSSF(.37,5.) THE u u s GAUSSF(3.6,5.4) d s GAUSSF(8.4,5.) d u s GAUSSF(.9,5.8) d u s GAUSSF(3.6,5.6) THE u 6.4u A possb T coo fuzzy us coud b: s GAUSSF( 8.34,4.4) d s GAUSSF(.7,6.07) THE u s GAUSSF(4.6,5.6) d s GAUSSF( 3.0,6.) THE u s GAUSSF(4.04, 5.5) d s GAUSSF(3., 5.3) THE u s GAUSSF( 6.0, 6.) d s GAUSSF( 9.7,6.) THE u s GAUSSF(3.86,6.07) d s GAUSSF(.6,6.54) THE u s GAUSSF(4.,5.) d s GAUSSF(4.8,7.8) THE u Th ITT-S fuzzy od of h p s h foog: s GAUSSF( 3.9,6.5(±%)) d s GAUSSF( 3.5,5.(±%)) d u s GAUSSF( 3.6,5.4(±%)) d u s GAUSSF( 3.,5.3(±%)) THE u 0.35u s GAUSSF( 6.0,5.(±%)) d s GAUSSF( 5.03,4.(±%)) d u s GAUSSF( 6.85,5.03(±%)) d u s GAUSSF( 5.4,5(±%)) THE u.3u s GAUSSF(0.68,4.(±%)) d s GAUSSF(.67,4.5(±%)) d u s GAUSSF(.6, 4.7(±%)) d u s GAUSSF(.59,4.9(±%)) THE u 0.498u s GAUSSF(8.54,5.5(±%)) d s GAUSSF(9.69,5.4(±%)) d u s GAUSSF(9.4, 5.(±%)) d u s GAUSSF(8.7,5.3(±%)) THE u 0.894u s GAUSSF( 8.5,4.9(±%)) d s GAUSSF( 5.4,3.3(±%)) d u s GAUSSF( 6.7,5.4(±%)) d u s GAUSSF( 9.8,4.8(±%)) THE u 44u s GAUSSF( 6.8,6.9(±%)) d s GAUSSF( 9.74,4.(±%)) d u s GAUSSF( 6.48,5.(±%)) d u s GAUSSF( 6.78,5.6(±%)) THE u 0.3u s GAUSSF(.8,6.(±%)) d s GAUSSF(3.07,5.(±%)) d u s GAUSSF(.37,5.6(±%)) d u s GAUSSF(.37,5.(±%)) THE u u s GAUSSF(3.6,5.4(±%)) d s GAUSSF(8.4,5.(±%)) d u s GAUSSF(.9,5.8(±%)) d u s GAUSSF(3.6,5.6(±%)) u 6.4u THE hp://.s-c.og

16 A possb ITT-S coo coud b: s GAUSSF( 8.34,4.4(±%)) d s GAUSSF(.7,6.07(±%)) THE u s GAUSSF(4.6,5.6(±%)) d s GAUSSF( 3.0,6.(±%)) THE u s GAUSSF(4.04,5.5(±%)) d s GAUSSF(3.,5.3(±%)) THE u s GAUSSF( 6.0,6.(±%)) d s GAUSSF( 9.7,6.(±%)) THE u s GAUSSF(3.86,6.07(±%)) d s GAUSSF(.6,6.54(±%)) THE u s GAUSSF(4.,5.(±%)) d s GAUSSF(4.8,7.8(±%)) THE u AUTHORS L L, bo Puchg, Sh povc, Ch, Sp Sh gdud fo Jgsu Uvsy h doco s dg Agcuu Ecfco d Auoo 009. Sh s Assoc Pofsso og Fcuy of Copu Scc d Tcouco Egg, Jgsu Uvsy, Zhg, Ch. Sh s cuy ggd h foog sch fds: () Fuzzy Fu Dco d Dgoss;() Suo d Ig Coo;(3) Ig Agoh d Opzo. Yu Du s Gdu Sud Fcuy of Scc, Jgsu Uvsy, Zhg, Ch. 3 Y L, bo Luoyg, H povc, Ch, 963. H obd hs doco Coo Thoy d Coo Egg fo g Uvsy of Aoucs d Asoucs 005. H s Pofsso d Posgdu Supvso Fcuy of Scc, Jgsu Uvsy, Zhg, Ch. H s cuy ggd h foog sch fds: () odg of cop cosys d sudy of fus of bo-sys; () Th fuzzy coo hoy bsd o boogc fus; (3) Th hoy d ppco of Bocs g coo; (4) Typ- fuzzy coo hods hp://.s-c.og