SISTEM PERSAMAAN LINEAR FUZZY et Not Pogm Std Ilm Kompte Js Mtemtk FMIPA Uests Dpoegoo Jl Pof H Soedto, SH, Temblg Semg Eml : bethce@yhoocom Abstct Let AU V be fzzy system of le eqtos The fzzy system of le eqtos cosst of bles d eqtoswe ege the fzzy system of le eqtos becme bles d eqtos The ew system ws deoted by X* V* I ths ppe, we show tht solto of X* V* c be sed to fd AU V fzzy system of le eqtos, wheee - s o-egte Keywods: Fzzy mbes, system of le eqtos, d o-egte mtx PENDAHULUAN Poblem-poblem d bdg ekys d ss dpt dmodelk meggk pesm dfeesl bs tp pesm dfeesl psl Pd mmy, meetk sols eksk pesm dfeesl bs/pesm dfeesl psl tdk dpt dtemk deg mdh Sstem pesm le (SPL memegg pe petg dlm meetk sols pedekt pesm dfeesl bs tp pesm dfeesl psl [5] Oleh key, pe mtks tk meetk sols pedekt pesm dfeesl sgt bes Peget sft-sft mtks yg dgk dlm mklh mek pd [4 ] & [6] Teo fzzy dpt dgk dlm bdg teo kotol, teo kepts, d bebep bg dlm mgeme ss [3] & [7] dg-bdg tesebt memelk sstem pesm bebss teo fzzy sebg model mtemtky Fedm et l memsk lebh tegs mege sols sstem le fzzy, khssy deh fsbel d pemslh sstem le tesebt [] Lebh lt, blg fzzy yg dgk hy blg fzzy yg dss oleh fgs-fgs le Dlm mklh, ots R meytk hmp sem blg el lg fzzy yg dmksd dlh blg fzzy yg dss oleh fgs deg dom d kodomy d R Dlm mklh, dbktk syt pel d ckp g sols sstem pesm le dpt dgk med sols sstem pesm le fzzy Mtks koefse d sstem pesm b hslh besft o-egtf ILANGAN FUZZY lg fzzy dlm R ddefsk sebg psg fgs (, yg memeh sft-sft bekt: ( fgs mooto k, tebts, d kot k pd [0, ], (b fgs mooto t, tebts, d kot k pd [0, ], d (c ( ( tk setp dlm [0, ] Utk defs betk l blg fzzy dpt dlh sec detl dlm [3] & [7] Hmp blg-blg fzzy dytk deg F Utk selty, setp blg fzzy F dtls dlm betk pmete (, Opes lb blg fzzy meggk defs sepet dlm [] & [] Utk setp, F d blg el α ddefsk :
(d k d hy k (e + ( +, + (f α ( α, α tk α 0 (g α ( α, α tk α < 0 d 3 SISTEM PERSAMAAN LINEAR FUZZY Dbek sstem pesm le bel d pesm dpt dtls dlm betk mtks Ax y ( deg A mtks peseg yg etety blg el, d x, y dlh R Metode- ekto-ekto d dlm metode tk meyelesk pesm ( dpt dlht dlm [4] & [5] Model pemslh sstem pesm le fzzy delsk sebg bekt : Dbek,,,,,, d, R tk, Sstem pesm + + +,, + +,,,, + + + +,,,, F ( dmk sstem pesm le fzzy (SPL-fzzy Sstem pesm ( dpt dtls dlm betk mtks V d,, A,,,, AU V deg U,,,, Model sstem pesm le ( mempy sols fzzy k tedpt x ekto x X d dlm F sedemk x sehgg k, k x k, k d x, tk setp,,, Meggt opes lb pd blg fzzy (ksom (d-(g, fgsfgs d dpt dtls sebg kombs le d x d x Sstem pesm ( dbh ke betk ( bel d ( pesm med X V (3 b, b, b, deg b, b, b,, b, b, b, X V [ x ] T,, x, x,, x [,,,,, ] T d Et-et dtetk sebg bekt: k, 0 mk b +, +, b,, b +,, k, d, < 0 mk + d 0 tk ly Pesm (3 bk sstem pesm le fzzy Pesm (3 mepk pesm le bs yg l bely bed dlm g fgs Deg meggk pesm (3, dmgkk sstem pesm le fzzy dpt dselesk mell peyeles sstem pesm le bs Lebh lt, mtks pd pesm (3 dpt dtls dlm betk mtks blok
, sehgg mtks koefese A pd pesm ( dlh A Cotoh Dbek sstem pesm le fzzy x x x + x Mtks A sepet dlm pesm ( dlh Oleh ke t, mtks sepet dlm pesm (3 dlh 0 0 0 0 0 0 0 0 Cotoh Dbek sstem pesm le fzzy x x x + 3x Jk sstem pesm dbh med pesm (3, mk x + (-x x + 3x + (-x - (- x + 3( x - x Teoem Dbek dlh mtks koefese pd pesm (3 Mtks tk-sgl k d hy k mtksmtks A d + kedy tk-sgl kt : ( Deg meggk opes elemete bs/kolom pd mtks, ddpt mtks + + C Jk mtks C dke opes elemete mlh d + 0 kolom, ddpt D Mtks C dlh mtks yg dhslk d opes elemete mlh d bs/kolom d mtks Sedgk mtks D dlh mtks yg dhslk d opes elemete mlh d bs/kolom d mtks C Hl bekbt, det( det(c det(d, sehgg det( det(d det( + det( Ke tk-sgl mk det( 0 d det( + det( det( 0 Hl megkbtk det( + 0 d det( 0 Jd mtks A d + kedy tk-sgl ( Dketh mtks A d + kedy tk-sgl Jd det( + 0 d det( 0 Deg c sep sepet pd bg sebelmy, ddpt det( det(c det(d + + deg C d + 0 D Hl bekbt det( det(d det( + det( 0, ke l det( + 0 d l det( 0 Sehgg dlh mtks tk-sgl kt seles Teoem Dbek dlh mtks koefese pd pesm (3 Jk es mtks d, mk esy bebetk M N N M kt : 3
Mslk d bett- tt meytk et mtks d pd bs ke- d kolom ke- Ke d(, mk deg det( + ( det(, (4 det(, sb mtks yg dpeoleh deg c megelms bs ke- d kolom ke- d mtks Pehtk sb mtks +, d, + Mtks +, dpt dpeoleh mell opes elemete petk bs d kolom d, + sebyk p kl, deg p blg gep Oleh key, det( +, (- p det(, + det(, + D pesm (4 d meggt det( +, det(, +, mk b +, + + ( det(, det( + + + ( det( +, b, + det( tk setp, Smp d s, N ddpt N Pehtk g sb mtks d + +,, tk,, Ke mk +, + dpt dpeoleh meggk opes elemete petk bs d kolom d, sebyk q kl, deg q blg gep Oleh key, det(, (- q det( +, + +, + det( Hl bekbt + ( det(, det( + ( ( det( +, det( + ( + + ( + ( det( +, det( b +, + + tk setp, M N Tebkt bhw N M Pesm (3 mepk pebh betk d sstem pesm le fzzy Wlp pesm (3 mempy sols tggl, tdk bet sstem pesm le fzzy lgsg dpeeoleh solsy Jk dlm (3 tksgl, tdk d m bhw X V F, tk setp V F Cotoh bekt mempelhtk bhw pesm (3 mempy sols tggl tetp pemslh SPL-fzzy tdk mempy sols tggl Cotoh 3 Dbek pemslh SPL-fzzy x + x x (, 3 x x + x3 ( +,3 x + x + 3x3 (, Jk dbh dlm betk pesm (3, mk dpeoleh mtks-mtks : 0 0 0 0 0 0 + 3 0 0 0 A, X 0 0 0 0 0 0 3 0 0 0 3 + 0 0 0 0 0 0 3 0 0 0 d mempy 0 0 0 0 0 0 0 0 0 3 es, sehgg sols (peyeles pesm (3 dlh X [ 3+ 36, 06 077,08 5, 469 + 338,6 03,9 85] T 4
Mslk x 3+ 36,469 3 38, [ ] T x [ 06 077, 6 0 3] T + x3 [ 08 5, 9 + 85] T Vekto (, x x d x bk sols SPL-fzzy, 3 Mtks [ ] Q q,, ke x d x bk blg fzzy Teoem bekt mempelhtk syt ckp d syt pel g sols pesm (3 g med sols tk SPL fzzy seml Sebelmy, ddefsk peget sft ketkegtf yg dmlk st mtks dktk oegtf k tk setp d setp belk q 0 [4] & [6] Sebg cotoh,, mtks koefse pd pesm (3 d ts dlh mtks o-egtf Toeem 3 Dbek SPL-fzzy AU V deg ble d pesm Pesm X V sepet pesm (3, deg o-sgl Sols X V med sols SPL-fzzy AU V k d hy k mtks o-egtf kt : ( Mslk X [ x,, x, x,, ] T x X V x b, + Ke x, b + tk, Selty ke [, mk dpeoleh b +, + pesm (6 med x + x M N + N M ] d (5 (6 mk, sehgg (7 Jk pesm (7 dkg deg pesm (5, mk dpeoleh x x ( ( + b, + ( b,, + ( b + ( ( + + + ( (8 Dketh V F mk,,, F, sehgg ( 0 tk setp Dketh pl bhw x x 0 Hl bekbt 0 tk setp d Deg kt l mtks [ ] o-egtf ( Mslk [ ] mtks o-egtf Jd 0 tk setp d Deg c yg sep sepet pd bg sebelmy, ddpt pesm (8 Dketh pl x x ( ( + + ( [,,,,, ] T V sols pesm (3 d,,, F, mk ( 0 tk setp Akbty, x x ( ( + + ( 0 tk 5
Sehgg x, x,, x F t [ x, x,, x ] F Deg demk, sols med sols sstem pesm le fzzy kt seles Dlm cotoh 3, mtks dlh mtks o-egtf Tetp es mtks, yk dlh 769-0846 -0465 308-538 -05385-0465 03077 00769-05385 0693-00769 -693 0465 0654-3077 05385 03846 308-538 -05385 769-0846 -0465-05385 0693-00769 -0465 03077 00769-3077 05385 03846-693 0465 0654 6
els bk mtks o-egtf Sebb tedpt et mtks yg bel egtf Meggt teoem 3, sols pesm ley tdk lgsg med sols pesm le fzzy 4 KESIMPULAN Sstem pesm le fzzy (SPL-fzzy dpt dbh med betk sstem pesm le bs D sstem bel d pesm dbh med sstem bel d pesm Sols sstem pesm b, tdk sec lgsg med sols sstem pesm seml Cotoh 3 mempelhtk bhw sols sstem pesm b, tdk med sstem pesm seml Jk mtks koefse d sstem pesm besft o-egtf, mk solsy med sstem pesm seml Hl dtls dlm Teoem 5 DAFTAR PUSTAKA [] Fedm, M, M Mg, d A Kdel, (998, Fzzy le system, Fzzy Set d System, No 96, 0-09 [] K, MT, Asdy,, d Vecheh, AH, (005, A Itete Method fo Solg Dl Fzzy Nole Eqtos, AMC, No 67, 36-33 [3] Kwg F Lee, (005, Fst cose o Fzzy Theoy d Applctos, Spge, Gemy [4] Lkeplod, H, (996, Hdbook of Mtces, Joh Wley & Sos, Egld [5] Sd, Y, (996, Itete Methods fo Spse Le System, PWS Pblshg Compy, Dso of Itetol Thomso Pblshg Ic, VSA [6] Se, D, (00, Mtces : Theoy d Applctos, Spge, Gemy [7] Sdm, SN, Smth, S, d Deep, SN, (007, Itodcto to Fzzy Logc sg Mtlb, Spge, el-gemy