Fuzzy Transportation Problem Using Symmetric Hexagonal Fuzzy Numbers
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1 IOSR Jourl of Mhec IOSR-JM e-issn: p-issn: 9-7X. Volue Iue Ver. II Sep. - Oc.0 PP Fuzzy Trporo Prole g Syerc Hegol Fuzzy Nuer.ShySudh d K.R. Vylkh Depre of Mhec Nrl College Woe Coore Id rc: I h pper yerc hegol Fuzzy Trporo Prole FTP roduced wh fuzzy ded d upply d opl oluo oed he e. Th doe y ug uercl prole whch clerly defe he fuzzy rporo prole. Keyword: Rkg Syerc Hegol fuzzy uer Trporo prole.. I. Iroduco I rkg fuzzy uer y ehod hve ee preeed ll ow ech oe red ed o pecl drd proporo d chrcerc of fuzzy uer. Fuzzy uer rkg w fr codered y J [8]. Bell d Zedeh [] dcued ou deco kg fuzzy evroe. rpreekur d kur [] propoed ew ehod olvg fuzzy rporo prole ug rkg fuco. Nrehkur d Kur Ghuru [] olved fuzzy rporo prole ug yerc rgulr fuzzy uer. Rrewr d Shyudh e.l.[] roduced ew opero o hegol fuzzy uer. Ch e. l. [] developed ehod olvg rporo prole wh fuzzy upple d ded v he prerc progrg echque ug he Bel- Zdeh crero []. Ch d Kuch [] roduced ehod olvg rporo prole wh fuzzy co coeffce y rg he gve prole o crerl rporo prole wh crp oecve fuco whch provde oly crp oluo o he gve rporo prole. u Ko [] decred ehod olvg rporo prole ed o eeve prcple. G d Rzk [] preeed wo ge co zg fuzzy rporo prole FTP whch upple d ded re rpezodl fuzzy uer. Sce he everl ehod hve ee propoed y vrou reercher whch clude rkg fuzzy uer ug zg d zg e. I h pper we roduced fuzzy rporo prole wh yerc hegol fuzzy ded d upply d oed opl oluo of he e. II. Prelre. Fuzzy e [ 9 ] fuzzy e chrcerzed y eerhp fuco ppg elee of do pce or he uvere of dcoure X o he u ervl [0 ]..e. { ; X}. Here : X [0] ppg clled he degree of eerhp fuco of he fuzzy e d clled he eerhp vlue of X he fuzzy e. Thee eerhp grde re ofe repreeed y rel uer rgg fro [0 ].. Norl fuzzy e: fuzzy e of he uvere of dcoure X clled orl fuzzy e plyg h here e le oe X uch h =.. Fuzzy uer [0] fuzzy e defed o he e of rel uer R d o e fuzzy uer f eerhp fuco : R [0] h he followg propere u e orl fuzzy e. u e cloed ervl every 0 ]. The uppor of 0 u e ouded.. Hegol Fuzzy Nuer [] hegol fuzzy uer deoed y fuzzy uer H d re rel uer d eerhp fuco gve elow H = where DOI: / Pge
2 DOI: / Pge oherwe H 0. Rkg of Hegol Fuzzy Nuer [] effce pproch coprg he fuzzy uer y he ue of rkg fuco R: F R R where F R e of fuzzy uer defed o e of rel uer whch p ech fuzzy uer o rel uer where url order e For every H F R he rkg fuco R: F R R defed 8 8 R H. Syerc Trgulr Fuzzy uer [] If = he he rgulr fuzzy uer = clled yerc rgulr fuzzy uer. I deoed y = where Core lef wdh d rgh wdh of C..7 Syerc rpezodl fuzzy uer [7] fuzzy e Ā o R clled yerc rpezodl fuzzy uer f eerhp fuco defed follow: oherwe H 0 We deoe yerc rpezodl fuzzy uer Ā= α α d he e of ll yerc rpezodl fuzzy uer y FR
3 DOI: / Pge III. Syerc Hegol Fuzzy Nuer yerc hegol fuzzy uer Where d re rel uer d eerhp fuco defed oherwe H u 0 Fg... Grphcl repreeo of he yercl hegol fuzzy uer IV. Mhecl Forulo Of Fuzzy Trporo Prole The hecl odel of fuzzy rporo prole o ze he ol rporo co fro ource o deo follow ; d ll d o uec c Z Mze where c he fuzzy u rporo co fro h ource o he h deo.
4 S O R C E S Tle -.. Fuzzy rporo le DESTINTION N Supply c c c c c c..... M c c c Ded.. Fuzzy Vero of Be cdde Mehod Sep: Fro he Fuzzy Trporo le f he ol upply equl o he ol ded he he r lced. The proceed o Sep. If he ol upply o equl o he ol ded duy row or colu dded per he eed o ke he upply equl o he ded. So he rporo co h row or colu wll e ged o zero. Sep : The e cdde zg prole o he u co d zg prof o he u co eleced. Theree h ep doe y elecg e cdde ech row. Sep : Idefy he row wh he lle co cdde fro he choe coo. The lloce he ded d he upply uch pole o he vrle wh he le u co he eleced row or colu. lo he upply d ded dued y crog ou he row/colu d he g o zero. Sep : The proce repeed ul opu c fele oluo oed.. Nuercl eple Coder he followg fuzzy rporo prole. copy h hree fcore d four oule D D D d D. The fuzzy rporo co u quy of he produc h ource o h oule C where C The produco que per oh re d 80 o repecvely. The ded per oh D D D d D re d 80 repecvely. Soluo: Sep : Coruc fuzzy rporo le he gve rporo prole d he cover o lced oe. Here he gve prole lced oe o we ove o o ep. Tle.. Fuzzy Trporo Prole Oule Fcory D D D D Supply Ded Now ug hegol rkg ehod [.] he yercl hegol fuzzy rporo prole furher covered o rporo prole DOI: / Pge
5 R R7890 R90 R80 R78 R80 R79 R7890 R80 R98 R7890 R808 R808 R79 R80 Now we clcule R y pplyg he rkg ehod. R H 8 8 R = 8 8 = 0.97 Slrly R 80 =.9 R 79 =. R 98 =.9 R 808 =. R 7890 =. R 78 =. R 7890 =. R 7890 = R 79 =. R 90 =.9 R 80 =.0 R 80 =. R 808 = R 80 = R 79 =. R 08 =. R 70 =. R 80 =.9 Fuzzy rporo prole covered o orl rporo prole gve elow Tle.. Norl rporo Prole Oule Cuoer D D D D Supply Ded....9 Sep : Elec he cdde ccordg o ech row d colu d he y ug BCM we deere he e coo h wll produce he lowe ol wegh of he co. Tle -... Tle wh Seleced Cdde Sep : Idefy he row wh he lle co cdde fro he choe coo d lloce he ded d upply d lo dued ded/upply y crog ou he row/colu o e he ged o zero. DOI: / Pge
6 Tle -... Fl lloco le ug e cdde ehod Sep: The opl oluo ug e cdde ehod gve follow: Mze Z= Mze Z = = 9.7 V. Cocluo I h pper ew eerhp fuco yerc hegol fuzzy uer defed. The rporo co ource d ded re repreeed y yerc hegol fuzzy uer. Here he Be cdde ehod d cerod rkg o r he fuzzy rporo o crp rporo prole ued d flly he ol opl co rrved. Referece [] rpree Kur Kur ew ehod olvg fuzzy rporo prole ug Rkg fuco ppled Mhecl Vol -0. [] Bell R. E. d.. Zdeh. Deco kg fuzzy evroe. Mgee. Sc. 7B -970 [] Ch W.Kolodzeczyk d. Mch fuzzy pproch o he rporo prole Fuzzy Se d Sye [] Ch d D. Kuch cocep of he opl oluo of he rporo prole wh fuzzy co coeffce Fuzzy Se d ye [] Che S.H Rk fuzzy uer wh zg e d zg e Fuzzy e d ye [] G K.. Rzk Two ge fuzzy rporo prole J. Phy. Sc [7] K.Ge P. Veer Fuzzy ler progrg wh rpezodl fuzzy uer. Oper. Re [8] J.R Deco kg he preece of fuzzy vrle IEEE Trco o ye M d Cyerec [9] Klr George J d Bo Yu Fuzzy e d Fuzzy logc: Theory d pplco Prece Hllof Id 997. [0] Kuf. Gup M. M.Fuzzy hecl odel egeerg d Mgee Scece. Elever Scece Pulher erd Neherld988. [] S.T.u C. Ko Solvg fuzzy rporo prole ed o eeo prcple Europe J. Per. Re [] Nrehkur d Kur Ghuru olvg fuzzy rporo prole ug yerc rgulr fuzzy uer Ierol Jourl of dvced Reerch Mhec d pplco Pge:7-8 0 [] Rerewr P d Shy Sudh. d Krhk. R. ew Opero o hegol fuzzy uer Ierol Jourl of Fuzzy ogc Sye IJFS Vol. No.. pp - 0. DOI: / Pge
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