Statistical Optimization for Generalised Fuzzy Number
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1 Ierol Jourl of Moder Egeerg Reserh IJMER wwwero Vol Issue Mrh-Aprl pp ISSN: Ssl Opzo for Geerlsed Fuzzy Nuer Sk Khdr Bu Resh AdB Mdhusudh ReddyK MVRh 4 KrhkeyK 5 5 Shool of Adved Sees VIT Uversy Vellore SV Uversy Truph 57 5 Asr: I hs pper ep hs ee de o propose ehod sed o Psl rgulr grded e represeo o solve he wo-oeve fuzzy ssge prole uder fuzzy evroe I hs oss d es re o e fuzzy vrles Ad we pply ssl erpreo for ew pproh o solve he fuzzy ssge prole Here we ke he oeffes of fuzzy uers fro Psl rgles d develop ew proedure o solve fuzzy ssge prole Gve hrough he uerl eple Keywords: Assge prole Trgulr Fuzzy uer Psl rgulr grded e represeo I Iroduo Assge prole s oo prole he rel syse For hs prole deers evroe lo of odels d lgorhs hve ee preseed up o ow I ree yers y reserhers eg o vesge hs kd of prole uder he uer evroe Tde d Rrd [] gve he soluos of he ullevel ssge proles BogoolA d MoulA & gve ew soluo for rdo ssge prole d developed proedure for sple ssge prole wh uque soluo The oher uery he rel world s fuzzess I order o del wh fuzzess Zdeh [4] gve foro ou he he fuzzy se heory 965 For he ssge prole y e lso osdered uder he fuzzy evroe whh uses he reserh of fuzzy ssge prole osruve ouds d e epeo of he rdo ssge prole ws dsussed y oppersh d Sork 4 L d We [7] fred d desged lelg lgorh for Rdw [8] dd sple preferee sed rff ssge prole fuzzy pproh A ul-rer fuzzy ssge ehod ws rodued y Belel d Boulssel I ler progrg prole he ssge prole s prulr se o ssg he dffere os o dffere workers I hs ee dsussed wh he suo whh os re o e ssged o persos for eeuo The ssge prole s derved ers of Ler progrg forulo ws gve y D Kog [5] Le uer of os e gve h us e perfored y workers where he oss d he es deped o he spef ssges Eh o us e ssged oe worker d eh worker hs o perfor oe d oly oe o so h he ol os d he ol e s zed fer ll he os re opleed SMurugd el gve spel proedure o solve he wo-oeve ssge prole hrough he grded e egro represeo The Hugr ehod [6] whh s he os populr very ovee d effe erve proedure for solvg ssge prole Bsed o he uery deso-kg we lwys re soe preers s uer vrles whh o o her oree vlues I hs pper we osder wo oeve ssge prole uder fuzzy evroe whh he oss d he es re supposed o e fuzzy vrles Ths pper s orgzed s follows: I seo we osru he hel odel for he prole I seo he ehodology s rodued I seo 4 ssl pleeos re gve I seo 5 uerl eple s gve d seo 6 we gve oluso for our prole II Mhel Model Assue here re os d workers For he oveee of desrpo he oos = d = re used o deoe he dees of he dffere workers d os The purpose of he wo oeve ssge prole hs pper s os d workers so h he ol os d he ol e s zed fer ll he os re opleed If worker hs ly o uderke soe os d we hk h he wll proly produe uh less prof or osue very log e suh odos worker y e deprved of opporuy o uderke hese os I he proess of deso kg f o s ssged o worker he he orrespodg oss d osued es deoed y d = = respevely Geerlly he opl pl s de efore he os re opleed hus s possle for us o kow he oree vlues of d dve I order o o deso d = = hve ee gve The he os r d he osued e r y e deoed y wwwero 647 Pge
2 Ierol Jourl of Moder Egeerg Reserh IJMER wwwero Vol Issue Mrh-Aprl pp ISSN: wwwero 648 Pge T I order o odel he ove fuzzy ssge prole he followg vrles re eployed: oherwse o sossged o wor f ker Where = = The wo oeve fuzzy ssge prole ow e sed s equo: Mze Mze Sue o = = = or Se he elees of he os r d he osued e r re fuzzy vrles follows h he ol os d he ol osued e re lso fuzzy vrles I order o opze he oeve we rodue he ehodology he e seo III Mehodology Trgulr Fuzzy Nuer A fuzzy uer A s rgulr fuzzy uer deoed y d s eershp fuo A s gve elow: A Trgulr Fuzzy Nuer he [9] hs ee rodued fuo prple for fuzzy rhel operos We shll use hs prple s he opero of ddo ulplo suro d dvso of fuzzy uers Suppose d re wo rgulr fuzzy uers The The ulplo of d s where } { T T T If re o-zero posve rel uers he
3 v Ierol Jourl of Moder Egeerg Reserh IJMER wwwero Vol Issue Mrh-Aprl pp ISSN: Where re ll o-zero posve rel uers he he dvso of d s k R The for k k k k for k v Le Grded Me Iegro Represeo Mehod he d Hseh [ ] propose grded e egro represeo for represeg geerlzed fuzzy uer The SMurugd desred for geerlzed fuzzy uer Suppose L d R re verse fuos of fuos L d R respevely d he grded e h-level of geerlzed fuzzy uer s A : s h [ L h R ]/ The he defuzzfed vlue P A y grded 4 w e egro represeo of geerlzed fuzzy uer sed o he egrl vlue of grded e h - level s P A h L [ h R w h dh h ] dh Where h s ewee d w w If A s rgulr fuzzy uer he d Hseh [ ] lredy fd he geerl forule of he represeo of geerlzed rgulr fuzzy uer s follows: PA = h[ h h hdh ] dh ; PA = 4 4 Psl rgulr grded e pproh he d Hseh [] proposed grded e egro represeo for represeg geerlzed fuzzy uer d SMurugd el desred oe ore grded e represeo for geerlzed fuzzy uer Ths s useful o o he soluo of he geerlzed fuzzy vrles for ssge prole Bu he prese pproh s very sple wy of lyzg ul oeve fuzzy vrles for ssge prole he we pply Hugr ehod we ge he opu soluo Here we pply sple ssl ess o lyze d opre he ove wo ehods Ths pproh s lso pplle for ul-oeve fuzzy ssge prole Bu hs proedure s sply ke fro he followg Psl rgles These re useful o ke he oeffes of fuzzy vrles re Psl rgulr uers d we us dd d dvded y he ol of Psl uers he we ll s Psl s rgulr proly pproh Ths s lso he lerve proure for grded e represeo 6 wwwero 649 Pge
4 Ierol Jourl of Moder Egeerg Reserh IJMER wwwero Vol Issue Mrh-Aprl pp ISSN: Le he re wo rgulr fuzzy uers he we ke he oeffe of fuzzy uers s psl rgulr ype d pply he sple proly pproh Le he d re wo rgulr fuzzy uers he we ke he oeffe of fuzzy uers fro psl s rgles d pply he sple proly pproh he we ge he followg forul: P A 4 The oeffes of re Ths pproh e eeded for desol Psl Trgulr fuzzy order lso IV Ssl Ipleeos 4 For Seduers F-Tes Le us ssue X s for geg vlues fro Grded egro e ehod d Y e he Vrle s for geg vlues fro Psl Trgle pproh The o vres of he oh vrles d fd F luled vlue d he opre wh F le vlues 5% level of sgfe If F l Vlue > F Vlue he we ree hypohess Ho oherwse we do o 4 For Sude -es Apply -es for he ove wo vrles X d Y he lule vlue d opre o le vlue 5% level of sgfe If luled > - le vlue we ree hypohess Ho oherwse we do o ree Ho 5 Resuls d Dsussos I hs seo we gve soe sple resuls d dsussos hough he followg uerl eple o show he effey of he ehodology The os d e r re gve rgulr fuzzy uers T T Applyg he grded e egro represeo for defuzzfo 4 P A 6 T By Psl rgulr pproh P A 4 5 Ssl erpreo For F Tes : Le we sed he hypohess Ho: There s o sgfe dfferee ewee he vres of he ove wo vrles X : wwwero 65 Pge
5 Ierol Jourl of Moder Egeerg Reserh IJMER wwwero Vol Issue Mrh-Aprl pp ISSN: Y : VreX = 558 ; VreY = 5969 d Fl Vlue = 9:F Vlue =44 5%level of sgfe; F l vlue s very les so we do o ree hypohess For -es : Le he Hypohess Ho: There s o sgfe dfferee ewee he es of he wo vrles Me of X s 667 d Me of Y s 68 d -l Vlue = - Vlue s he we ree Hypohess Bsed o ssl ess e d vres re he se he we sy h hese wo grouped vlues re e fro he orl populo Ad for he soluo of hese wo ehods re oprvely se Therefore hs pproh s lerve for he prevous oe Applyg he Hugr ehod he soluo s Opl lloo: Therefore he opu fesle soluo s ++=4 V oluso Ths esure s ore pplle for geerlzed fuzzy uer y oprg grded e verge ehod d s lso useful o solve he ssge prole y Hugr ehod For ssl ess here s o sgfe dfferee ewee he wo ehods By oprso Psl rgulr ehod s lso pplle for fuzzy ssge prole I s lso pplle o solve he ul-oeve fuzzy ssge proles lso Bsed o ssl ess e d vres re he se he we sy h hese wo grouped vlues re e fro he orl populo Ad for he soluo of hese wo ehods re oprvely se Therefore hs pproh s lerve for he prevous oe Referees [] Bogool A d MoulA A New soluo o he Rdo Assge Prole Jourl of Eoo Theory : 95-8 [] Bogool A d Moul H A Sple Rdo Assge prole wh Uque Soluo Eoo Theory 9: 6 66 [] Belel N d Boulssel MR Mulrer Fuzzy Assge Mehod: A Useful Tool o Asss Medl Dgoss Arfl Iellgee Mede : 7 [4] oppersh D d Sork GB 999 osruve Bouds d E Epeo for he Rdo Assge Prole Rdo Sruure d Algorh 5: 44 [5] Glle Blly E Iroduo o Operos Reserh A opuer Oreed Algorh Approh T M-Grw Hll New Delh [6] Kuh HW 956 he Hugr Mehod for he Assge Prole Nvl Res Logs Qur : [7] L J d We UP 4 Lelg Algorh for he Fuzzy Assge Prole Fuzzy Ses d Syses 4: 7 9 [8] Rdw M 4 Fuzzy preferee Bsed Trff Assge Prole Trsporo Res Pr :9 [9] Sh-Huo he985 Operos o Fuzzy Nuers wh Fuos Prple Tkg J Mgee S 6: 5 [] Sh-Huo he d hh Hsu Hseh Grded Me Iegro Represeo of Geerlzed Fuzzy Nuer Proeedg of oferee of Tw Fuzzy syse Assoo Tw [] Sh-Huo he d h Hsu Hseh Grded Me Iegro Represeo of Geerlzed Fuzzy Nuer ourl of he huese Fuzzy Syse Assoo Tw 5: -7 [] Sh-Huo he d h Hsu Hseh Represeo Rkg Dse d Slry of L-R Type Fuzzy Nuer d Applo Ausrl Jourl of Iellge Iforo Proessg Syses Ausrl 64: 7 9 [] Tde R d Nole Rrd:X 999 The Dy Mullevel Assge Prole s Sohs Eerl Proess Europe Jourl of Operol Reserh 7: [4] Zdeh L A 965 Fuzzy Ses Ifor orol 8: 8 5 wwwero 65 Pge
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