Super-Mixed Multiple Attribute Group Decision Making Method Based on Hybrid Fuzzy Grey Relation Approach Degree *

Transcription

1 Supe-Med Multple Attbute Goup Decso Mkg Method Bsed o Hybd Fuzzy Gey Relto Appoch Degee Gol K Fe Ye b Cete of Ntul Scece vesty of Sceces Pyogyg DPR Koe b School of Busess Adstto South Ch vesty of Techology Gugzhou Ch (yefe@scuteduc Abstct The fetue of ou ethod dffeet fo othe fuzzy gey elto ethod fo supeed ultple ttbute goup decso-kg s tht ll of the subectve d obectve weghts e obted by tevl gey ube d tht the goup decsokg s pefoed bsed o the eltve ppoch degee of gey TOPSIS the eltve ppoch degee of gey cdece d the eltve ebeshp degee of gey cdece usg 4-desol Euclde dstce The weghted Bod ethod s used to obt fl k by usg the esults of fou ethods A eple shows the pplcblty of the poposed ppoch Keywods: Gey fuzzy decso kg Supe-ed ultple ttbute Gey cdece degee 4-desol Euclde dstce Itoducto A ultple ttbute decso kg (MADM whch ttbutes e el ube tevl el ube lgustc d ucet lgustc vlue hs bee ledy ppled pctce such s the evluto of etepse effect the selecto of vestet poect the selecto of peso the esech of lty equpet schee the evluto of sttegy effect the elblty ssesset d the tblty ssesset etc (Yogq X 004 Dg uo Sfeg u 005 Yogqg We Pede u 009 Eteded TOPSIS Method wth Itevl-Vlued Itutostc Fuzzy Nubes fo Vtul Etepse Pte Selecto hs bee eseched by Fe Ye(00 Chug Dg (007 defed ew slty degee fo vous types of ttbute d olzed the clculto of slty degee of the ttbute vlue of ech type ufed etc spce Also by ths slty degee the copso of ech pl wth del pl ws pefoed d decso kg ethod ws gve Chug (007b bsed o the TOPSIS (Techque fo Ode Pefeece by Slty to Idel Soluto tsfoed the ttbute vlue of pl to fou-desol ttbute vlue ufed vous types of ttbute vlue defed foudesol ppoch degee d by ths ppoch degee solved the ultple ttbute ed-type decso-kg poble ssocted wth el ube tevl el ube lgustc d ucet lgustc vlue Yogq X (004 studed ethod cosdeg suffcecy degee of foto d pefeece to dge o the bss of the gey-fuzzy copehesve evluto ethod of tevl vlue pefeece I the ethod they epeset the weght d the ttbute vlue by two tevl ube p by cosdeg ebeshp d gey degee t the se te Sfeg u Yoguo Dg Jglg Wg Zhegpeg Wu (009 bsed o the deftos of etopy poposed ethod of gettg weght tht cosdes the chcte of gey cluste decso-kg d -tuple lgustc ssesset d poposed the ethod of -tuple lgustc ssesset bsed o gey cluste Zhe Zhg Choghu Guo (0 tsfoed ucet lgustc evluto foto of ech decso ke to tpezodl fuzzy ubes d the deoted by solvg two optzto odels the collectve evluto of the ltetves by tpezodl fuzzy ubes Ths ppe ws suppoted pt by South Ch vesty of Techology Ch

2 Yogqg We Pede u (009 costucted evluto dcto s syste d the evluto pocedues bsed o the ucet lgustc d TOPSIS ethod Pede u Yu Su (00 toduced cocept of the tpezod fuzzy lgustc vbles d defed the dstce betwee two tpezod fuzzy lgustc vbles They deteed the cobed weghts of ech ttbute by the l devto ethod d the ole weghted copehesve ethod d defed eltve closeess degee to detee the kg ode of ll ltetves by clcultg the dstces to both the postve del soluto d egtve del soluto espectvely Alecos M Kelees D Th Askous (009 poposed ult-cte ppoch to del wth goup decso kg ude fuzzy evoet d toduced ew efeece pot pt fo the postve del soluto d the egtve del soluto Ng-g Zhu J-u Zhu Ye Dg (009 studed the MADM poble of ucet thee-pot lgustc foto d obted the weght vecto of dctos by le gol pogg They poposed the clculto steps of MADM poble of ucet thee-pot lgustc foto Tg-yu Che (0 by etedg the TOPSIS poposed useful ethod bsed o geelzed tevl vlued tpezodl fuzzy ubes (GITFNs fo solvg ultple cte decso lyss (MCDA pobles whch eployed the cocept of sged dstces to estblsh sple d effectve MCDA ethod bsed o the stuctue of TOPSIS I ths ppe we popose geelzed fuzzy gey decso kg ethod tkg to cosdeto of the gey degee of the weght d the ttbute vlue t the se te whee ttbutes hve the geelzed supe ed-type vlues gve by el ube tevl vlue lgustc vlue d ucet lgustc vlue Fst we obt the gey degee coespodg to fuzzy pt of the gey fuzzy copehesve decso t d the obt by usg the foto suffcecy degee geelzed decso t coposed of fou-desol vecto delg wth the gey pt of decso t Secod we obt fou ks fo the geelzed decso t coposed of fou-desol vecto by fou ethods Flly usg the ks obted fo the bove fou ethods the fl k e deteed by the weghted Bod ethod A eple s gve to show the dvtge of ou ethod The foulto of decso kg poble wth supe-ed ultple ttbutes If the ttbutes of se clss clude the vlues of ech othe dffeet type the ts ttbutes e clled supe ultple ttbute ed type et A { A A A} be set of pls G { G G G} be set of ttbutes d T { T T T3 T4} {el tevl el lgustc ucet lgustc} be set of ttbute type (the cocete defto s gve below [Defto ] et µ S( be lgustc vlue whee S ( s lgustc esue They e gve by S { S( 5 S( 4 S(4 S(5} { eteely low vey low low coptvely low lttle low geel lttle hgh coptvely hgh hgh vey hgh eteely hgh} { } Supposg tht S( 5 S( 4 S(4 S(5 f ( ( ( the { S ( S( S( } S( d { S( S( S( } S( M Ech lgustc vlue c be epeseted by tgle fuzzy ube S [ ] M d ts ebeshp fucto s gve by M M ( /( M M µ S ( ( /( 0 othewse The epesso fos of tgle fuzzy ube coespodg to S e gve s follows

3 eteely low [0 0 0] vey low [0 0 0] low [0 0 03] coptvely low [ ] lttle low [ ] ody [ ] lttle hgh [ ] coptvely hgh [ ] hgh [ ] vey hgh [ ] eteely hgh [09 0 0] [Defto ] et A [ β γ δ ] be tpezod fuzzy ube The ts ebeshp fucto s defed by ( /( β β β < < γ µ ( A ( δ /( δ γ γ δ 0 othewse et A [ β γ δ] d B [ β γ δ ] be tpezod fuzzy ubes espectvely The the opetol lws of tpezod fuzzy ube e s follows A B [ β β γ γ δ δ ] A B [ β β γ γ δ ] k A B [ k kβ kγ k ] δ M δ M [Defto 3] et S [ ] d S [ b b b ] A tpezod fuzzy µ M M b b defed by the ebeshp fucto such s ube ( M M ( /( M M b µ ( M M ( b /( b b b b 0 othewse s clled ucet lgustc vlue wth lowe boud S d uppe boud S ( ( (3 (4 ( ( (3 (4 [Defto 4] et ( d The s clled geelzed ttbute vlue of th pl fo ttbute ( ( (3 (4 The cocete types of ( e such s ( ( (3 (4 - el ube type: ; ( ( (3 (4 - tevl el ube type: < ; ( ( (3 (4 - lgustc vlue type: < < ; ( ( (3 (4 - ucet lgustc vlue type: < < [Defto 5] The decso kg of ed type ult ttbute whch ttbute vlues of ech othe dffeet ttbute type og the se ttbute e cluded s clled supe- ed ult ttbute decso kg ( ( (3 (4 ( ( (3 (4 [Defto 6] et ( d b ( b b b b be the geelzed ttbute vlues espectvely A dstce of betwee d b s defed by ( ( ( ( d( b ( b ( b ( b ( b et { } be ttbute vecto of pl d R {( [ ν ν ] } be decso t whee [ ν ν ] s tevl gey ube epesetg gey degee of The olzed decso t X s obted by X {( [ ν ν ] } s cost-type ttbute tevl ube ] s obted by olzto such s If / (/ / (/ (3 [ (3 (4 (4 3

4 d f s s effect-type ttbute tevl ube s obted by olzto such olzto such s If [ ] the [ ] s obted by the If [ ] [ ] s obted by olzto such s 3 Deteg of ttbute weghts 3 Subectve weght of ttbutes et l [ l l l ] ( l be the ttbute weghts deteed by AHP fo the decsokg goup The weght of ttbute G s gve s tevl gey ube ( ] whee { } { } [ l l l 3 Obectve weght of ttbutes 3 Obectve weght by optzto We defe the devto of decso pl A fo ll othe decso pls fo ttbute G ( olzed decso t X ( k ( D ( β opt k d( s follows k β opt ( ( ( (3 (3 (4 (4 ( ( ( β ( opt k k k k I ode to choose pope weght vecto β opt such tht su of ovell devto fo the decso pl tts u we defe devto fucto such s D ( β d( k k β d solve the followg ole pogg poble [P] D( d( k β β s t k β β 0 [Theoe ] The soluto of poble P s gve by β d ( k k k d ( k l 4

5 By the olzto ofβ β d we obt ( k opt k k d ( k 3 Obectve weght by etopy ethod ( ( (3 (4 The etopy weghts of the geelzed ttbute vlue ( e obted fo ech (k ( k 34 s follows The vlue The etopy vlue of the th ttbute s E (k ( k 34 s olzed by p ( k ( p l k p ( I l the bove foul f p 0 the we put tht p l p 0 The devto coeffcet fo the th ttbute s clculted by η E ( et et ( k et et et Thus the etopy weght β ( β β β β fo the copoet (k ( k 34 s such s η E E et β ( k 4 η ( E 33 Deteg of copehesve obectve weghts The copehesve obectve weght s deteed by the tevl gey ube β ( β ( β ( β ( β ( β ( β β ] ( E ( k [ opt ( et ( et (3 et (4 et β ( { β β β β β } opt ( et ( et (3 et (4 et β ( { β β β β β } 33 Deteg of fl copehesve weghts The fl copehesve weght s deteed by ( β ( w ( ( β ( whee ( d β ( e the subectve weght d the obectve weght fo th ttbute espectvely Thus the weght of the ttbute ube w ( w w ] 0 w w [ G s gve by the tevl gey 4 Evluto ethods fo decso kg pls I the cse whch gey degee of ttbute weght vlue s lso gve t the se te the copehesve weghts s epeseted by the gey-fuzzy ube such s B [([ w w ][ ]([ w w ] [ ] ([ w w ][ ]] whee [ ] s gey tevl ube epesetg the gey degee of the gey-fuzzy weght w By olzg B we hve the weght vecto such s ( 5

6 W whee ( [( w ( s ( ( w ( s ( ] w ( s ( w w w w w w s ([ w w ][ s s ] s 4 Evluto of pl by the eltve ppoch degee of gey TOPSIS ethod Assue tht the subectve pefeece vlue of the pl A s gve by the geelzed ( ( (3 (4 vlue q ( q q q q et Z { z } be the olzed decso t wth the subectve pefeece such s ( ( ( ( (3 (3 (4 (4 z ( ( ( ( q q q q The the olzed gey-fuzzy decso t wth the subectve pefeece s gve by Z { z [ µ µ ] } d the copehesve weghted decso t s gve by Y W Z y ( y y whee y w ( z ( ( ( (3 (4 y y y y d µ ( s ( [ t t ] s the fuzzy pt d gey pt of y espectvely Thus we obt the y decso t Y {( y [ t t ] } The gey pt s pocessed by dge de s follows Fo the tevl gey ube [ t ] [0] let M ( t t D ( t t F ( M ( D [0] d t 0 G ( F ( t ( t t G s coveso foul of foto suffcecy whee s clled dge de The ( degee Gve the dge de of the decso ke we obt the fl decso t Y ( ( (3 (4 whee ( y y y y k ( y d y y G ( ( the copehesve weghted decso t s gve by y y y y y } ( { t ( y ( k 4 The ttbute vecto of ech pl fo ( ( (3 (4 [Defto 6] et y { y y y y } d y { y } ( k 34 A - desol tevl gey ube vecto y { y y y } s clled postve del ttbute pl vecto et ( ( (3 (4 ( k y ( y y y y d y { y } ( k 34 The y y y y } s { clled egtve del ttbute pl vecto Eucld dstce betwee ech pl ttbute vecto y d the postve o egtve del pl ttbute vecto D y o y s ( ( ( ( (3 (3 (4 (4 [ ( y y ( y y ( y y ( y y ] 6

7 o D ( ( ( ( (3 (3 (4 (4 [ y y ( y y ( y y ( y y ] ( The eltve ppoch degee betwee ech evluto pl d the del pl s D C D D The best pl s oe coespodg to the lgest C 4 Evluto of pl by the eltve ppoch degee of gey cdece [Defto 7] et Y be the olzed copehesve weghted decso t d d { y } y be the postve d egtve del pl ttbute vecto espectvely We defe The d( y y ρ d( y y d( y y d( y y d( y y ρ d( y y d( y y d( y y ( s clled the coeffcet of postve (egtve del gey tevl cdece wth espect to the postve del ttbute vlue y ( y whee ρ (0 d geellyρ 0 5 s tke [Defto 8] The t P { } ( P { } s clled gey cdece coeffcet t of the gve pl wth espect to the postve (egtve del pl [Defto 9] et G( y y G( y y The G ( y ( G ( y y y s clled degee of gey tevl cdece of the copehesve ttbute vecto fo the pl A wth espect to the postve (egtve del pl ttbute vecto [Theoe ] The gey tevl cdece degees G ( y y d G( y y stsfy the fou os of gey cdece degee e olty p-syety wholeess d closeess The degee of gey cdece eltve ppoch s defed by toducg the pefeece coeffcets s follows G( y y θ ; 0< θ < θ < G( y y θ G( y y θ C G( y y ; θ θ 0 whee θ d θ e the pefeece coeffcets espectvely Geelly we egd s θ > θ d choose t so s to stsfy 0< θ 0< θ θ θ The optl pl coespods to the lgest vlue og of the eltve ppoch degee C 43 Evluto of pl by the eltve ebeshp degee of gey cdece If the ebeshp degee of the postve del pl wth espect to the pl A s u the ebeshp degee of the egtve del pl coespodg to the pl A s u Theefoe we c fd the ebeshp degee vecto u u u u by solvg the followg poble ( [P] F( u [( u G( y y ] [ u G( y y ] 7 { } [Theoe 3] The optl soluto of the optzto poble P s gve by y

8 u G ( y y ( G ( y y G ( y y The optl pl s oe hvg the lgest ebeshp degee u 44 Evluto of pl by the gey elto eltve ppoch degee usg u etopy estto [Defto 0] et G ( y y d G( y y be the gey tevl cdece degees fo the pl A wth espect to the postve del pl d the egtve del pl espectvely We deote the weghts of these two gey tevl cdece degees by β d β ( β β β β 0 espectvely The '' C β G( y y β [ G( y y ] ( s clled gey copehesve cdece degee of the fcto vecto y We deteeβ d β by etopy ethod Thus we solve the followg optzto poble [P3] { [ β G( y y β ( G( y ] β lβ } y β β s t β 0 β 0 The soluto of [P3] s such s 8 ( G( y y G( y y ( G( y y G( y y e ( e β ( G( y y G( y y ( e β The best pl s oe hvg the lgest vlue of C 45 Fl k ethods fo decso kg pls The fl k s deteed by the weghted Bod ethod usg k vectos obted fo the bove fou ethods 5 A llusttve eple et s cosde the decso-kg poble fo the fghte developet pl of soe types The decso t s gve by the supe ultple ttbute ed type Tble The eg of ttbutes s such s; G - weght epty of body(kg G - flght dus(k G 3 - u flyg speed(k/h G4 - developet cost (te thousd Yu G 5 - evesl of body hed(h G 6 - tece possblty G 7 - secuty G 8 - elblty level of developet goup G 9 - degee of evoetl fluece Assue tht two epets e vted to detee the subectve ttbute weghts by AHP ethod Thus the subectve weght obted fo goup AHP ethod s gve by the gey ube such s ( ([ ][ ][ 3 3][ 4 4][ 5 5][ 6 6][ 7 7][ 8 8] [ 9 9] ([ ] [ ] [06 076] [ ] [ ] [ ] [ ] [ ] [ ] The subectve pefeece vlues of decso-kg goup to pl A 5 e q ( q ( q ( q 4 ( q 5 ( The eltve ppoch degee of gey TOPSIS ethod s C C C C C ( ( C 3 4 5

9 Tble Decso t Pl Ide A A A 3 A 4 G G G 3 G 4 G 5 (360 [0 04] ([ ] [03 05] (3700 [003] ([ ] [0 04] (490 [03 05] (50 [004] ([460500] [0305] (470 [003] ([465485] [005] ([480490] [0506] (470 [003] ([460475] [0305] (4890 [04 06] ([ ] [0 04] ([ ] [03 05] (475 [0 03] ([850950] [0 04] ([800900] [04 06] ([700800] [05 07] ([700750] [04 06] A 5 (3690 [03 04] ([490530] [004] ([470485] [0406] ([ ] [0 03] ([750850] [04 05] Tble Decso t (cotued Ide Pl A A A 3 A 4 A 5 G 6 G 7 G 8 G 9 (vey hgh [0305] ([the hgh vey hgh] [0305] ([the hgh hgh] [0306] (geel [005] (the hgh [0306] (the hgh [0406] (hgh [0607] ([ lttle hgh hgh] [0407] ( lttle hgh [0306] ([the hgh ey hgh ] [005] ([ lttle hgh the hgh] [0507] ([hgh vey hgh] [004] (hgh [0305] ([geel the hgh] [0406] ([the hgh hgh] [0305] (the low [0305] ([low the low] [0506] ([vey low the low] [004] ([the low lttle low] [0305] ([vey low low] [004] Theefoe we obt the k such s Pl pls 5 pl pl 3 pl 4 The we clculte the degee of gey elto eltve ppoch wth the pefeece coeffcets Fo the pefeece coeffcetsθ θ 0 5 we obted C C C C C C ( ( d we obt the pl k such s Pl pls 5 pl pl 3 pl 4 The eltve ebeshp degee betwee the gve pls d the postve del pl s u ( u u u3 u4 u5 ( d we obt the k such s Pl pls 5 pl pl 3 pl 4 The gey cdece eltve ppoch degee usg the u etopy estto s '' '' '' '' '' C ( 5' ' C C C3 C4 C ( d the coespodg k s Pl pls 5 pl pl 3 pl 4 The fl k deteed by the weghted Bod ethod s Pl pls 5 pl pl 3 pl 4 6 Cocluso We poposed geelzed fuzzy gey decso kg ethod whch tkes to cosdeto of the gey degee of the weght d the ttbute vlue t the se te fo the MADM whee 9

10 ttbutes hve the geelzed supe ed-type vlues gve by el ube tevl vlue lgustc vlue d ucet lgustc vlue Fst bsed o the ttbute vlues gve by decso ke we obted the gey degee coespodg to fuzzy pt of the gey fuzzy copehesve decso t d the obted geelzed decso t coposed of fou-desol vecto delg wth the gey pt of decso t by usg the foto suffcecy degee Secod we obted fou ks by fou ethods of pl evluto such s the evluto by the eltve ppoch degee of gey TOPSIS the evluto by the eltve ppoch degee of gey cdece the evluto by the eltve ebeshp degee of gey cdece d the evluto by the gey elto eltve ppoch degee usg the u etopy estto Flly usg the ks obted fo the bove fou ethods the fl k e deteed by the weghted Bod ethod Refeeces [] Fe Ye(00 A Eteded TOPSIS Method wth Itevl-Vlued Itutostc Fuzzy Nubes fo Vtul Etepse Pte Selecto Epet Systes wth Applctos [] Chug Dg (007 A techque fo selectg schees of tspot o ugecy bsed o fou-deso close degee Joul of Nvl vesty of Egeeg 9( [3] Yogq X (004 A cet of ed type ultple ttbutve decso poble TOPSIS odel ethod Joul of syste egeeg [4] Dg uo Sfeg u (005 Gey cdece decso-kg wth coplete foto Joul of ppled sceces [5] Sfeg u Yoguo Dg Jglg Wg Zhegpeg Wu (009 Study o -tuple lgustc ssesset ethod bsed o gey cluste wth coplete ttbute weght foto Poceedgs of the 009 IEEE Itetol Cofeece o Systes M d Cybeetcs S Atoo TX SA - Octobe [6] Zhe Zhg Choghu Guo (0 A ethod fo ult-gulty ucet lgustc goup decso kg wth coplete weght foto Kowledge-Bsed Systes 6 9 [7] Yogqg We Pede u (009 Rsk evluto ethod of hgh-techology bsed o ucet lgustc vble d TOPSIS ethod Joul of Coputes [8] Pede u Yu Su (00 The Eteded TOPSIS Bsed o Tpezod Fuzzy gustc Vbles Joul of Covegece Ifoto Techology [9] Alecos M Kelees D Th Askous (009 A eteso of fuzzy TOPSIS fo pesoel selecto Poceedgs of the 009 IEEE Itetol Cofeece o Systes M d Cybeetcs S Atoo TX SA - Octobe [0] Ng-g Zhu J-u Zhu Ye Dg (009 TOPSIS-bsed Attbute Weght Soluto sg Thee-pot gustc Ifoto Poceedgs of 009 IEEE Itetol Cofeece o Gey Systes d Itellget Sevces Novebe 0- Ng Ch [] Tg-yu Che (0 Sged Dstced-bsed TOPSIS Method fo Multple Cte Decso Alyss Bsed o Geelzed Itevl-Vlued Fuzzy Nubes Itetol Joul of Ifoto Techology & Decso Mkg [] Chug Dg (007b Techque of hybd ultple ttbute decso kg bsed o slty degee to del soluto Systes Egeeg d Electocs 9(