Off-target deviation degree method for grey multi-attribute group decision-making

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Jennifer West
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1 " m s G T è ) Ü ] è 34 3 ol34 No Systms Engnrng Thory & Practc Mar 04 : (04) : N945!"#$%&')()*+) : A -/0 /34 (56789;:<>?;@BA7C;:D EF 3008) HJILKNMPOLQLRLSUTQLRLWNXPYLZL[L\LWNXP]LN_L`PaLbNcPdLZL[NPf gph dlllkllutm klllyldllnnopklllpncpqlr sntlu alvlwlqlrlnnopklllpldlzl[lxny z dlzl[ncp{l L}L~L ƒ ˆ Š c x Œ z d k l Ž o d m k l c x Œ x Œ t u a v w Q R d Z [ f c Z [ š c œ ž Ÿ s t u m d k l ž d k l cp L LxNy ˆL ; L dllnnopklllpncp L LKLªLxLŒNc L«L L L L L± w³²µĺdlzl[ L L L¹LºN» up¼ xnylcp LLR ¾L LÀÁdLZL[ _L`Pb dllnnopklllp alklzl[ ; ; ; Off-targt dvaton dgr mthod for gry mult-attrbut group dcson-makng DAI Wn-zhan LI Ju-lang (School of Informaton and Elctronc Engnrng Zhang Gongshang Unvrsty Hangzhou 3008 Chna) Abstract Th off-targt dvaton dgr mthod s prsntd for gry mult-attrbut group dcsonmakng problm n whch ts attrbut valu attrbut wght and authorty wght ar ntrval gry numbrs Th concpts of postv group targt ngatv group targt and group off-targt dvaton dgr ar rspctvly proposd Th approach for masurng group off-targt dvaton dgr s gvn to dtrmn whch program s bst on from th vwpont of postv and ngatv dal solutons basd on TOPSIS Th smulaton rsults show th mthod s vry ffctv Kywords group dcson-makng; ntrval numbr; group off-targt dvaton dgr; gry targt dcsonmakng ÂÄÃ ÅLLÇLÈLÉLÊLËLÌLLLÐLÑ LÓLÔ LÕLÖL L TÚÙLÛ ÜLÝLÞLßL ál LLæLçLèLéLê ælçlëlëlìlålí ÛLî å Lÿ LðLñLòLóLôLõNö LLùLúLûLüLýLþ ñlò [] LòLÓ L Ü ; [] LòLÓLÜ L ý ; î [3] Ó LûLüLýLþ! L L & ÿ TOPSIS â # $ %LÓLý ; [4] ' (Lý LûLü! ñlòló L ) * LLæLç ý ó+ â [5] - LûLü / 0 þ LéLê 3 4 LÉLÊ ælç 7LL LòLÓLÜ 5 6 â 9 Lê : ; ý 8 ý â < [6] LòLÓLÜ >Lß A B C D ý 8 C E H F GLÓLý 8 C E ß I J ; " [7] ý 8 LKPLþ M N # $ %LûLü þ M N ; [8] O P LÉLÊ ÖLé TW è X Ó Q RLþLý 8 ñlòló S 8 T ULâ 8 T!Lâ â ULâ ; [9] ' ( Y Z [ \ ] 8 T U Å _ Í Î ü ` 5 a blñlòló Y Z8 T! c dló 5 6 ] 8 TLý 8 ; [0] O PLÓ ÐLìLÅL LLLþ ûlülþ ÖLé l Q f 0Lþ Q Lþ g h Z Lý 8 ; [] klß n ËLÌ olë olë q Lå r U ý 8 â p O PLÓ ý 8 LL T LéLêLèL tlélê u - LûLüLýLþ LÉLÊ v wl 8 T xzy {~} z z z z z : : ƒz ~ z zẑ zš (63740); ƒz z zœz zžz z z z z z (009AA04Z39) z (958 ) œ zž Ÿzz z z E-mal: dwz@zsuducn : š

2 Å t H b S Á - ö Ç Á s ) á» Þ í ] è ; S ; 788 ª «34 8 T! ß ¼¾¾ ¾À ô Lò gl 8 T! ± ² ³LáL µ L â p ' ( L º¹Lâ LLÉLÊL ÃL A {A A A n } Â Ä B {B B B m } LK m C D ; Ä M {M M M l } L l L t L M Å ä å ä å k ÿ B úç û ü ý þ ñ ò È Í Î ( ) [u(k) u(k) ] ÉÊ K u(k) L M k ÈL ÁL R (k) ( ( )) n m LéLê M k Í Î B LûLüLýLþ ω (k) m ω (k) ( ) [ω (k) ω (k) ](0 ω (k) ω (k) ; m k l) á tllélê ßLû ülýlþ Ð ÈL : α k ( ) [α k α k ] 0 α k α k k l 3 ¼¾¾Ñ¾¾Ó¾Ô Õ Ö b H Ú ³ Û Ü Ý Þ ß T! ± ² ³LáL 3 ç è é ê ë ì í î L Kº6 : ω (k) T LéLêLèL tlélê u á L µll v wl : n ( A õ ôl ûlülýlþ Ỹ (k) (y (k) ( ) Í Î y (k) : â â ) x(k) n (u(k) ) qll ( )) n m ( ) [y(k) 3 ù ú û ü ý þ ÿ é ê L y(k) ( ) [mn {ω(k) Ö é ö 8 T ã Û ÜL ² ³ Ù ð n ( n (u(k) LÖLé ö! ³ ñ ò LûLüLýLþ ] 8 T 8 T! Ð ä å l k α k l k α k LÉLÊ L ó 6L LÜ ôl õ s 5 6L ô Lò gl 8 T æl ã ËLÌ ö» A ( ) L Ù 8 õ ôl n m k l () ) ) n m k l () R (k) ( ( )) n m S õ S ( ) [x(k) x(k) ] u [0 ] ] ω(k) ( ) ( ) n m k l (3) ω(k) ω(k) ω(k) Í Î Ë õ n k l Ỹ (k) N " max { (y n [ + y (k) + y (k) ] + y (k) { + y (k) + y (k) L ) ý 8 A Ỹ (k) N " mn { (y n [ y (k) y (k) ] y (k) { y (k) ý 8 y (k) L ) µ ÌL (k) +y(k) ) } Ý á ÅLLÌ ä å + y m (k) } {[+ y (k) (k) +y(k) ) ³ M k ÅLLÌ } Ý y m (k) } {[ y (k) A ³ M k } max {ω(k) ³ y (k) N ò ÈL + y (k) ] 8 T N ò ÈL y (k) ] [+ y (k) ] [ y (k) 8 T ( ) (y (k) + (k) ¹ ò + y (k) (k) ¹ ò y (k) ω(k) ω(k) ω(k) }] (4) ( ) y(k) ( ) y(k) m ( )) HLL ] [+ y (k) m + y (k) m HLL ] [ y (k) m y (k) m ÈL + y (k) ]} (5) ÈL y (k) ]} (6)

3 Ù Å Å Ð Ð y (k) 3 š Å 8 T î :<; 8T ( C D : + ε (k) A ε (k) [(y(k) [(y(k) M k Y Z l L t á)( [ \ % A A H Â ä å! " >Lú # $ z : 789 Þ â ã (y (k) +y(k) ) (y (k) +y(k) ) 8 T % & ' û ü þ LÉLÊ + y (k) ) + (y (k) + y (k) ) + + (y (k) m + y (k) m ) + (y (k) m + y (k) m ) ] (7) ] 8 T U y (k) ) + (y (k) y (k) ) + + (y (k) m y (k) m ) + (y (k) m y (k) m ) ] (8) 8 T U 8 T! n S L 8 T! tlìlålé +Lå - α k ( )s (k) S α s (k) + ε (k) 8 T! * % ε (k) + ε (k) S ÈL s () s () s (l) s () s () s (l) S s () n s () n s (l) n S / α ( )s () α ( )s () α l ( )s (l) α ( )s () α ( )s () α l ( )s (l) α ( )s () n α ( )s () n α l ( )s (l) n [α k s (k) α k s (k) ] 7 8 S α A B C D E F G H I J K L M TOPSIS N O P Q R S α 6S k T U max { (α k s (k) n [ + α k s k + α k s k ] +α k s (k) ) } W60TXYZ > b (9) (0) () + k [XY\6]Z > y + k y + {y + y+ y+ l } {[+ α s + α s ] [+ α s + α s ] [+ α l s l + α l s l ]} () C D S α 6S k T U mn { (α k s n [ α k s k α k s k ] _ C D (k) +α k s (k) ) } W60TXYZ > k [XY\6]Z > y k y {y y y l } {[ α s α s ] [ α s α s ] [ α l s l α l s l ]} (3) ε + [(α s () + α s () ) + (α s () + α s () ) + + (α l s (l) > ` a A b C D 6 C D d ε [(α s() α s () ) + (α s () > ` a A b _ C D 6 C D d f α s () ) + + (α l s (l) + α l s (l) ) + (α l s (l) + α l s (l) ) ] (4) α l s (l) ) + (α l s (l) α l s (l) ) ] (5) s ε + ε + ε (6) > ` a A A B C D E

4 790 ghklmonpq r 34 s t u 0 s n v s w x \ 6 ` a A w y C D { } _ C D ~ ƒ s ˆ s w x \ 6 ` a w 34 Š Œ Ž H I J K L N O P R > c \ A B C D E? š œ ž Ÿ 9 : () () š 7 8 R (k) ( ( )) n m > ª «š 7 8 R(k) ( š 6 ω (k) ( ) ª «š 7 8 R(k) ( ( )) ƒ n m (3) (4) ± š 6 ª «š 7 8 Ỹ (k) (y (k) ( )) n m; 3 ²³ (5) (6) µ š 6 _ C D + y (k) y (k) (k l); (7) (8) ± (9) ¹ œ ` a š 6 A B C D E s (k) / A B C D E 7 8 S; 4 š 6» A B C D E 7 8 S S α ; S α () C _ C D (4) (5) (6) ¼ ` a A B C D E s ; 6 ¾ s 6 ] x À Á 6 Â ˆ Ã ` a 6 Ä ˆ :<; s 6 Å x ] \ 6 ` a > Å ` a ( )) n m; 4 ÇÉÈÉÊÉË ÌÍÎ Í uó á 6ÑÐ ÔÕÖ ÕÙ xúñû ÜÝÕÖ6ÜÞß0 š â /0ã ä å 6 æ ç ( ) è : B : é ] (ê ë ); B : ì í ] î (%); B 3 : ð î (%); B 4 : ñ î (%); B 5 : ò ó ô õ ý þ è b ö< ³ 4 Ù ` a ²³ù X š ú Ù ` a û ü Ã š 7 8 ÿ 3 M R () š Ù 6 B B B 3 B 4 B 5 A [4353] [5974] [4353] [8] [0506] A [885985] [6075] [3858] [49] [035045] A 3 [9303] [7085] [3343] [7] [0809] A 4 [788888] [5964] [34] [94] [0708] M R () B B B 3 B 4 B 5 A [3040] [6580] [4045] [05] [055065] A [33] [5873] [3540] [7] [0607] A 3 [3] [676] [530] [50] [09] A 4 [905005] [7489] [337] [6] [085095] 3 M 3 R (3) B B B 3 B 4 B 5 A [844944] [786] [5055] [6] [055065] A [0707] [6883] [4853] [49] [065075] A 3 [4858] [7893] [3843] [38] [085095] A 4 [9303] [566] [3035] [38] [085095] Î µ : ω () ( ) ([05 09] [ ] [ ] [006 0] [03 036]) ω () ( ) ([07 0] [ ] [ ] [0 00] [ ]) ω (3) ( ) ([03 040] [08 038] [ ] [00 00] [ ]) š 6» > α( ) ([ ] [ ] [ ]) 34 A B C D E? š œ è B 3 > ð æ ç () / 0 ª «3 4 : ô õ æ ç > / 0 ª «3 4 À ª «š 7 8 R(k) ( ( )) n m [ ] [ ] [ ] [ ] [ ] R () [ ] [ ] [ ] [ ] [ ] [ ] [ ] [04 076] [ ] [ ] [ ] [ ] [ ] [08 066] [ ] æ ç ()

5 r 3 :! " # $ % & ' ( ) * + 79 ± [ ] [ ] [ ] [ ] [ ] R () [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] R (3) [ ] [04 063] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] š 6 ω (k) ( ) ª «š 7 8 R(k) ( ( )) n m š 6 ª «š 7 8 Ỹ (k) (y (k) ( )) n m - [04 069] [ ] [ ] [ ] [ ] Ỹ () [ ] [ ] [ ] [ ] [ ] [009 04] [04 070] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [04 036] [ ] [ ] [ ] [ ] Ỹ () [ ] [ ] [ ] [008 04] [ ] [006 06] [ ] [ ] [007 09] [ ] [ ] [00 069] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] Ỹ (3) [ ] [ ] [ ] [ ] [ ] [06 037] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] 3 ²³ (6) (7) š 6 _ C D : + y () {[04 069] [04 070] [ ] [ ] [ ]} y () {[ ] [ ] [ ] [ ] [ ]} + y () {[04 036] [00 069] [ ] [ ] [ ]} y () {[ ] [ ] [ ] [007 09] [ ]} + y (3) {[ ] [ ] [ ] [ ] [ ]} y (3) {[ ] [ ] [ ] [ ] [ ]} (8) (9) (0) ¼ A B C D E S š 6» [ ] [ ] [045 05] [05 07] [ ] [09 0] S α [05 08] [005 0] [05 056] [ ] [047 05] [ ] 0673 ý þ S α (3) (4) y + {[ ] [005 0] [05 C _ C D ƒ (3) (4) y {[ ] [ ] [09 0]} (5) (6) (7) `a 6?@ABCDE s s 003 s s 4 6 Ý/0 s 6 x Á Å 6 ƒ À \ 6 4 Ù ` a 6 ˆ > A 3 > A > A 4 > A ` a A : C š ; š š < 6 > ð A B š ] š C > Î

6 ô ` 79 ghklmonpq r 34 s 6? š < D _ C A B C D E 6 FHG _? C D? C D d 6 ¹ A B C D E 6 x Á ` a 6 Ä / 0 IHJ > ; š? š < M 6 œ Å 5 Ý N O \ PQ [ ` 6 è R S T U [] W X Y Z! " ( ) * [ \ ] + _ ` [J] a b n ) * 00 5(): Xu Yngun L Dong Approach to rachng consnsus n multpl attrbut group dcson makng[j] Control and Dcson 00 5(): [] c d gfh ( ) * k l m n o + [J] p q n a b (): 3 6 Zhang Xnbo Gry analytcal mthod of mult-obctv group dcson-makng problm[j] Informaton and Control (): 3 6 [3] r s d! " ( ) * m TOPSIS [J] t u v w x y y z 008(): 5 Chn Xaoxn TOPSIS mthod of gry multpl attrbut group dcson[j] Journal of Jangx Unvrsty of Fnanc and Economcs 008(): 5 [4] r s d { } ] ~ n p q m! " ( ) * + [J] g h k ng ƒ 009 3(4): Chn Xaoxn Lu Sfng Gry multpl attrbut group dcson-makng mthod wth partal wght nformaton[j] Systms Engnrng and Elctroncs 009 3(4): [5] ˆ gš c Œ Ž x m! " ( ) * + [J] g h k l m n p q 0 3(0): Q Xaown Lang Changyong Zhang Enqao t al Approach to ntrval-valud ntutonstc fuzzy multpl attrbuts group dcson makng basd on maxmum ntropy[j] Systms Engnrng Thory & Practc 0 3(0): [6] Y š œ ž ] ~ Ÿ m % [J] ª n «l 005 4(6): L Xaoya Cu Jnchuan A gry targt valuaton arthmtc usd for productvty valuaton[j] Opratons Rsarch and Managmnt Scnc 005 4(6): [7] { } { Ž m ± h % ) * ² m _ ` [J] ³ k y 005 7(8): 3 35 Dang Yaoguo Lu Sfng Lu Bn Study on th mult-attrbut dcson modl of gry targt basd on ntrval numbr[j] Engnrng Scnc 005 7(8): 3 35 [8] µ ¹ p q º m gfh % ) * + [C]// r 9» g h ¼ ¾ À 00: 5 56 Luo Dang Sun L Th mult-obctv gry targt dcson mthod undr th nformaton of thr-para mtr ntrval gry numbr[c]// 9th Workshop on Gry Systm Thory and Its Applcatons Bng 00: 5 56 [9] Á Â Ã Ä d Ä Å % & % ) * ² [J] g h k l m n p q 00 30(0): 8 87 Song J Dang Yaoguo Wang Zhngxn t al Nw dcson modl of gry targt wth both th postv clout and th ngatv clout[j] Systms Engnrng Thory & Practc 00 30(0): 8 87 [0] Ç È É Ê Ê Ë Ì ² ± h % ) * ² _ ` [J] h Í n ) * 00(): 7 0 Shn Chunguang Dang Yaoguo P Lnglng Study on th mxd mult-attrbut dcson modl of gry targt[j] Statstcs and Dcson 00(): 7 0 [] Ã Ä d Î Ð Ñ m gfh % ) * + [J] g h k ng ƒ 009 3(): Wang Zhngxn Dang Yaoguo Yang Hu Improvmnts on dcson mthod of gry targt[j] Systms Engnrng and Elctroncs 009 3():

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