Approach to multiple attribute decision making based on different intuition istic preference structures

Transcription

1 ( JOURNAL O F SOU THEAST UN IV ERS ITY (N atural Sciece Editio V ol137 N o14 Ju ly ( 1, ( 2, :.,,,.,,.. : ; ; ; : C934 : A : ( Approach to ultiple attribute decisio akig based o differet ituitio istic preferece structures D ai Yueqiag 1 X u Zeshui 2 D a Q igli 1 ( 1 School of Ecoo ics ad M aage et, Southeast U iversity, N ajig , Chia ( 2 Istitute of Scieces, PLA U iversity of Sciece ad Techology, N ajig , Chia Abstract: The itu itioistic fuzzy ultip le attribute decisio akig p roble s are ivestigated, w here the attribute values are g ive as real u bers ad the decisio akers have p referece ifor atio o attributes. The p rovided p referece ifo r atio is exp ressed i the for of ituitioistic judg et a2 trix o r ico p lete ituitio istic judg et atrix. So e cocep ts, such as itu itioistic judg et a2 trix, cosistet ituitioistic judg et atrix, ico p lete ituitioistic judg et atrix, ad cosist2 e t ico p lete ituitio istic judg et atrix, are itroduced. The, tw o odels are established for u ltip le attribute decisio ak ig based o ituitioistic judg et atrix ad ico p lete i tuitio is2 tic judg et atrix, resp ectively, ad a odel is established for u ltip le attribu te group decisio akig based o itu itioistic judg et atrices ad ico p lete ituitio istic judg et atrices. Further ore, a app roach is develop ed to u ltip le attribute decisio akig based o differet itu2 itioistic p referece structu res. The ethod does ot eed to u ify d ifferet p referece structu res ad ca derive the op ti al w eight vector fro the established odel directly, w hich ca avo id losig or disto rtig the orig ial p referece ifo r atio i the p rocess of uify ig the structures. Fially, the de2 veloped app roach is app lied to the evaluatio of the co petece of e terp rise techo logy iovatio i J iagsu p rovice. Key words: ultip le attribute decisio akig; itu itioistic judg et atrix; ico p lete i tuitio2 istic judg e t a trix; techo logy iova tio : : ( ( (( : ( 1962,,; (,,,, dqlseuj@126. co..,. : Chia Acadeic Joural Electroic Publishig House. All rights reserved.

2 4,: 707. [ 1 ], ; [ 2 ] [ 3 ] ( [ 4 ]. [ 3 ],, [ 5-6 ].,,,, 3. [ 7 ] ( 3,., [ 8-9 ],, [ 8 ] ; [ 9 ],,.,,,,,, (...,.,,. 1,X = { x 1, x 2,, x }, G = {G 1, G 2,, G }. w = {w 1, w 2,, w } T (,, [ 0, 1 ], w. x j,g i, x j G i a, D = ( d.,m = {1, 2,, }, N = {1, 2,, }.,,,. I 1 I 2., D : r = r = d ax ( d i I 1 ; j N (1 i i ( d i i I 2 ; j N (2 d R = ( r. R, z j (w z j (w,x j.. 1 [ 9 ] G = r j N (3 = {G 1, G 2,, G },, A = ( a,, a = (, v, i, jm, G i G j G i,v G j, v, [ 0, 1 ], v [ 0, 1 ], ji = v, v ji =, ii = v ii = 015, + v 1, i, j M, A. 1 A a (, v, + v 1, 1 - v., [ 9 ] a = (, v ga = [, 1 - v ]. A = ( a [ 9 ] ga = ( ga,, ga = [ a īj, a + ] = [, 1 - v ], i, j M, a īj + a + ji = a + + a - j, a + a īj 0 a + ii = a īi = 015 i, j M (4,A = ( a,, a = [, 1 - v ],, + v = 1,A = ( a. 2 [ 1 ] C = ( c, c = + w j i, j M (5, = w j = 0,c = 015. C Chia Acadeic Joural Electroic Publishig House. All rights reserved.

3 708 ( 37 : 2, 3 A = ( a,, a = [, 1 - v ], i, j M, w = {w 1, w 2,, w } T, 1 - v i, j M (6 + w j, 0, w, A.,(6 (1 - v i, j M (7 A, (7., (7, e īj e + (7 : - e īj (1 - v + e + i, j M (8, e īj e +., e īj e +, (8 (7. e īj e +, A.,(3 (8, M 1: ax ( z 1 (w, z 2 (w,, z (w i ( e + e + īj i, j = 1 s. t. - e w īj i (1 - v + e + i, j M 0, w i M e īj, e + 0 i, j M, M 1 M 2: ax e j - j = 1 i, j = 1 ( e īj + e + s. t. z j (w e j j N - e īj (1 - v ( + w j + e + i, j M 0, w i M e īj, e + 0 i, j M, w = {w 1, w 2,, w } T, e e. +, (3 īj z j (w ( j N,. 2 ( - 1 /2,,,, [ 9 ] : 4 [ 9 ] A = ( a,, a v = [, 1 - v ], [ 0, 1 ] [ 0, 1 ], ji = v, v ji = ii = v ii = 015, + v 1 (9 A. 34, : 5 A = ( b, Q A, a = [, 1 - v ] Q, = { ( i, j a = [, 1 - v ] Q }. w = {w 1, w 2,, w } T, (1 - v ( i, j (10, 0, w, A. A, (10., (10, - e īj (1 - v + e + ( i, j (11, e īj e +,., (3 (11, M 2, M 3: ax e j - j = 1 ( i, j ( e īj + e + s. t. z j (w e j j N - e īj (1 - v ( + w j + e + ( i, j 0, w i M e īj, e + 0 ( i, j, w = {w 1, w 2,, w } T, e e. +, (3 īj z j (w ( j N, Chia Acadeic Joural Electroic Publishig House. All rights reserved.

4 4,: ,.,,.,,,., 2. t, E = { E 1, E 2,, E t }.,E k ( k = 1, 2,, t 1 A k = ( a ( k, t 1,, a ( k E k ( k = t 1 = ( a ( k 1 - v ( k = [ ( k, 1 - v ( k ( k = 1, 2, ], i, j M, + 1,, t A k ( k = t 1 + 1,, t,, a ( k = [ ( k, ] Q k, Q k A k., M 2 M 3,M 4: ax j = 1 t 1 e j - k = 1 i, j = 1 ( e - ( k + e + ( k - t ( e - ( k + e + ( k ( i, j k k = t 1 +1 s. t. z j (w e j j N ( k - e - ( k (1 - v ( k + e + ( k i, j M; k = 1, 2,, t 1 (k - e - (k (1 - v (k + e + (k ( i, j k ; k = t 1 0, w i M e - (k, e + (k 0 i, j M; k = 1, 2,, t 1 e - (k, e + (k, k = { ( i, j a ( k k = t 1 + 1,, t. 0 ( i, j k ; k = t 1 + 1,, t + 1,, t = [ ( k, 1 - v ( k ] Q k },, w = {w 1, w 2,, w } T, e - ( k, e + ( k M; k = 1, 2,, t 1, e - ( k, e + ( k ( i, j ( ( i, j k ; k = t 1 + 1,, t., (3 z j (w ( j N,. 4,. 6x j ( j = 1, 2,, 6 5: 1 (G 1. 2 (G 2. 3 (G 3. 4 (G 4 (. 5 (G D x 1 x 2 x 3 x 4 x 5 x 6 G G G G G E k ( k = 1, 2 8, A 1 A 2 : A 1 = A 2 = (015, 015 (017, 012 (018, 012 (016, 013 (015, 014 (012, 017 (015, 015 (016, 013 (014, 015 (013, 016 (012, 018 (013, 016 (015, 015 (014, 016 (013, 014 (013, 016 (015, 014 (016, 014 (015, 015 (014, 016 (014, 015 (016, 013 (014, 013 (016, 014 (015, 015 (015, 015 (016, 012 x (015, 013 x (012, 016 (015, 015 x x (014, 015 x x (015, 015 (013, 015 x (013, 015 x (015, 013 (015, 015 (013, 016. x (015, 014 x (016, 013 (015, 015,, (1 D, Chia Acadeic Joural Electroic Publishig House. All rights reserved.

5 710 ( 37 2 R x 1 x 2 x 3 x 4 x 5 x 6 G G G G G M 4 w = { , , , , } T e 1 = , e 2 = , e 3 = e 4 = , e 5 = , e 6 = = e + (1 12 = 21 = e + (1 21 = 0 e - ( 1 13 = 31 = , e + ( 1 13 = e + (1 31 = 0 14 = e + (1 14 = 41 = e + (1 41 = 0 15 = e + (1 15 = 51 = e + (1 51 = 0 23 = e + (1 23 = 32 = e + (1 32 = 0 24 = e + (1 24 = 42 = e + (1 42 = 0 25 = e + (1 25 = 52 = e + (1 52 = 0 34 = e + (1 34 = 43 = e + (1 43 = 0 35 = e + (1 35 = 53 = e + (1 53 = 0 45 = 54 = = e + (2 12 = 21 = e + (2 21 = 0 14 = e + (2 14 = 41 = e + (2 41 = 0 e - ( 2 25 = 52 = , e + ( 2 25 = e + (2 52 = 0 34 = e + (2 34 = 43 = e + (2 43 = 0 45 = e + (2 45 = 54 = e + (2 54 = 0, (3 z 1 (w = , z 2 (w = z 3 (w = , z 4 (w = z 5 (w = , z 6 (w = z j (w x 2 : x 6 : x 5 : x 3 : x 1 : x 4, ( x 2. 5, (..,..,,,.. ( Refereces [ 1 ]. [M ]. :, 2004: [ 2 ] Saaty T L. The aa lytic hiera rchy p rocess [M ]. N ew York: M cg raw 2H ill, 1980: [ 3 ]. A H P[ J ]., 1999, 19 (7 : X u Zeshui. S tudy o the relatio betw ee tw o classes of scales i A H P [ J ]. Syste s EgieerigTheory & P ractice, 1999, 19 (7 : ( i Chiese [ 4 ] O rlovsky S A. D ecisio2 akig th a fuzzy p referece re2 latio [ J ]. Fuzzy Sets ad Systes, 1978, 1 (2 : [ 5 ]. [ J ]., 1995, 5 (3 : W ag Y ig ig. A overview of p riority ethods of co pariso atrix [ J ]. J oura l of D ecisio M akig ad D ecisio Support Syste s, 1995, 5 ( 3 : ( i Chiese [ 6 ],. [ J ]., 2001, 19 (5 : Fa Zhip ig, J iag Yap ig. A overview of p riority ethods of fuzzy judg et atrices [ J ]. Syste s Egi2 eerig, 2001, 19 ( 5 : ( i Chiese [ 7 ] A taassov K T. Ituitioistic fuzzy sets [ J ]. Fuzzy Sets ad Syste s, 1986, 20 (1 : [ 8 ] Sz idt E, Kacp rzyk J. A cosesus2reachig p rocess u2 der ituitioistic fuzzy p referece relatios [ J ]. Itera2 tioa l J oura l of Itelliget Syste s, 2003, 18 ( 7 : [ 9 ] X u Zeshui. A survey of p referece relatios [ J ]. Iter2 a tioa l J oura l of G eera l Syste s, 2006, 35 ( 2 : Chia Acadeic Joural Electroic Publishig House. All rights reserved.