一种群决策中专家客观权重的确定方法_梁

l :2004-03-06; :2004-07-13。 “:SE1 S(70371023);p V(20030358052) 5Te: (1962-), 3, q,p V,1Z_ %s, 3T5 。B %E Z4 ZE梁 ,熊 立,王国华(中国科学技术大学商学院,安徽合肥 230026)K 1:给出一种确定群决策中各专家客观权重的方法。将专家客观权重分为个体可信度权值和群体可信度权值;通过提取专家判断矩阵信息,确定专家在具体判断中自身的相对个体可信度权值,通过比较群决策中各专家信息的相似程度,确定各专家的相对群组可信度权值;最终得出专家判断信息合成时的各专家客观权重。给出的算例说明该方法的可行性和有效性。1oM:判断矩阵;群决策;可信度ms |:O223 DS M :ANew method for determining the objective weight ofdecision makers in group decisionLIANG Liang, XIONG Li, WANG Guo-hua(BusinessSchool, University of Scienceand Technology of China, Hefei230026, China)Abstract:A new method for determining the objective weight of decision makers is proposed.It provides the ob-jective weight of decision makers in two parts as personal reliability weight and group reliability weight.T he informa-tion from every judgment matrix is derived to determine the personal reliability weight, and then the similarity of alljudgment matrices is given to determine the group reliability weight.In the end, the personal reliability weight and thegroup reliability weight are combined into the final objective weight of the decision makers.T his method is illustratedby an example.Key words:judgment matrix;group decision;reliability1 %V,B 5 %sYT1- , |t v ZE“8 %T。yN,E B F %ZEB1。 YV :E B5/n 1 ,N9 E B1 p _ ,YVBZE|Ein,K 。D1,2,V, E F% ,B E 1o。 kml“E ” ,7 L= “ ” %C Q, % |Mrf “ % 9rf H, rf M1。+ s “9 F , 5。 rf “, V U % % H1,9 % %V % 。D3,4 E 、 0, B T A(k)=1 a(k)12 a(k)1na(k)21 1 a(k)2na(k)n1 a(k)n2 1OA(k) Q ,a(k)ji =1/a(k)ij , Oi,j=1,2,n。A(k)a(k)ij =a(k)ih a(k)hj ,5A(k) B 。NL A(k) CRB1 q , eL,:A=A(k),aij =a(k)ij 。8 V E8B1,8BE B。yN,4 |E , B, E8 V B VZE。* , 4 |E ?/ , 8 VvD8。 1 iBnQ A,VA n-1 / Hq , ?/B B :n-1 iB ? n-2 。 2 iBnQ A, N =n(n-2) 1Hq F(n -1 iB ? n -2 ), VFB 。 1、2 V,Bn A,K V4 |BE n(n-2)。4 |BE ,/ZE E8 V 。1 - ,4 |N =n(n-2)/B F,i|t FB F“,:。2 “B ,/B ,sY:Al,l =1,2,n(n-2),i O VB _ Wl =(wl1 ,wl2 ,wln)T#BMZ Bl =(bl1,bl2,bln)T,l=1,2,N ; ,bliV U l ZiZ ), bli =jV Ul ZiZ)j。3 I N ,K ?VEin B =(b1 ,b2 ,bn)。 E _ BZE, y Qf 。l1 l Z, QSf l(i,j)=1 l Z,iZ |j H0 (1)T:i,j =1,2,n;l =1,2,NA7n,Nl=1 ni=1l(i,j)=N,ni=1 nj=1l(i,j)=n。l2 Qf u(i)=nj=1ju(i,j) (2)T:u(i,j)=1N Nl=1l(i,j) QS q。 l V,0 u(i,j)1,nj=1u(i,j)=1。iO, u(1)u(2),5w1 w2。yN, V A _ 。wi =wj) , V ; wi wj, wi wj。 f , V 。4 1 N Bl =(bl1 ,bl2 ,bln)TB=(b1 ,b2 ,bn)W1“,E8B。ZE /。l3 EEk Zi ( Mpki =Nl=1bli -biNEEk MPk =ni=1pkiMT:Mn Kv M。M = n2/2 nl2 (n2 -1)/2 nl3 EEk 8BSk =1 -Pk5 E8B,9 E V 。kE 8BSk,Q E1 i j)N_ WB,Q mE sB。 %M Rki 、RjiWB, VV Ucos (ki,ji), EEkEiWsEEjEiWsBcos (ki,ji)。(3)cos (ki,ji)v,5EEkEiWsEEjEiWsM,9 EEkEj WB;Q,B。7Sikj =cos (ki,ji),lSkj = 12(m -2)(mi=1Sikj+mi=1Sijk), Oik、j,SkjV UEEkEEjW (B。Sk = 1m -1mj=1Skj, Oj k,SkV UEEk EB (,V UkE (B。 v,5 ?Vv E in。yN, V 7kE 8M V :k =Sk/mi=1Sk ,k =1,2,m。4 E HEK :EEkK k,8M V k, 8M V k,5EK Z4 k =(kk)1/2。N, %E HKE 。5 L !4E A(1)=1 7 5 41/7 1 1 1/21/5 1 1 1/31/4 2 3 1A(2)=1 6 7 51/6 1 1 11/7 1 1 11/5 1 1 1A(3)=1 6 8 41/6 1 1 1/21/8 1 1 11/4 2 1 1A(4)=1 3 2 11/3 1 1/2 1/31/2 2 1 21 3 1/2 11 9 E8M V 4E VsY 316B ,sY16 _ # ,isYK ?VEin B =(b1 ,b2 ,bn)/。EE1B1 =(b1 ,b2 ,bn)=(1,4,3,2)EE2B2 =(b1 ,b2 ,bn)=(1,2,4,3)EE3654 “d0/ 2005 M B3 =(b1 ,b2 ,bn)=(1,3,4,2)EE4B4 =(b1 ,b2 ,bn)=(1,4,3,2) BsZE, VM =8;P1 =3/64;P2 =7/64;P3 =0;P4 =17/64E8M V 1 =0.266 4 2 =0.248 9 3 =0.279 5 4 =0.205 22 9 E 8M V 2s %M p T, VE W %M N_ ,sYR12 =(0.266 2,0.297 3,0.291 1,0.145 4)R21 =(0.215 4,0.192 9,0.197 1,0.394 6)R13 =(0.241 2,0.431 2,0.219 4,0.108 2)R31 =(0.204 6,0.114 4,0.225 0,0.456 0)R14 =(0.107 8,0.222 5,0.554 6,0.115 0)R41 =(0.382 2,0.185 2,0.074 3,0.358 2)R23 =(0.235 1,0.376 3,0.195 5,0.193 1)R32 =(0.247 3,0.154 5,0.297 3,0.300 9)R24 =(0.086 4,0.159 6,0.406 4,0.347 7)R42 =(0.499 5,0.270 3,0.106 2,0.124 1)R34 =(0.078 0,0.090 1,0.441 2,0.390 7)R43 =(0.456 0,0.386 2,0.078 8,0.089 0) T(8) V %M WB, V1。V1 %M WBcos (12,13) 0.958 18 cos (12,32) 0.914 942 cos(13,23) 0.982 674 cos (14,24) 0.888 752cos (12,14) 0.857 93 cos (12,42) 0.861 965 cos(13,43) 0.907 321 cos (14,34) 0.855 992cos (13,14) 0.751 531 cos (23,24) 0.770 073 cos(23,43) 0.900 279 cos (24,34) 0.990 215cos (21,31) 0.983 456 cos (21,23) 0.864 589 cos(31,32) 0.946 87 cos (41,42) 0.885 444cos (21,41) 0.926 995 cos (21,24) 0.895 281 cos(31,34) 0.902 108 cos (41,43) 0.829 169cos (31,31) 0.890 355 cos (32,42) 0.771 289 cos(32,34) 0.912 729 cos (42,43) 0.974 456E W (BS12 =0.925 9;S13 =0.866 2S14 =0.891 7;S23 =0.976 6S24 =0.899 5;S34 =0.795 8E (BS1 =0.894 6;S2 =0.934 0;S3 =0.880 4;S4 =0.862 3E 8M V 1 =0.250 5;2 =0.261 5;3 =0.246 5;4 =0.241 53 9 EK Z4 E HK Z4 1 =0.258 3 2 =0.255 1 3 =0.262 5 4 =0.222 66 B % E Z4 ZE。 n5YV 4 |E ,E8 V ; Q,YV1 FE M ,E 8 V ;K HKE Z4 。 S % %E E 5,|E 8 V 8 VsYF I n,4 4、ZLi pZE。 ,E % H,E B 5, ZEM1B)Z,t| 。 ID:1 Vargas L G.An overview of the analytic hierarchy process and itsapplicationJ.EuropeanJournal of Operational Research,1990,48(1):2-8. 2 .QsE M.?:?v,1988.3 o.KZ “S %ZE J.“d,1995,13(4):43-46.4 o,.BKZ “S %ZE J.“d,1998,16(4):57-61. 5 Ramanathan R ,Ganesh L S.Group preference aggregation methodsemployed in AHP:an evaluation and an intrinsic process