基于方案达成度和综合度的交互式多属性决策法_徐泽水

第17卷第4期Vol.17 No.4 e %Control and Decision2002年7月July 2002cI|: 1001-0920(2002)04-0435-04Zr8 T %E徐泽水( 2v65 , 2210096)K1: 定义了方案达成度和方案综合度,对于属性权重信息不能完全确知且对方案有偏好的多属性决策问题,提出一种基于方案达成度和综合度的交互式决策方法。该方法既能充分利用已知的客观信息,又能最大限度地发挥决策者的主观能动性,并通过对方案达成度和综合度的给定和修正来实现人机交互决策。应用实例说明了该方法的有效性和实用性。1oM: 多属性决策;方案达成度;方案综合度ms |: C 934DS M : AInteractive method based on alternative achievement scaleand alternative comprehensive scalefor multi-attribute decision making problemsXU Ze-shui(Collegeof Economics andManagement, Southeast University, Nanjing 210096, China)Abstract: The definitions of alternative achievement scale and alternative comprehensive scale arepresented, and an interactivemethod based on them for multi-attributedecision making problems isproposed. The method makesuse of thesubjectiveinformation providedbyadecision makerandtheobjectiveinformation to form single-objectiveprogrammingmodels. Theprocess of interactivedecisionmaking can be realized by giving and revising thealternativeachievement scaleand thealternativecomprehensive scale. An illustrative example is given to verify the developed approach and todemonstrateitsfeasibilityand practicality.Key words: multi-attributedecision making; alternative achievement scale; alternative comprehensivescale1引 言 % C % S1Fs, !9a6a5 + Y 5 zj(w2),5L(zj(w1) L(zj(w2),L(zj(w) 1z j(w)9f bl5 c(w) = nj= 1(zj(w) - zminj ),5c(w)Z8bZrQ Zr f ,7Z85Q Z9 vlb8 I n Z y ,L V %V LC %Z98 r %1 p,i PZ V ?r1- z ,V7 Z b 8X /: S H, Vy “S (SOP2): max c(w)s.t. wHp ,KwaZ8 z j(w)Z8c(w),i pZrL(zj(w)(jN)b % N4 SZrK0j(jN)#Z8Kc0b 1 “S5(SOP2)K436 控 制 与 决 策 第17卷 “S5(MOP)rb bZ8Sz,5Z98 ? %1 pb V ? P tZr ,V7 1- z ; 6BZ , TZr,5 V ?r LCZW ;i OZW b 8ty ,y / “S % (SOP3): max J = nj= 1Kj,jNs.t. c(w)c0L(zj(w)KjK0jwHp (SOP3), ,5 % !SZr#Z8K; K,5/ : 2 “S5(SOP3)K “S5(MOP)rb 1 2 “S % (SOP2)(SOP3)K “S % (MOP)rb % (SOP3) T i,5 V9 Z8 ,i vlZ ,V7 % iZ;5, % V a4 tZKr, H 6BtZKr, A1 VZ8K9 a, p (SOP3), % T ibG , BZ8Zr T %ZE:1) %5/ % A = (aij)mn,i aZE A?S % R =(rij) mnb2) (SOP1) pZxj8 Klzminj ,i %4Z z-j(jN)b3) p “S5(SOP2),Kw0,Z8 zj(w0)#Z8c(w0),i pZrL(zj(w 0)(jN)b% N4 SZrK0j(jN)#Z8Kc0,k = 1b4) p “S % (SOP3),Kwk,Z8c(wk),Zr_ Kk#MZ8 _ z(wk)b5) T % TX1 p,541 p,i6);5, % 1 a4 tZKr, H 6BtZKr, A1 VZ8K9 abk = k + 1,4)b6)Z8 vlZ, % iZb7) b4算 例 7? , E 5gZxj(j = 1,2,l,5),Z V1bV1Z x1 x2 x3 x4 x5g-u1 5.20 10.08 5.25 9.72 6.60Cu2 5.20 6.70 4.20 5.25 3.75B u3 4.73 5.71 3.82 5.54 3.30B u4 0.473 1.599 0.473 1.313 0.803 “, Cu2B u3rm ,g-u1B u4 , ui wi(i = 1,2,3,4) ? bXs :H = w = (w1,w2,w3,w 4)T 0. 3w10.45, w20.15,0.1w30.35,w40.03;w1+ w2 + w3 + w4 = 1,wj0,j = 1,2,3,4b kZ4b ZEZ , 8 /:1)V1 y % A = (aij)45,i / T|A?Sbrij =aijmaxj aij,iT1,minj aijaij,iT2,jN,T1T2sYV Urm/S“b ?S R = (rij)45 =1 0.516 0.990 0.535 0.7880.776 1 0.627 0.784 0.5600.828 1 0.669 0.970 0.5781 0.296 1 0.360 0.5892) (SOP1) pZ8 Kl:zmin1 = 0.906,zmin2 = 0.432,zmin3 = 0.824,zmin4 =0.474,zmin5 = 0.64; %4Z :z-1第4期 徐泽水:基于方案达成度和综合度的交互式多属性决策法 437= 0.97,z-2= 0.65,z-3= 0.90,z-4= 0.55, z-5= 0.75b3) ( SOP2) , VKw0=(0.45,0.15,0.35,0.05)T,Z8 z1(w0) = 0.906,z2(w0) = 0.747,z3(w 0) = 0.824,z4(w0) = 0.716, z5(w0) = 0.670,#Z8c(w0) = 0.586,i pZrL(z1(w0)= 0, L(z2(w0) = 1.445, L(z3(w0) = 0,L(z4(w0) = 3.184,L(z5(w0) = 0.266b % N4 SZr:K01 = 0.50,K02 = 0.90,K03= 0.50,K04 = 2.00,K05 = 0.30,#Z8Kc0 = 0.50b4) “S % (SOP3), VKw1 = (0.45,0,0.35,0.20)T,Z8 :z1(w1) = 0.940,z2(w1) = 0.641,z3(w 1) = 0.880,z4(w1) = 0.652, z5(w1) = 0.675,#Z8c(w1) = 0.51,i pZr: L(z1(w1)= 0.530,L(z2(w1) = 0.959, L(z3(w1) = 0.737,L(z4(w1) = 2.342,L(z5(w1) = 0.312b %N i,yNzj(w1)(j = 1,2,l,5)vlZ :x1 : x3 : x5 : x4 : x2,#KZx1b5结 语 ? OZ z %5,4BZr8 T %ZEbZE; ? s X Z4, ?KvK I n %1 p,? %4 ?, P % %VbYVZr8 LC %, P %Z98 r %1 p,i PZ V ?r1- z , O4r,9 LCb ID(References):1 Hwang C L, Yoon K S. Multiple Attribute DecisionMaking: Methods and Applications M . Berlin:Springer,1981.2S. %sM.: S,1987.3 2 , S % ZEM. 2: 2v,1996.4 . KvZES % J.“d0/ ,1998,20(7):24-26.(Wang Yingming. Using themethodof maximizing de-viations tomakedecisionformulti-indicesJ. Syst Eng&Electr,1998,20(7):24-26.)5 ,S.KZ “S %ZEKZ “S %J. e %,1993,8(1):25-29.(Wang Yingming, FuGuowei. Usingmultiobjectivede-cision making method to make decision for multiat-tributesJ. Control &Decision,1993,8(1):25-29.)6 . / “SZEJ.“d,1996,11(2):1-6.( Wang Wenping. Study on multi-objective optimalmethod under incomplete informationJ. J of SystEng,1996,11(2):1-6.)7 Xu Zeshui. Research on method for priorities of fuzzysyntheticevaluationsA. Syst Eng, Syst Sci & Com-plexity Resear