一种群决策中专家客观权重的确定方法梁

:2004-03-06;:2004-07-13。:(70371023);(20030358052):(1962-),,,,,。梁　,熊　立,王国华(中国科学技术大学商学院,安徽合肥230026)　　　: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。:判断矩阵;群决策;可信度:O223　　　　:ANewmethodfordeterminingtheobjectiveweightofdecisionmakersingroupdecisionLIANGLiang,XIONGLi,WANGGuo-hua(BusinessSchool,UniversityofScienceandTechnologyofChina,Hefei230026,China)　　Abstract:Anewmethodfordeterminingtheobjectiveweightofdecisionmakersisproposed.Itprovidestheob-jectiveweightofdecisionmakersintwopartsaspersonalreliabilityweightandgroupreliabilityweight.Theinforma-tionfromeveryjudgmentmatrixisderivedtodeterminethepersonalreliabilityweight,andthenthesimilarityofalljudgmentmatricesisgiventodeterminethegroupreliabilityweight.Intheend,thepersonalreliabilityweightandthegroupreliabilityweightarecombinedintothefinalobjectiveweightofthedecisionmakers.Thismethodisillustratedbyanexample.Keywords:judgmentmatrix;groupdecision;reliability1　　　　,,。,。:n,,,。[1,2],,,。“”,“”,,。,。,,。[3,4]、、、。[5,6],。[7],AHP、Delphi。,,,,,,,,,。,,,,[7]。,,。,,20054Apr.2005　27　4SystemsEngineeringandElectronicsVol.27　No.4:1001-506X(2005)04-0652-04。,,;,,;。2　n,1,2,…,n;m,E1,E2,…,Em;EkA(k)=a(k)ijn×n,k=1,2,…,m,a(k)ij0,A(k)=1a(k)12…a(k)1na(k)211…a(k)2na(k)n1a(k)n2…1A(k),a(k)ji=1/a(k)ij,i,j=1,2,…,n。A(k)a(k)ij=a(k)ih·a(k)hj,A(k)。A(k)CR,,A=A(k),aij=a(k)ij。,。,,,。,?,[8]。1　nA,An-1,:n-1n-2。2　nA,N=n(n-2)1(n-1n-2),。1、2,nA,n(n-2)。,。1　,N=n(n-2),,Ψ。2　Ψ,,Al,l=1,2,…,n(n-2),Wl=(wl1,wl2,…,wln)TBl=(bl1,bl2,…,bln)T,l=1,2,…,N;,blili,bli=jlij。3　N,B＊=(b＊1,b＊2,…,b＊n)。B＊,。1　l,δl(i,j)=1　l,ij0　(1):i,j=1,2,…,n;l=1,2,…,N,∑Nl=1∑ni=1δl(i,j)=N,∑ni=1∑nj=1δl(i,j)=n。2　u(i)=∑nj=1j·u(i,j)(2):u(i,j)=1N∑Nl=1δl(i,j)———。,0≤u(i,j)≤1,∑nj=1u(i,j)=1。,u(1)≤u(2),w1≥w2。,A。wi=wj,wi≤wj,wi≥wj。,。4　NBl=(bl1,bl2,…,bln)TB＊=(b＊1,b＊2,…,b＊n),。。3　Ekipki=∑Nl=1bli-b＊iNEkPk=∑ni=1pkiM:M———n。M=n2/2n2(n2-1)/2n3　　EkSk=1-Pk　　5　,。kSk,,,,Ekαk=Sk/∑mk=1Sk　k=1,2,…,m　27　4·653　　·　3　m,EkA(k)=a(k)ijn×n,k=1,2,…,m。,CR。A(1)=a(1)ijn×n,A(2)=a(2)ijn×nE1E2。R=diag[r1,r2,…,rn],S=diag[s1,s2,…,sn],∑ni=1ri=1,ri=s-1i,i=1,2,…,n。R、SA(1)(RA(1)S)A(2)。RA(1),SA(2)。∑ni=1ri=1,A(1)1,riA(1)i。ri=s-1i,A。,A=[aij]n×n,RAS。RAS=riaijsjn×n=riaij1rjn×n(3)riaijsjn×n=riaij1rjn×n=rjajisi-1n×n=rjaji1ri-1n×n(4)　riaijsj·rjajksk=ri1rjaijajkrjsk=riaiksk(5)　riaijsj=riaikskrjajksk(6)(,RA(1)SA(2))R、SJ=min∑ni=1∑nj=1ln(ria(1)ijsj)-lna(2)ij2(7)　　(7),R、SA(1)A(2)[9]。,A(1)A(2),A(1)A(2)。,R=diag[r1,r2,…,rn],,cosθi,j=Ri,RjRiRj=∑nk=1rikrjk∑nk=1r2ik∑nk=1r2jk(8):Ri,Rj=RiRjcosθij———。cosθij,。,。(1)RijiA(i)jA(j)。(2)Rij(i,j=1,2,…,m;i≠j),m。Rki、Rji,cosθ(ki,ji),EkEiEjEicosθ(ki,ji)。(3)cosθ(ki,ji),EkEiEjEi,EkEj;,。Sikj=cosθ(ki,ji),Skj=12(m-2)(∑mi=1Sikj+∑mi=1Sijk),i≠k、j,SkjEkEj。Sk=1m-1∑mj=1Skj,j≠k,SkEk,k。,。,k:βk=Sk/∑mi=1Sk,k=1,2,…,m。4　Ekλk,αk,βk,λk=(αkβk)1/2。,。5　　4A(1)=17541/7111/21/5111/31/4231　A(2)=16751/61111/71111/5111A(3)=16841/6111/21/81111/4211　A(4)=13211/311/21/31/2212131/21　　1　416,16,B＊=(b＊1,b＊2,…,b＊n)。E1B＊1=(b＊1,b＊2,…,b＊n)=(1,4,3,2)E2B＊2=(b＊1,b＊2,…,b＊n)=(1,2,4,3)E3　·654　　·2005　B＊3=(b＊1,b＊2,…,b＊n)=(1,3,4,2)E4B＊4=(b＊1,b＊2,…,b＊n)=(1,4,3,2),M=8;P1=3/64;P2=7/64;P3=0;P4=17/64α1=0.2664　α2=0.2489　α3=0.2795　α4=0.20522　2,,R12=(0.2662,0.2973,0.2911,0.1454)R21=(0.2154,0.1929,0.1971,0.3946)R13=(0.2412,0.4312,0.2194,0.1082)R31=(0.2046,0.1144,0.2250,0.4560)R14=(0.1078,0.2225,0.5546,0.1150)R41=(0.3822,0.1852,0.0743,0.3582)R23=(0.2351,0.3763,0.1955,0.1931)R32=(0.2473,0.1545,0.2973,0.3009)R24=(0.0864,0.1596,0.4064,0.3477)R42=(0.4995,0.2703,0.1062,0.1241)R34=(0.0780,0.0901,0.4412,0.3907)R43=(0.4560,0.3862,0.0788,0.0890)　　(8),1。1　cosθ(12,13)0.95818cosθ(12,32)0.914942cosθ(13,23)0.982674cosθ(14,24)0.888752cosθ(12,14)0.85793cosθ(12,42)0.861965cosθ(13,43)0.907321cosθ(14,34)0.855992cosθ(13,14)0.751531cosθ(23,24)0.770073cosθ(23,43)0.900279cosθ(24,34)0.990215cosθ(21,31)0.983456cosθ(21,23)0.864589cosθ(31,32)0.94687cosθ(41,42)0.885444cosθ(21,41)0.926995cosθ(21,24)0.895281cosθ(31,34)0.902108cosθ(41,43)0.829169cosθ(31,31)0.890355cosθ(32,42)0.771289cosθ(32,34)0.912729cosθ(42,43)0.974456　　S12=0.9259;S13=0.8662S14=0.8917;S23=0.9766S24=0.8995;S34=0.7958　　S1=0.8946;S2=0.9340;S3=0.8804;S4=0.8623　　β1=0.2505;β2=0.2615;β3=0.2465;β4=0.2415　　3　λ1=0.2583　λ2=0.2551　λ3=0.2625　λ4=0.22266　　。,;,,;。,,、。,,,,。:[1]VargasLG.Anoverviewoftheanalytichierarchyprocessanditsapplication[J].EuropeanJournalofOperationalResearch,1990,48(1):2-8.[2].[M].:,1988.[3].[J].,1995,13(4):43-46.[4],.[J].,1998,16(4):57-61.[5]RamanathanR,GaneshLS.GrouppreferenceaggregationmethodsemployedinAHP:anevaluationandanintrinsicprocessforderivingmenbers'weightages[J].EuropeanJournalofOperationalRe-search,1994,(79):249-265.[6],.[J].,1996(3):52-56.[7],.[J].,2001,19(4):83-89.[8],.[J].,2003,(3):270-273.[9],.[J].,2002,5(2):91-94.　27　4·655　　·