一种主客方交互式群体评价方法及其应用张发明

张发明(南昌大学经济管理学院)　　:传统的群体评价方法均不考虑被评价对象的参与,针对此缺陷提出了一种新的群体评价方法———主客方交互式群体评价方法。首先对主客方交互式评价的过程进行描述;然后给出交互过程中基于优先排序概率的单轮评价结果呈现方式;其次,给出群体评价的稳定性、满意性指标,以此探讨交互终止的条件;最后,定义了2个主客方交互加权算子,以此对各轮交互结果进行集结,得出最终的群体评价结论。:;;;:C93　:A　:1672-884X(2011)11-1714-05AGroupEvaluationMethodBasedonSubject-ObjectInteractionandItsApplicationZHANGFaming(NanchangUniversity,Nanchang,China)Abstract:Themajorityofthetraditionalgroupevaluationmethodstakesnoaccountofthein-volvementofevaluatedobjects,thereforeanewgroupevaluationmethod,thesubject-objectinterac-tiongroupevaluationmethodisproposedtofillinthisgap.Firstly,theprocessofthesubject-objectinteractiongroupevaluationmethodisdescribed;secondly,single-roundevaluationresultsbasedonthepriorityandprobabilityarepresentedaccordingly;thirdly,theindicatorsofStabilityandSatisfac-tionforevaluationareputforward,andconditionsunderwhichtheinteractionbetweensubjectandobjectcometoanendarediscussed;finally,twocross-weightedoperatorsaredefinedinordertoag-gregatetheresultsofinteractionsbetweensubjectandobjectineachroundandreachthefinalevalua-tionresults.Keywords:groupevaluation;interaction;subjectandobject;aggregation:2010-05-05:(71001048);“”(10YB222)　　,、,(),。,[1～11]。,2,,,,,“”[12],“”[9～11]。,“”,,。,,,,———“”。,,,4:①;②;③;④,。,4。1　主客方交互式评价的过程描述,S=1714　　811201111　　　　　　　　　　　　　　ChineseJournalofManagement　　　　　　　　　　Vol.8No.11Nov.2011　　{s1,s2,…,sm},O={o1,o2,…,on}。,l(l≥3),ptijt(t=1,2,…,l)sj(j=1,2,…,m)oi(i=1,2,…,n)(,,p0ij),tp(t)(,n≥3,m≥3),M={1,2,…,m},N={1,2,…,n},L={1,2,…,l},p(t)=[p(t)ij]n×m=p(t)11p(t)12…p(t)1mp(t)21p(t)22…p(t)2mp(t)n1p(t)n2…p(t)nm　　,。,:1　;2　,,“”;3　,“”;4　“”。:,t(t∈L)p(t),“”;“”p(t),,()w(t);,,c(t);,w(t)c(t),p(t),p(t+1);,(“-”)。,(),c。“”,w(t),p(t),()。1。2　单轮评价结果的呈现方式,,,pwt(t∈L)1　　,p(t)w(t)。t(t∈L),p(t),w(t),w(t),[13],iyi=∑mj=1wijpij,wijij。,(4),“”,,∑mj=1wijpij。,,“”,,,。,:1　　“”,oi,sj(wij),。,:yi=max∑mj=1wijpij,s.t.∑mj=1wij=1,wj(1-σj)wijwj(1+σj),wij0,j∈M,(1),wj(j∈M)p;σj(“”,,0≤σj≤0.5,j∈M),(σj:σj=0.1,1715———;σj=0.2,;σj=0.3,;σj=0.4,;σj=0.5,)。(1),wij。,wjp,[14]。sj,Hj=-1lnn∑ni=1pj∑ni=1pijlnpj∑ni=1pij。(2)　　,sj,,wjwj=1-Hjn-∑mj=1Hj。(3)　　oiwi=(wi1,wi2,…,wnm)T。1　no1,o2,…,onw1,w2,…,wn,,Θ,Θ=wi∑mi=1wij=1,wj(1-σ0i)wijwj(1+σj),wij0,i∈N。　　,n,Θ。2　w*=(w*1,w*2,…,w*m)T,w*∈Θ,2oi′、oi″,(i′≠i″;i′,i″∈N),φ(oi′oi″)oi′oi″φ(oi′oi″)=P∑mj=1w*jpi′j≥∑mj=1w*jpi″j(4),P。φ(oi′oi″):(1)归一性　φ(oi′oi″)+φ(oi′oi″)=1;(2)等价性　φ(oi′～oi″)φ(oi′oi″)=φ(oi′oi″)=0.5;(3)自反性　φ(oi′oi″)=0.5。Θ,,,:1　2oi′、oi″(n,n2-n)。2　c(,c=0)。3　Θ,mw*。4　r(,r=0)“φ(oi′oi″)”,∑mj=1w*jpi′j≥∑mj=1w*jpi″j,r=r+1。5　c=c+1,c=n(n,,n),6,2。6　φ(oi′oi″),φ(oi′oi″)=r/n,。,,1。,nφ,φij=φ(oi,oj),φ=[φij]n×n=φ11φ12…φ1nφ21φ22…φ2nφn1φn2…φnn。　　3　ci(i=1,2,…,n)oi(φi),ci=1n-1∑nj=1φij-0.5,　(i,j∈N),(5),0≤ci≤1。,ci=1,,;,ci=0。t(t∈L)c(t)=(ct1,ct2,…,ctn)T,,c(t)t。3　交互终止条件,,p(t),()。3,,,“”,。,2。4　εttp(t)t-1p(t-1),εt=1-1mn∑ni=1∑mk=1(ptik-pt-1ik)2。(6)　　(6),1716811201111。,ε=(ε1,ε2,…,εt)T。Δct=ct-ct-1=(Δct1,Δct2,…,Δctn)T。,Δctt(t∈L)。δt-=∑Δct1(i,Δcti0),δt+=∑Δct1(i,Δcti0)。5　vttvt=sgn∑ni=1Δcti|δt+||δt+|+|δt-|,(7),sgn(),()。(7):vt0,ctct-1();,。,v=(v1,v2,…,vl)T。“-”:t(t∈L),ωtα　　vt0,(8),,α(0α1),ωtα,vt0,。4　集结最终的评价结果,。,cti(t∈L)ci,;,,。。6　〈vt,cti〉(t∈L;i∈N)SO-DOWA,vt,cti,oi(i∈N)t。IOWA[15],SO-DOWA,F(〈v1,c1i〉,〈v2,c2i〉,…,〈vl,cli〉)=∑lt=1wtbli,(9),w=(w1,w2,…,wl)TF,wt∈[0,1],∑lt=1wt=1;blivt(t∈L)vtSO-DOWA2,FlSO-DOWA。7　〈vt,cti〉(t∈L;i∈N)SO-DOGWA,vt,cti,oi(i∈N)t。IOWGA[16],SO-DOG-WA,F(〈v1,c1i〉,〈v2,c2i〉,…,〈vl,cli〉)=∏lt=1(bti)wi,(10),w=(w1,w2,…,wl)TF,wt∈[0,1],∑lt=1wt=1;btivt(t∈L)vtSO-DOGWA2,FlSO-DOGWA。SO-DOWASO-DOGWA“”“”,,,,2[17]。,F()w=(w1,w2,…,wl)T。,wtv1,v2,…,vlt。vt(t∈L),,v1,v2,…,vl,,wt,。2　　。2,:max∑lt=1l-tl-1wt,s.t.wl…w2w1,w1≤w2+w3+…+wl,w2≤w3+…+wl,　　wl-1≤wl,wt0,t∈L。(11)　　(11),w=(w1,w2,…,wl)T。5　应用实例,。6(m=6)5(n=5),,1717———“”,,“”。65,(,,),7(l=7),pt(t=0,1,…,7),tt。,σj=0.2(j=1,2,…,6),α=0.95(,)。p0=453486483726524793638353742658,p1=458376694684379547563385357622,p2=548265863673367457784365255831,p3=763624488624237528372645452836,p4=352486483726524783638353742658,p5=453486483726524793638353742658,p6=452486483726524793638353742658,p7=352486483726524793638353742657。　　:(1)确定评价主方权重　p,(2)、(3):ω1=(0.172,0.170,0.155,0.169,0.157,0.177),ω2=(0.157,0.165,0.173,0.164,0.179,0.162),ω3=(0.169,0.167,0.168,0.168,0.159,0.169),ω4=(0.166,0.165,0.169,0.164,0.169,0.167),ω5=(0.166,0.167,0.167,0,169,0.168,0.164),ω6=(0.166,0.167,0.167,0.169,0.168,0.164)。　　(2)计算各单轮交互结果　Ck(k=1,2,…,7),(5),,C1=(0.452,0.396,0.413,0.368,0.575)T,C2=(0.359,0.461,0.585,0.431,0.558)T,C3=(0.504,0.271,0.561,0.727,0.745)T,C4=(0.445,0.278,0.595,0.749,0.773)T,C5=(0.502,0.210,0.555,0.743,0.748)T,C6=(0.502,0.210.0.555,0.743,0.746)T,C7=(0.502,0.210.0.555,0.743,0.746)T。　　(3)计算各轮的稳定、满意指标　(6)、(7)ε=(0.873,0.847,0.883,0.954,0.943,0.965,0.972)T;v=(0.873,0.847,0.833,0.954,0.943,0.965,0.972)T。(4)集结最终的评价结果　(10),ω=(0.152,0.155,0.145,0.139,0.147,0.137,0.125)T,SO-DOWA,:C=(0.465,0.301,0.546,0.637,0.696)T,:o5o4o3o1o2。6　结语,,,,:①,———“”;②,,,“”,、;③,,,;④,“-”,;⑤,2(DOWADOWGA),。,,3:①;②,;③,。[1]ZELENYM.CriteriaDecisionMaking[M].Berlin:Springer-Verlag,1975.[2]HOLLOWAYCA.DecisionMakingunderUncer-tainly:ModelsandChoice[M].EnglewoodsCliff:PrenticeH