一种基于AHP和模糊理论的多方案综合评价方法

第31卷第4期2003年8月JOURNALOFZHEJIANGUNIVERSITYOFTECHNOLOGYVol.31No.4Aug.2003:1006-4303(2003)04-0355-05:2002-12-06;:2003-04-20:(60074035);(600042):(1973-),,,,AHP1,1,2(1.,310032;2.,315012):AHP将定性分析和定量分析有效结合,是解决多规则决策问题的一个强有力的工具。但在多方案评价问题中,由于判断矩阵的一致性检验难以通过,AHP不适于求取各方案的权重值。因此,提出了一种基于AHP和模糊理论的多方案综合评价方法。该方法采用AHP求取各层次指标的权重,采用模糊方法确定各方案的属性值,最后归并获得评价结果。并结合具体实例,在Matlab环境下对该方法在供应商的选择和评价展开了应用研究。事实表明,该方法不仅可以公平合理地获得评价结果,而且在实际应用中切实可行。:层次分析法;模糊理论;对数最小二乘法;模糊关系矩阵:N94:AAmulti-plansyntheticevaluationmethodbaseduponAHPandfuzzytheoryCAOJian1,ZHOUGen-gui1,ZHANGDing-yue2(1.CollegeofBusiness&Administration,ZhejiangUniversityofTechnology,Hangzhou310032,China;2.ZhejiangvocationalBusinissInstitute,Ningbo315012,China)Abstract:AHPcombinesqualitativeanalysiswithquantitativeanalysisefficientlyandisthereforeapowerfulmethodtothesolutionofmulti-criteriadecisionproblems.Butintheevaluationofmulti-planproblems,AHPisnotwellsuitedtoacquiretheweightofeachplangenerallyduetotheinconsistencyofthejudgmentmatrix.Thus,Amulti-plansyntheticevaluationmethodbaseduponAHPandfuzzytheoryisproposed.Inthismethod,theweightofdecisioncriteriaineverylevelofthehierarchyiscalculatedbyAHP,andtheattribute-valueofeveryplanisdecidedbyfuzzytheorywiththeevaluationresultacquiredbymergingfinally.ConcreteexamplesshowhowtoapplythismethodtotheselectionandevaluationofsuppliersintheMatlabenvironment.Itismanifestedthatthismethodisnotonlysuitedtogettheresultimpartiallyandreasonably,butalsosuitedtobeappliedwidelyinpractice.Keywords:AHP;fuzzytheory;logarithmicleastsquares;fuzzyrelationmatrix0AHP(AnalyticHierarchyProcess)ThomasLSatty[1],,,[25]AHP(7),,(n7,0.1,30%[6]),,AHP,AHP,1AHPAHP[1]:,7,AHP,(),AHP(7),AHP,,AHP,:(1)U={u1,u2,,un}V={v1,v2,,vm},ui(i=1,2,,n)n7,,,,6m,,m357,,(2)w=(w1,w2,,wn)TAHP,,(1),Z,=(1,2,,n)T,,w=(w1,w2,,wn)T,,Z=ni=1nj=1lnaij-lnij2(1),,,aij(),(1)Z=ni=1nj=1bk=1(lnaijk-lni+lnj)2(2),b,Z,(2)p(p=1,2,,n),0lnaipk=ln(1apjk),35631nlnp-nj=1lnj=1bnj=1bk=1lnapjk(3)(3),p=(bk=1nj=1j)1bn(bk=1nj=1apjk)1bn=t(bk=1nj=1apjk)1bn(4),t=(bk=1nj=1j)1bn,pw=(w1,w2,,wn)T,np=1wp=1,wp=(bk=1nj=1apjk)1bnni=1(bk=1nj=1aijk)1bn(5)(3),Rui(i=1,2,,n),(Rui),(6)R[7]R=Ru1Ru2Run=r11r12r1mr21r22r2mrn1rn2rnmnm(6),rijuivj,,103(ABC)U3,:u1,u2,u3V3,3,:v1,v2,v3A,4,5,1,RAu1=(0.4,0.5,0.1)(7)(4)S,S=wR=(w1,w2,,wn)r11r12r1mr21r22r2mrn1rn2rnm=(s1,s2,,sm)(8)(8),S,V;M(,),j=1,2,,m,sj=(w1r1j)(w2r2j)(wnrnj)=min(1,ni=1wirij)(9),,T=mj=1skjjmj=1skj(10),T,Vk3574,:AHP(k=2),sj(j=1,2,,m),T,V,图1　造纸企业木材供应商二级递阶评价结构图2,,,1:,10(,AJ)Matlab,:(1)(3)(4)(3),;10,(2)AHPWp,(11)(5),1(1,1,1)(1,1,3/2)(2,3/2,2)(3/2,1,2)(1,1,2/3)(1,1,1)(3/2,3/2,1)(3/2,3/2,1)(1/2,2/3,1/2)(2/3,2/3,1)(1,1,1)(3/2,1,4/3)(2/3,1,1/2)(2/3,2/3,1)(2/3,1,3/4)(1,1,1)(11)1WpW1W2W3W40.32250.27120.20900.1973(3),RV={v1,v2,v5},vi(i=1,2,,5),2,,A(12)2ViV1V2V3V4V5RA=0.30.40.30000.20.50.300.20.70.1000.10.30.40.10.1(12)(4)SX(X),35831(8),SX,3,,,,I,F(10),TX,4,I,G,D3SXSA(0.1583,0.3887,0.3322,0.1011,0.0197)SF(0.0542,0.3255,0.4040,0.1840,0.0323)SB(0.1459,0.2605,0.4604,0.1332,0)SG(0.2888,0.5000,0.1914,0.0197,0)SC(0.1650,0.3118,0.3637,0.1559,0)SH(0.1040,0.3446,0.4504,0.1001,0)SD(0.2091,0.4384,0.1960,0.1294,0.0271)SI(0.2904,0.6084,0.1012,0,0)SE(0.1701,0.3628,0.3350,0.1123,0.0197)SJ(0.1112,0.5572,0.2848,0.0469,0)4TXTATBTCTDTETFTGTHTITJ2.35982.70932.55102.09752.38382.75281.87582.62011.84062.18013,AHP,AHPAHP,,,,,,,;,,,,,,:[1].[M].:,1992.[2]AmacostRL.AnAHPframeworkforprioritizingcustomerrequirementsinQFD:anindustrializedhousingapplication[J].IIETransaction,1994,26(4):72-79.[3],,.AHP[J].,2001,13(1):16-18.[4]ChinKS,PunKF.AnAHPbasedstudyofcriticalfactorsforTQMimplementationinShanghaimanufacturingindustries[J].Technovation,2002,22(4):707-715.[5],.[J].,1999,19(2):82-87.[6].[M].:,1990.[7],.[M].:,2000.(:翁爱湘)3594,:AHP