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29120142JOURNALOFSYSTEMSENGINEERINGVol.29No.1Feb.2014,,(,410083):,.,,,;,;,;,..:;;;:TP311.52:A:1000¡5781(2014)01¡0048¡08Multi-attribute&multi-stagelargegroupdecision-makingmethodforpreferenceconflictoptimizationXuXuanhua,WangMinsai,ChenXiaohong(SchoolofBusiness,CentralSouthUniversity,Changsha410083,China)Abstract:Aimingatthemulti-attribute&multi-stagelargegroupdecision-makingproblems,whichhavethecharactersthatthedecisionmakingpreferenceisconflictiveandthattheweightsinformationisunknown,adecision-makingmethodisproposedbasedonthepreferenceconflict.Theweightofeachattributeisdeter-minedaccordingtotheimpactoftheattributeonthedecisionresultstoobtaintheattributeweightscorrespond-ingtothedecision-makers,andtheweightedaverageoperatorsareappliedtoaggregatetheobtainedattributeweightstogettheattributeweights.Thedecision-makers’weightsareobtainedbyminimizingthesumofpreferenceconflictofanypairofthedecisionmakers’finaldecisionresults.Thevalidiyisderivedaccordingtotheconflictratioofthedecisionresultsofeachstage,thenthestageweightsareconfirmed.Thefinalrankingisderivingbycalculatingthepreferencesoftheoriginaldecisionmakersusingthethreeattributes:theattributeweights,thedecisionmakers’weightsandthestageweights.Theeffectivenessofthemethodisverifiedbyanumericalillustration.Keywords:preferenceconflict;multi-attribute&multi-stage;largegroup;decision-makingmethod.1,,,;,,,;,.,:2013¡01¡07;:2013¡06¡03.:(71171202);(71221061).1:49.,,,,.[1],,,;[2],;[3],,.,,,.[4],,;LeanYu[5],;You[6],.[7],.,,,.Wang[8],;Xu[9];Yue[10]TOPSIS;,,,[11,12];[13¡15];,,,.,.,,,.22.1N,C=fC1;C2;:::;CNg;S,(t1;t2;:::;tS);,M.,,U=fU1;U2;:::;UPg,,,.ABC,DEF,fABCDEFg(,).,ABCDEF,DEF,0,.A,,A,A0,A,,A,,,A,0.,DEF0(),,.,fABCDEFg(0,).,5029,,.iljvlij,vlij0,i=1;2;:::;M;j=1;2;:::;N;l=1;2;:::;P,Vlj=(vl1j;vl2j;:::;vlMj)j,Vl=0BBBB@vl11vl21:::vlM1vl12vl22:::vlM2............vl1Nvl2N:::vlMN1CCCCAl.,,.2.2,,,.,,,;,,,0,,,.,,.,,.,.,(,),(),,,.i(i=1;2;:::;M),l(l=1;2;:::;P)!li=(!li1;!li2;:::;!liN),NPj=1!lij=1,06!lij61,ilzli=NPj=1!lijvlij,izi=(z1i;z2i;:::;zPi),i,CV(zi)=PPl1=1PPl2=1(zl1i¡zl2i)2,zl1izl2izi.,,,,MaxCV(zi)=PXl1=1PXl2=1(zl1i¡zl2i)2:Matlab,l,i!li¤=(!li¤1;!li¤2;:::;!li¤N),!li¤ji,lj.lwl=(wl1;wl2;:::;wlM)(2.3).,l!l¤=0BBB@MPi=1wli!li¤1NPj=1MPi=1wli!li¤j;MPi=1wli!li¤2NPj=1MPi=1wli!li¤j;:::;MPi=1wli!li¤NNPj=1MPi=1wli!li¤j1CCCA:(1)1:51,,,.,,,,;,.2.3,,,.ilzli=NPj=1!l¤jvlij,vlijilj,izi=ÃNXj=1!1¤jv1ij;NXj=1!2¤jv2ij;:::;NXj=1!P¤jvPij!:(2),,.,,,;,,.,i(i=1;2;:::;M)wi=(w1i;w2i;:::;wPi),Zi=Ãw1iNXj=1!1¤jv1ij;w2iNXj=1!2¤jv2ij;:::;wPiNXj=1!P¤jvPij!:(3)i1i2d(Zi1;Zi2)=1PPXl=1¯¯¯¯¯wli1NXj=1!l¤jvli1j¡wli2NXj=1!l¤jvli2j¯¯¯¯¯;i16=i2;i1;i2=1;2;:::;M:(4),,,,MinD(Z)=MXi1=1MXi2=1d(Zi1;Zi2):(5)Matlab(2.2,),wi=(w1i;w2i;:::;wPi);wii(i=1;2;:::;M),((1)).,Z=MXi=1Zi=ÃMXi=1Ãw1iNXj=1!1¤jv1ij!;MXi=1Ãw2iNXj=1!2¤jv2ij!;:::;MXi=1ÃwPiNXj=1!P¤jvPij!!:(6),,,,;,,,,,.,:,;,;,5229.2.4,,,,.S(t1;t2;:::;tS),s=(st1;st2;:::;stS);SXk=1stk=1;stk0;k=1;2;:::;S:,,;,.,tkDtk(Z)=NXi1=1NXi2=1d(Zi1;Zi2)tk:(7)(7)d(Zi1;Zi2)tktki1i2((4)),stk=1Dtk(Z)SPk=11Dtk(Z):(8),Z=SPk=1stkZtk,Ztktk((6)).Z,,,.,.1(1),,.2(5)1.3(8).41,2,3,.3,,1:,;2:;3:;4:.,:.20,,(0,100),,,100(),1,.1).1,1:53,(1)(4),,23.1Table1ThedecisionpreferencevaluesofallmemberstoallschemesI10.58240.42100.09210.02400.49110.81470.90580.12700.91340.632420.27830.33980.28730.17090.39930.09750.27850.54690.95750.964930.69760.20370.66630.44310.43330.15760.97060.95720.48540.800340.17520.19320.61640.26900.55970.14190.42180.91570.79220.9595II10.94480.71450.67920.95940.77530.65570.03570.84910.93400.678720.60770.94800.05960.26870.98670.75770.74310.39220.65550.171230.77220.47540.68090.41690.38010.70600.03180.27690.04620.097140.21330.38290.02970.47230.33340.82350.69480.31710.95020.0344...XIX10.37960.31910.98610.71820.41320.03260.56120.88190.66920.190420.09860.73460.63730.07380.12050.36890.46070.98160.15640.855530.98160.49680.02240.05380.14090.64480.37630.19090.42830.482040.89350.46580.56090.49450.06780.12060.58950.22620.38460.5830XX10.89760.28860.26900.59420.47590.25180.29040.61710.26530.824420.36830.65560.93820.62040.28280.98270.73020.34390.58410.107830.20520.43910.02730.87620.61010.90630.87970.81780.26070.594440.20360.51990.05380.86220.44290.02250.42530.31270.16150.17882Table2Attributeweights123451234510.19750.13550.24700.17610.24400.22770.18260.22680.15030.212620.13550.25080.20660.16880.23800.18270.24900.23780.12050.209930.31160.09450.11580.23500.24300.21710.22530.18580.20900.162940.14430.19710.24180.26660.15000.16560.20240.17680.23030.22503Table3Decisionmakersweights12341234I0.02800.05090.03060.02900.05450.06300.04700.0664II0.04310.06860.03030.06220.03490.03460.05420.0544III0.02400.04190.02980.10880.07220.03360.04190.0529IV0.03410.02300.09830.05810.03500.06610.05360.0573V0.01230.02390.02570.05290.05990.05340.05890.0344VI0.02580.02990.07460.01780.03220.05200.03290.0361VII0.06880.02690.05850.03230.02660.07710.05630.0324VIII0.04500.01340.06830.00890.07210.11380.07900.0922IX0.08950.09220.04720.01860.05980.03430.03410.0267X0.03960.04680.04110.06180.03890.02750.06890.0573XI0.05220.04270.05340.05390.07450.03440.06860.0106XII0.0