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05YB74705720601963—(,,410083);;;Multi-criteriaLarge-groupLinguisticDecision-makingApproachwithIncompleteCertainInformationWangJian-qiangSchoolofBusinessCentralSouthUniversityChangsha,410083ChinaAbstract:Forlarge-groupmulti-criteriadecision-makingproblemswithlinguisticassessmentinformation,anewmethodisproposed,inwhichthecriteria’sweightsareincompletecertain,andthedecision-makers’preferenceinformationmaytakestheformoflinguisticgrade,ormaybebetweentwostandardlinguisticgrade,ormaybenotgiven.Byusingtheevidentialreasoningalgorithmandtwo-tuple,thecriteriavaluesofalternativeforeachdecision-makerareintegratedThenonlinearprogrammingmodelisconstructedbasedontheincompletecertaininformationonthecriteriaweights,anddistancesbetweenalternativesandidealalternative.Andtheoptimalweightsoncriteriaaregainedbyusingparallelgeneticalgorithmstosolvethenonlinearprogrammingmodel.Theintegratingvaluesofalternativesforeachdecision-makerarecomputed.Byusinggroupcoherence,thefuzzyclusteringmodelisconstructed.Aftersolvingthefuzzyclusteringmodel,theweightsofdecision-makersareattained.Andtherankingofthealternativesisobtained.Finallyanexampleisalsogiventoshowthefeasibilityandavailabilityofthismethod.Keywords:large-groupmulti-criterialinguisticdecision-making,evidentialreasoning,two-tuple,groupcoherence;fuzzyclustering1[1~8][1],[2~3]OWALOWA[4~8]Herrera[7~8],},,,,{2210tHHHHHL=H(1)jijiHH(2)“Neg”tji2=+)(jiHNegH=(3)ji≥ijiHHHMax=),(jjiHHHMin=),(m},,,{21maaaAL=s},,,{21sDDDDML=q},,,{21qCCCCL=pDlCplwqmplijplcC×=)(plijcpDHlCia2),(iiHaiHiaiH)5.0,5.0[-∈ia[4][6]a+nH)1,0(∈anH1+nHnHa1+nHa-12.1AHPANPCNP3[7]1}0,0,:{1≥≥bbA}0,0,:{1≥≤bbA}0,0,:{1≥=bbA),,,(21=,1Anl×pDpΨ2.21pDpijcnHiajCnH1),,,(=njipT2pDpijca+nHiajCnH,1),,,(a-=njipT1+nHa=+)1,,,(njipT3pDpijcpDiajCiajCnH0),,,(=njipTtn2,,2,1,0L=pD),,,(njipT),,2,1(qjpjL=whqjtnnjipTampjijn,,2,1;2,,2,1,0),,,,()(,LL===wqjamamtnijnijh,,2,1,)(1)(20,,L=-=∑=nH[9])]()()()()()()[()(1,)(,1,)(,1,)(,)1()1(,ijhijJnijnijJhijnijJnijJijJnamamamamamamaKam+++++++=h()())()()()(1,,1)1(,ijhijJhijJijJhamamaKam+++=())()(1,1,iniJnamam=)2,,2,1,0(tnL=)()(1,)(,ihijJhamam=()()120201,,1))()(1()(-=≠=++∑∑-=txtxbbijbijJxijJamamaKianH[9]()())()(1)(1)(,,iqJniqJhihinamamaa--=bb()∑∑==-=qjtnpjihnjipTa120)),,,(1(wb)(inab)(ihab(=pw,,,21Lppww)pqw,),(pinawb),(pihawb2:ia),(0piawb,),(1piawb,),(2piawb),(,,2pitawbL),(0piawb+),(1piawb+),(2piawb+L+),(2pitawb),(pihawb+=1ftHHHH2210,,,,L)0,(0H)0,(1H)0,(2H,,L)0,(2tH)0,(*),()0,(*),(),(111010HaHaipipip--Δ+Δ=wbwbwqL+)0,(*),(212tpitHa-Δ+wbia1-Δ:tanaaaaipitpinpipipip2*),(*),(2*),(1*),(0*),(),(2210wbwbwbwbwbwq++++++=LL1),(piwq)],(),,([maxminppiiwqwqtaaaipitpipip2*),(2*),(1*),(),(221minwbwbwbwq+++=Ltaiipihpp2*),(),(),(minmaxwbwqwq+=]2,0[),(maxtip∈wq),(piwq1Δ),(piwq⎪⎩⎪⎨⎧-====ΔniiRoundnHHipipninp),()),((,),()),((wqawqawq(2)3:tH2+I+I0)(=+Inb,2,1,0=n12,-tL1)(2=+Itb1tI2)(=+qΔ+I)0,(2tHia+I))0,())),((((),(2tpiiHiad--Δ-ΔΔΔ=wq(3)=Δ-ΔΔ--)0,())),(((2tpHiwq))),((((|minpiwqΔΔ-2/|))0,())),(((||)0,(2max2tptHiH---Δ-ΔΔ+Δ-wqia+IΔ1-Δ3)),(2(),(1piiitadwq-Δ=(4)taiipihpp*),(),(),(min1wbwqwq+=ia⎪⎪⎩⎪⎪⎨⎧Ψ∈=-Δ=∑=ppqppsipjpiitsitad),,(1.)),(2(),min(2111(5)Δ[9]255)(..),(*),(*2),(min20tsatantadpihtnpinpiwbwbw--=∑=+(6)6(6)..)),(*),(*2(min201tsataBntdtnpihinmipp∑∑==--=wbw(7)7,,2,1,),,(,,2,1,1..))),(*),(*2((min2112011⎪⎪⎩⎪⎪⎨⎧=Ψ∈==--=∑∑∑∑====spsptsataBntdppqppsipjtnpihinmisppLLL),(pinawb),(pihawb8,,,,,,,,,{212121111111LLL--qq},1sq-wLs111{,,,}(1,2,,)iiiqis=LLs(1,2,,;1,2,,)plpslqw==LL1pDla[,]ppllbc2.35[10]2/|)11||11(|1,1,1kipkkpikipkkpipicscbsbZ∑∑≠=≠=--+---=piZpDiaFCM[11]2211112min(,)()(())(,).,1,2,,csmpkpjkjkpjfjjcjJUVuZeUUcssteeejm====-∈⎧⎪⎨=⎪⎩∑∑∑LLkjekjk[12]k12kCCCLi12{,,,}miiieeeLi111mlilikmpijpeel====∑∑∑piDC∈1ipklllnlll==∑lnlC[,]llbc1spllppbbl==∑1spllppccl==∑,lilibbcc==liaa=,lilibbcc≥,lilibbcc≥liaalliibcbc+≥+liaaf31215,,,DDDL15321,,aaa3,,,321CCC3H={}=,{0H},,,4321HHHH11211ww5.02.011≤≤w4.015.012≤≤w5.03.013≤≤w2.05.0232221≥≥≤≤w4.02.032≤≤w4341ww4241ww7.04.04342≤+≤ww5152ww5352ww45.02.052≤≤w4.02.053≤≤w636261==25.055.07372≥≥ww5.02.08182≤≤≤ww4.02.091≤≤w5.03.092≤≤w4.015.092≤≤w5.03.0101≤≤w4.025.0102≤≤w103102ww3.0113111≥ww25.0112=w25.0122121≥ww35.0123=w35.0132=w4.0131=w25.0133=w142141ww=3.0143=w5.035.0151≤≤w4.02.0152≤≤w5.025.0153≤≤w11D2D3D4D5D1a7.1H3H5.2H2H4H2a1H2H5.0H0H2H1C3a5.1H5.3H2H0H5.0H1a5.1H2H2H2a1H2H1H5.0H5.1H2C3a5.0H3H5.2H5.0H2H1a2H5.2H5.3H2.3H5.3H2a5.1H2H2H5.1H3C3a5.0H2H2H5.2H6D7D8D9D10D1a2H5.3H2H5.3H5.3H2a5.0H2H1H5.1H2H1C3a5.3H3H1.5H1.8H2H1a5.2H2H3H5.3H5.3H2a5.0H5.0H2H5.1H1H2C3a0H5.1H2H5.2H5.1H1a5.1H5.2H1.7H2H5.3H2a5.0H2H2H1H5.2H3C3a5.1H2H1H5.1H2H11D12D13D14D15D1a3H4H2.5H8.3H4H2a0.8H2H1.5H1H2H1C3a5.3H3H2.7H2H1a2H2.5H3H4H4H2a1H5.0H1.7H5.1H0.5H2C3a1H2H2.3H1H1a2H5.2H2.5H2H5.3H2a5.0H8.1H2H1H5.2H3C3a2H1H1H2.5Hmatlab231aaaff14[1].[J].2002152148~152[2].[M].[3].[J].2003182173~176[4]HerreraF,MartnezL.A2-tuplefuzzylinguisticrepresent