三角直觉模糊决策的变权方法

243Vol．24No．320156OPEＲATIONSＲESEAＲCHANDMANAGEMENTSCIENCEJun．20152013-10-097123100371171055708711172012J0128022015J01287JA14295201311311023。1986-1965-。1211．3650042．350108。。C934A1007-3221201503-0120-07Variable-weightBasedMethodforIntuitionisticTriangularFuzzyDecisionMakingYUGao-feng1LIDeng-feng2QIUJin-ming1．SchoolofInformationSanmingUniversitySanming365004China2．SchoolofManagementFuzhouUniversityFuzhou350108ChinaAbstractFormulti-attributedecisionmakingproblemswheretheattributevaluesareintuitionistictriangularfuzzynumbersanewdecisionmakingmethodisdevelopedonthebasisofvariable-weightvector．Firstlytheconceptoftriangularintuitionisticfuzzynumbersisintroducedandanewrankingmethodoftriangularintuition-isticfuzzynumbersispresented．Secondlythetriangularintuitionisticfuzzyvariable-weightweightedaveragingoperatorandtriangularintuitionisticfuzzyvariable-weightweightedgeometricaveragingoperatorareproposed．Thenamethodformultipleattributedecisionmakingbasedontriangularintuitionisticfuzzyvariable-weightaggregationoperatorsisdeveloped．Finallyanillustrativeexampleshowstheeffectivenessoftheproposedapproach．Keywordsvariable-weightvectortriangularintuitionisticfuzzynumberdecisionmakingaggregationoperators0Atanassov121986、。3～5。6。7。8～10。1112、、。1314、、、。1516。17。18Vague。19LINMAP。20。21、。22。。。80。20～27。。1x=x1x2…xmIm=x1x2…xmT|0≤xj≤1ＲmI+mImp=p1p2…pmq=q1q2…qm0=00…0mωx=ω1xω2x…ωmxm。a≥bab。127p∈Imωx∈C1I+m．ω1ωx≥02eTωx=13j∈12．．．mωjxj≤0xj＜pj≥0xj＞p{j4vx=xTωx。ωxppωx。22．12珘αμ珘αx=w珘αx－aa－aa≤x＜aw珘αx=aw珘α珔a－x珔a－aa＜x≤珔a0x＜ax＞珔av珔ax=a－x+uax－aa－aa≤x＜au珔ax=ax－a+uax－a珔a－aa＜x≤珔a1x＜ax＞珔a0≤w珘a≤10≤μ珘a≤10≤w珘a+μ珘a≤1珘a=〈aa珔aw珘aμ珘a〉TIFNw珘aμ珘aπ珘a=1－w珘a－μ珘a珘a12131。1珘a=＜aa珔aw珘aμ珘a＞a≥0珔a＞0珘a=〈aa珔aw珘aμ珘a〉珘a＞0。珔a≤0a＜0珘a=〈aa珔aw珘aμ珘a〉珘a＜0。珘a=〈aa珔aw珘aμ珘a〉a。珘aa珔a。珘aaw珘au珘a珘aa珔a01a珔axw珘axu珘ax。w珘a=1u珘a=0TIFNTFN。3珘a=〈aa珔aw珘aμ珘a〉0≤w珘a≤10≤μ珘a≤10≤w珘a+μ珘a≤10≤a≤a≤珔a≤1珘a珘a+=〈a+a+珔a+w珘a+u珘a+〉=〈11110〉珘a－=〈a－a－珔a－w珘a－u珘a－〉=〈00001〉珘a1=〈a1a1珔a1w珘a1u珘a1〉珘a2=〈a2a2珔a2w珘a2u珘a2〉λ珘a1+珘a2=〈a1+a2a1+a2珔a1+珔a2w珘a1^w珘a2u珘a1ˇu珘a2〉珘a1珘a2=〈a1a2a1a2珔a1珔a2w珘a1^w珘a2u珘a1ˇu珘a2〉λ珘a1=〈λa1λa1λ珔a1w珘a1u珘a1〉珘aλ1=〈aλ1aλ1珔aλ1w珘a1u珘a1〉。2。4珘a=〈aa珔aw珘au珘a〉0≤α≤w珘a珘aα=x|μ珘a≥α珘aα。珘aα=L珘aαＲ珘aα。L珘aαＲ珘aα=w珘a－αa+αaw珘aw珘a－α珔a+αaw珘a5珘a=〈aa珔aw珘au珘a〉u珘a≤β≤1。珘aβ=x|υ珘ax≤β珘aβ。珘aβ=L珘aβＲ珘aβ。L珘aβＲ珘aβ=1－βa+β－u珘aa1－u珘a1－βa+β－u珘a珔a1－u珘a6珘a=〈aa珔aw珘au珘a〉E珘a珘a。E珘a=∫w珘a012a+珔a+2a－a－珔aαw珘aαdα+∫1u珘a12a+珔a+2a－a－珔a1－β1－u珘a1－βdβ=2a+a+珔aw2珘a+1－u珘a2617珘a=〈aa珔aw珘au珘a〉LG珘a珘aLG珘a=E珘aw珘a+λ1－w珘a－u珘a22λ∈01λ。λ＞0．5λ＜0．5λ=0．5λ=0．5。珘a1珘a21LG珘a1＞LG珘a2珘a1＞珘a22LG珘a1=LG珘a2珘a1=珘a23LG珘a1≥LG珘a2珘a≥1珘a2。、。22120152471珘a珓bw珘a=w珓bu珘a=u珓bE珘a+珓b=E珘a+E珓bLG珘a+珓b=LG珘a+LG珓b。2珘a珓bw珘a=w珓bu珘a=u珓b。a＞珋b珘a＞珓b。3珘a珓b珓cw珘a=w珓bu珘a=u珓ba＞珋b珘a+珓c＞珓b+珓c。4珘a珓ba=ba=b珔a=珋bw珘a＞w珓bu珘a＜u珓b珘a＞珓b。121～4。2～4珘a珓b珘a珓b珘a＞珓b珘a珓b珘a＞珓b珘a珓c珓b珓c珘a珓b珘a珓b珘a珘a＞珓b。珘a、珓b珓cWang281珘a≥珘a2珘a≥珓b珓b≥珘a珘a=珓b3珘a≥珓b珓b≥珓c珘a≥珓c。2．28珘aii=12…nE珘aiTIFN-VWAAIn→I。TIFN-WAA珘a1珘a2…珘an=∑ni=1wiE珘a珘ai3ITIFNwE珘apE珘a=E珘a1…E珘an0≤wiE珘a≤1i=12…n∑ni=1wiE珘a=1TIFN-VWAAnTIFN。p=0wE珘ap=ewE珘ap∈01nwE珘awE珘a。9珘aii=12…nE珘aiTIFN-VW-GAIn→I。TIFN-WGA珘a1珘a2…珘an=∑ni=1珘aiwiE珘a4TIFN-WGAnTIFN。p=0wE珘ap=ewE珘ap∈01nwE珘awE珘a。3213。。1珘aii=12…n5TIFN-WAA珘a1珘a2…珘an=〈∑ni=1wiE珘aai∑ni=1wiE珘aai∑ni=1wiE珘a珔aiw珘a1w珘a2…w珘anu珘a1u珘a2…u珘an〉。2珘a2i=12…n6TIFN-WGA珘a1珘a2…珘an=〈∑ni=1aiwiE珘a∑ni=1aiwiE珘a∑ni=1珔aiwiE珘aw珘a1w珘a2…w珘anu珘a1u珘a2…u珘an〉。1212。2．3X=x1x2…xng=g1g2…gmw0=w01w02…w0mTw0j∈01j=12…m∑mj=1w0j=1。槇A=珘aijn×m珘aij=〈aijaij珔aijw珘aiju珘aij〉xigiaij≤aij≤珔aijw珘aij∈01μ珘aij∈01i=12…nj=12…m。xii=12…nmai=珘a1i珘a2i…珘ami。Step1、、A=珘aijn×m珘aij=〈aijaij珔aijw珘aiju珘aij〉。Step2珓rij=〈rijrij珋rijw珘aiju珘aij〉珓rij=〈1－珘aij珔a+j1－aij珔a+j1－aij珔a+jw珘aiju珘aij〉5珓rij=〈aij珔a+jaij珔a+j珔aij珔a+jw珘aiju珘aij〉6珘a+j=max珘aij|i=12…nj=12…m。Step3。1E珓rij=rij+2rij+珋rijw2珘aij+1－u珘aij26Step4。Step5。56xii=12…n。Step6。2xii=12…nxii=12…n。33．113x1、x2x3。5g1、g2、g3、g4、g5w=0．140．30．120．30．14T。1。4212015241g1g2g3g4g5x1〈5．77．79．30．70．2〉〈5790．60．3〉〈5．77．790．80．1〉〈8．339．67100．60．4〉〈3570．60．3〉x2〈6．58．6100．70．2〉〈89100．60．3〉〈8．39．7100．80．1〉〈89100．60．3〉〈79100．60．2〉x3〈6．58．6100．80．1〉〈79100．70．2〉〈09100．50．2〉〈6890．60．2〉〈6．38．39．70．70．2〉16。2。2g1g2g3g4g5x1〈0．0830．1110．1340．70．2〉〈0．150．210．270．60．3〉〈0．0680．0920．1080．80．1〉〈0．2490．2910．30．60．4〉〈0．0420．070．0980．60．3〉x2〈0．0910．120．140．40．5〉〈0．240．270．300．60．3〉〈0．100．1160．120．70．2〉〈0．240．270．300．60．3〉〈0．0980．1260．140．60．2〉x3〈0．0910．1150．130．80．1〉〈0．210．270．30．70．2〉〈0．0840．1080．120．50．2〉〈0．180．240．270．60．2〉〈0．0880．1160．1360．70．2〉205ut=16t3－14t2+1312t25～26wijErijErijErij=w0j12Erij2－12Erij+136∑5k=1w0k12Erik2－12Erik+136i=123j=12…533。44。3x1x2x3TIFN-VWAA〈0．1450．1860．2160．60．4〉〈0．1820．2100．2330．40．5〉〈0．1520．1980．2220．50．2〉TIFN-VWGA〈3．2933．4903．6130．60．4〉〈3．4963．6113．6850．40．5〉〈3．3903．5683．6520．50．2〉〈0．5920．7740．9100．60．4〉〈0．7690．9031．0000．40．5〉〈0．6530．8490．9560．50．2〉4x1x2x3TIFN-VWAA0．0260．0130．037x3＞x1＞x2TIFN-VWGA0．5000．2210．683x3＞x1＞x20．1100．0550．159x3＞x1＞x23．25ρ1=0．333ρ2=0．526ρ3=0．671。x3＞x1＞x2x3x3。TIFN-VWAA。0．5TIFN-VWAA。521341。234。1AtanassovKT．IntuitionisticfuzzysetsJ．FuzzySetsandSystems198620187-96．2AtanassovKTGargovGIntervalvaluedintuitionisticfuzzysetsJ．FuzzySetsandSystems198931343-349．3LiDFNanJXZhangM