序与区间混杂多属性决策方法研究（完整版）实用资料(可以直接使用，可编辑完整版实用资料，欢迎下载）MultipleAttributeDecisionMakingBasedonPreferenceOrderingsandIntervalNumbersPengJinQuanZhangSchoolofInformationScienceandEngineering,ShenYangUniversityofTechnology,ShenYang,110178,ChinaEmail:jAbstract:Thispaperfocusesonthemultipleattributedecisionmakingproblemswiththeattributevaluesbeingpreferenceorderingsandintervalnumbersevaluations.Fortheattributeswithpreferenceorderingsevaluations,thefuzzypreferencerelationbetweenthealternativesarecalculatedandthetheirrankingsvaluesarefurthernormalizedbymeasuringtheirrelativedistancestotheidealpoint;Fortheattributeswithintervalnumberevaluations,bycalculatingtherelativedistancesbetweentheintervalevaluationsandtheirnegativeidealpoint,intervalevaluationsarenormalizedintosinglepointones.Thedecisionmatrixisthusnormalized,basedonwhichamathematicalprogrammingmodelissetuptofigureouttheattributeweightswiththeoverallvaluesofthealternativesbeingthegoals.Therefore,theoverallvaluesofthealternativesareobtained,andthereforethealternativesareranked.Anexampleisusedtoillustratetheproposedapproach,whichissuitableforextensiveapplicationsintheend.Keywords:Multipleattributedecisionmaking;Preferenceorderings;Intervalnumbers;Weights;Ranking1．IntroductionMultipleattributedecisionmaking(MADM)referstomakingpreferencedecisions(e.g.evaluation,prioritization,selection)overtheavailablealternativesthatarecharacterisedbymultiple,usuallyconflicting,attributes[1].Itisaproblemwithextensivetheoreticalandpracticalbackground[1].Duetoitscomplexity,theMADMproblemcanbemodelledeitherbysubjectivepairwisecomparisonmatrices[2]oradecisionmatrix[1].Subjecttothesubjectandobjectivefactors,inthecomplexMADMproblems,theattributevaluesinthedecisionmatrixarealwaysexpressedintheformsofpreferenceorderings[3]andintervalnumbers[4,5].Whenevaluatingalternativesagainstsomeattributes,itisdifficulttogiveaprecisenumericvalue,andattributevaluesarejustexpressedbypreferenceorderingsoranorderedvector,e.g.,(2,3,4,1).Ontheotherhand,dueto