8/14/2019 22897_FuzzyReasoningSolvingMultipleObjective

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Fuzzyreasoningforsolvingfuzzymultiple

objectivelinearprograms

ChristerCarlsson

ccarlsso@ra.abo.fiRobertFuller

rfuller@ra.abo.fi

Abstract

Weinterpretfuzzymultipleobjectivelinearprogramming(FMOLP)prob-lemswithfuzzycoefficientsandfuzzyinequalityrelationsasmultiplefuzzyreasoningschemes(MFR),wheretheantecedentsoftheschemecorrespondtotheconstraintsoftheFMOLPproblemandthefactsoftheschemearetheobjectivesoftheFMOLPproblem.Thenthesolutionprocessconsistsoftwosteps:first,foreverydecisionvariablexR

nandobjectives{1,...k},

wecomputetheeffectiveattainmentofthes-thobjectivefunction,Es(x),viasup-minconvolutionoftheantecedents/constraintsandthes-thfact/objective,thenasolutiontoFMOLPproblemisanypointwhichisagoodcompromise solutiontothecrispmultipleobjectiveproblem

maxxR

n{H1(x),...Hk(x)},

whereHsisanapplicationfunction(measuringthedegreeoffulfillmentofthedecisionmakersrequirementsaboutthes-thobjectivefunction)s{1,...k}.

1StatementofFMOLPproblemswithfuzzycoef-

ficients

WeconsiderMOLPproblems,inwhichallofthecoefficientsarefuzzyquantities(i.e.fuzzysetsofthereallineR),oftheform

maximize(c1x,...,ckx)

subjecttoaix