22897_fuzzyreasoningsolvingmultipleobjective
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8/14/2019 22897_FuzzyReasoningSolvingMultipleObjective
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Fuzzyreasoningforsolvingfuzzymultiple
objectivelinearprograms
ChristerCarlsson
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