A Different Approach for Solving the Shortest Path Problem Under Mixed Fuzzy Environment

Int. J. Fuzzy Syst. Appl. Pub Date : 2020-04-01 DOI:10.4018/ijfsa.2020040106

Ranjan Kumar, S. Jha, Ramayan Singh

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引用次数: 36

Abstract

Theauthorspresentanewalgorithmforsolvingtheshortestpathproblem(SPP)inamixedfuzzy environment.Withthisalgorithm,theauthorscansolvetheproblemswithdifferentsetsoffuzzy numberse.g.,normal,trapezoidal,triangular,andLR-flatfuzzymembershipfunctions.Moreover,the authorscansolvethefuzzyshortestpathproblem(FSPP)withtwodifferentmembershipfunctions suchasnormalandafuzzymembershipfunctionunderreal-lifesituations.Thetransformationof thefuzzylinearprogramming(FLP)modelintoacrisplinearprogrammingmodelbyusingascore functionisalsoinvestigated.Furthermore,theshortcomingsofsomeexistingmethodsarediscussed andcomparedwiththealgorithm.Theobjectiveoftheproposedmethodistofindthefuzzyshortest path(FSP)forthegivennetwork;however,thisisalsocapableofpredictingthefuzzyshortestpath length(FSPL)andcrispshortestpathlength(CSPL).Finally,somenumericalexperimentsaregiven toshowtheeffectivenessandrobustnessofthenewmodel.Numericalresultsshowthatthismethod issuperiortotheexistingmethods. KEywoRDS Fuzzy Linear Programming, Normal Fuzzy Number, Score Function, Shortest Path Problem

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混合模糊环境下求解最短路径问题的一种不同方法

Theauthorspresentanewalgorithmforsolvingtheshortestpathproblem(SPP)inamixedfuzzy环境。Withthisalgorithm，theauthorscansolvetheproblemswithdifferentsetsoffuzzy numberse.g，normal，trapezoidal，triangular，andLR-flatfuzzymembershipfunctions。Moreover，the authorscansolvethefuzzyshortestpathproblem(FSPP)withtwodifferentmembershipfunctions suchasnormalandafuzzymembershipfunctionunderreal-lifesituations。Thetransformationof thefuzzylinearprogramming(FLP)modelintoacrisplinearprogrammingmodelbyusingascore functionisalsoinvestigated。Furthermore，theshortcomingsofsomeexistingmethodsarediscussed andcomparedwiththealgorithm。Theobjectiveoftheproposedmethodistofindthefuzzyshortest path> (FSP)forthegivennetwork;however，thisisalsocapableofpredictingthefuzzyshortestpath length> (FSPL)andcrispshortestpathlength(CSPL)。Finally，somenumericalexperimentsaregiven toshowtheeffectivenessandrobustnessofthenewmodel。Numericalresultsshowthatthismethod issuperiortotheexistingmethods。关键词:模糊线性规划，正规模糊数，分数函数，最短路径问题

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Int. J. Fuzzy Syst. Appl.

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