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zn zlgorithT for Solving Fuzzy TzxiTzl Flow aroilxTs Using GxnxrzlizxK TrzaxzoiKzl Fuzzy NuTixrs
APit TuPar a and Panjot Taur a
aPZAool of PatAxPatiZP and ZoPputxr AppliZationP, TAapar UnivxrPity, India
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Abstract:
Kumar et al. (A new approach for solving fuzzy maximal flow problems, Lecture Notes in Computer Science, Springer-Verlag, Berlin Heidelberg 5908 (2009) 278-286) proposed a new algorithm to find the fuzzy maximal flow between source and sink by representing the flow as normal triangular fuzzy numbers. Chen (Operations on fuzzy numbers with function principal, Tamkang Journal of Management Science 6 (1985) 13-25) pointed out that in many cases it is not to possible to restrict the membership function to the normal form and proposed the concept of generalized fuzzy numbers. There are several papers in the literature in which generalized fuzzy numbers are used for solving real life problems but to the best of our knowledge, till now no one has used generalized fuzzy numbers for solving the maximal flow problems. In this paper, the existing algorithm is modified to find fuzzy maximal flow between source and sink by representing all the parameters as generalized trapezoidal fuzzy numbers. To illustrate the modified algorithm a numerical example is solved and the obtained results are compared with the existing results. If there is no uncertainty about the flow between source and sink then the proposed algorithm gives the same result as in crisp maximal flow problems.
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Keywords: Fuzzy maximal flow problem; ranking function; generalized trapezoidal fuzzy numbers
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*Corresponding author; e-mail: manjot.thaparian@gmail.com
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©
2010
CSME , ISSN 0257-9731
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