|Authors:||Stanojević, Bogdana||Affiliations:||Mathematical Institute of the Serbian Academy of Sciences and Arts||Title:||Extended procedure for computing the values of the membership function of a fuzzy solution to a class of fuzzy linear optimization problems||Journal:||Fuzzy Sets and Systems||Volume:||272||Issue:||1||First page:||47||Last page:||59||Issue Date:||1-Jan-2015||Rank:||M21a||ISSN:||0165-0114||DOI:||10.1016/j.fss.2014.11.002||Abstract:||
In 1994, Chanas and Kuchta suggested one approach to determine the membership function of a fuzzy solution to the fuzzy linear optimization problem with fuzzy coefficients in the objective function, based on computing the sum of lengths of certain intervals. In 2012, Dempe and Ruziyeva introduced a methodology for realizing Chanas and Kuchta's idea, and derived explicit formulas for computing the endpoints of the suggested intervals in the particular case of triangular fuzzy numbers. The purpose of this paper is to extend Dempe and Ruziyeva's approach by handling the possible degeneracy of basic feasible solutions, and derive new formulas for computing the values of the membership function. The special example considered by Dempe and Ruziyeva is again used to illustrate the relevance of the extended solving procedure and new formulas.
|Keywords:||Bi-objective optimization | Fuzzy mathematical programming | Linear optimization | Membership function | Pareto optimal solution||Publisher:||Elsevier||Project:||Optimization of Distributive and Reverse Flows in Logistic Systems|
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