Extended procedure for computing the values of the membership function of a fuzzy solution to a class of fuzzy linear optimization problems

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.