On the calculation of a membership function for the solution of a fuzzy linear optimization problem

• Published in: Fuzzy sets and systems Vol. 188; no. 1; pp. 58 - 67
• Main Authors: Dempe, S., Ruziyeva, A.
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier B.V 01.02.2012; Elsevier
• Subjects: Applied sciences; Calculus of variations and optimal control; Circuit properties; Computer science; control theory; systems; Digital circuits; Electric, optical and optoelectronic circuits; Electronic circuits; Electronics; Exact sciences and technology; Fuzzy; Fuzzy logic; Fuzzy optimization; Fuzzy set theory; Fuzzy systems; Information, signal and communications theory; Intervals; Mathematical analysis; Mathematical methods; Mathematics; Membership function; Miscellaneous; Multicriteria optimization; Optimization; Pareto optimal solution; Pareto optimality; Sciences and techniques of general use; Telecommunications and information theory; Theoretical computing; Pareto optimal solution; Multicriteria optimization; Membership function; Fuzzy optimization; Fuzzy system; Level set; Optimal solution; Optimization method; Information processing; Pareto optimal solution: Membership function; Fuzzy set
• ISSN: 0165-0114; 1872-6801
• DOI: 10.1016/j.fss.2011.07.014

In the present paper the fuzzy linear optimization problem (with fuzzy coefficients in the objective function) is considered. Recent concepts of fuzzy solution to the fuzzy optimization problem based on the level-cut and the set of Pareto optimal solutions of a multiobjective optimization problem are applied. Chanas and Kuchta suggested one approach to determine the membership function values of fuzzy optimal solutions of the fuzzy optimization problem, which is based on calculating the sum of lengths of certain intervals. The purpose of this paper is to determine a method for realizing this idea. We derive explicit formulas for the bounds of these intervals in the case of triangular fuzzy numbers and show that only one interval needs to be considered. ► The fuzzy optimization problem with fuzzy coefficients in the objective is considered. ► Recent concepts of the fuzzy solution to the fuzzy optimization problem are applied. ► The determination of the membership function values of fuzzy solutions is described. ► Explicit formulas for the case of triangular fuzzy numbers are given.