Maximizing and minimizing sets in solving fuzzy linear programming

Abstract

Linear programming with fuzzy information is a continuous field of researches in uncertain programming. Since the lack of a certain and deterministic solution is a natural characteristic of problems under uncertainty, different methods proposed various schemes to solve such problems. In this paper, a new framework is developed to solve fuzzy linear programming where the problem’s parameters, include objective function coefficients, technological matrix elements and right hand side values, are stated as fuzzy numbers. The proposed method is based on the notion of maximizing and minimizing sets, as a well known and widely accepted method of fuzzy numbers ranking, and tries to find a solution which optimizes the utility function of fuzzy objective functions by considering fuzzy constraints which are analyzed based on the concept of α-cuts and interval numbers relations. To show the applicability of the proposed method, its application is illustrated in a numerical example and its results are compared with a current method.