Analytic description of fuzzy set solutions to fuzzy "LP" problems

Abstract

We aim to solve fuzzy linear programming problems with coefficients expressed by non-negative trapezoidal fuzzy numbers. Approaching the same class of problems, a recent work from the literature provided a methodology to derive numerical description of the membership function of the optimal fuzzy value of the objective function, and informed on its impossibility to disclose relevant characterization of the optimal fuzzy solutions. We expand that results by proposing analytic descriptions to the fuzzy sets representing the optimal values and solutions through a parametric analysis of the optimal solutions to crisp linear optimization problems. We illustrate our theoretic results through a numerical example recalled from the literature.