Fuzzy Big-M Method for Solving Fuzzy Linear Programs with Trapezoidal Fuzzy Numbers

Abstract

The fuzzy primal simplex method [15] and the fuzzy dual simplex method [17] have been proposed to solve a kind of fuzzy linear programming (FLP) problems involving symmetric trapezoidal fuzzy numbers. The fuzzy simplex method starts with a primal fuzzy basic feasible solution (FBFS) for FLP problem and moves to an optimal basis by walking truth sequence of exception of the optimal basis obtained in fuzzy primal simplex method don't satisfy the optimality criteria for FLP problem. Also this method has no efficient when a primal fuzzy basic FBFS is not at hand. The fuzzy dual simplex method needs to an initial dual FBFS. Furthermore, there exists a shortcoming in the fuzzy dual simplex method when the dual feasibility or equivalently the primal optimality is not at hand and in this case, the fuzzy dual simplex method can't be used for solving FLP problem. In this paper, a fuzzy Big-M method is proposed to solve these problems in which the primal FBFS is not readily available. A numerical example is given to illustrate the proposed method.