A Formulation of A Linear Programming Problem in A Fuzzy Environment

Abstract

A new formulation of a linear programming problem in a fuzzy environment is given for the case when constraints are fuzzy. In this formulation the goal is not transformed to a constraint and is treated as the objective function which should be maximized. In the maximization of the objective function, a concept of soft optimization is introduced for obtaining plural solutions which can be regarded as almost best. The solution in this formulation is defined as a fuzzy set. The proposed method is applicable in a situation when it is not appropriate to restrict to the unique solution.