Fuzzy linear programming using a penalty method

In this paper we begin with a standard form of the linear programming problem. We replace each constant in the problem with a fuzzy number. We then reformat the objective and constraints into an unconstrained fuzzy function by penalizing the objective for possible constraint violations. The range of this fuzzy function lies in the space of fuzzy numbers. The objective is then redefined as optimizing the expected midpoint of the image of this fuzzy function. We show that this objective defines a concave function which, therefore, can be maximized globally. We present an algorithm for finding the optimum. (C) 2001 Elsevier Science B.V. All rights reserved.