Solving a Fuzzy Linear Programming Problem with Triangular Membership Function

Abstract

This paper deals with the linear problem under the equality constraintswhose right hand side parameters are asymmetric triangular fuzzynumbers. The right hand side values are defuzzified by using thetriangular membership functions. Each of these triangular functionsis algebraically replaced with two piecewise linear functions. Andthe desired objective value is also a fuzzy number. The membershipfunction of the objective is assumed to be piecewise linear. Then,according to Zimmermann�s approach, by using these membership functionsand the max-min rule, the fuzzy linear problem is transformed intothe crisp linear programming problem. Consequently a fuzzy solutionis obtained by solving this linear programming problem.