Fuzzy Goal Programming with Polynomial Membership Functions of Higher Order for Multi-Objective Transportation Problem

Abstract

In the present paper, a fuzzy goal programming model with polynomial membership functions of higher order is developed for the solution of Multi-objective Transportation problem. In literature, fuzzy goal programming approaches with linear, hyperbolic and exponential membership functions exist for the solution of Multi-objective Transportation problem. These methods often produce the same compromise optimal solution for the Multi-Objective Transportation problem. In the present method, a polynomial membership function of a general higher order is constructed for each objective, based on the aspiration levels and the highest tolerance levels of all the objective functions. The method then consists of applying the fuzzy goal programming technique with polynomial memberships of various orders, starting from one, i.e., linear membership functions. Successively increasing the order of the membership functions and repeatedly applying the fuzzy goal programming technique, the order which produces a compromise optimal solution nearest to the ideal solution can be selected. Application of the   method on numerical examples has shown that the method with polynomial membership functions of some orders can produce better compromise optimal solutions than fuzzy goal programming approaches with linear, exponential and hyperbolic membership functions.        

Mathematics Subject Classification (MSC2010): 90C29.