Bilevel Programming Problem with Fuzzy Parameters: a Fuzzy Goal Programing Approach

This paper describes how fuzzy goal programming can be efficiently used to solve bilevel programming problems with fuzzy parameters. In the model formulation of the problem, the tolerance membership functions for the fuzzily described objective functions of decision makers are defined by determining individual optimal solution of each of the level decision makers. Since the objectives are potentially conflicting in nature, a possible relaxation of the upper level and lower level decision are considered by providing preference bounds on the decision variables for avoiding decision deadlock. Then fuzzy goal programming approach is used for achieving highest degree of each of the membership goals by minimizing negative deviational variables. Three fuzzy goal programming models are presented. Distance function is used to identify which fuzzy goal programming models offers better optimal solution. A numerical example is presented to demonstrate the potential use of the proposed approach.