Fuzzy Goal Programming Approach to Quadratic Bi-Level Multi-Objective Programming Problem

This paper deals with fuzzy goal programming approach to quadratic bi-level multi-objective programming problem involving a single decision maker with multiple objectives at the upper level and a single decision maker with multiple objectives at the lower level. The objective functions of each level decision maker are quadratic in nature and the system constraints are linear functions. In the model formulation of the problem, we first determine the individual best solution of the quadratic objective functions subject to the system constraints and construct the quadratic membership functions of the objective functions of both levels. The quadratic membership functions are then transformed into equivalent linear membership functions by first order Taylor series at the individual best solution point. A possible relaxation of each level decision is considered by providing preference bounds on the decision variables for avoiding decision deadlock. Fuzzy goal programming approach is then used to achieve maximum degree of each of the membership goals by minimizing negative deviational variables. To demonstrate the efficiency of the proposed approach, an illustrative numerical example is provided. General Terms Quadratic bi-level multi-objective programming.