A fuzzy goal programming approach for quadratic multiobjective bilevel programming under fuzzy environment

Abstract

This paper presents a fuzzy goal programming procedure to solve multiobjective quadratic bilevel programming problems, where all the parameters involved in objectives of each level decision maker and in system constraints are fuzzily defined. In model formulation process the fuzzy numbers associated with the parameters are described by using the concept of α-cut of fuzzy numbers. Then the model is decomposed on the basis of the tolerance limits of fuzzy numbers. Individual decision at each objective at each level is found in isolation to find the fuzzy goals of the objectives. Then a fuzzy goal programming model is developed to minimize the group regret of degree of satisfactions of both the decision makers and to achieve the highest degree (unity) of each of the membership goals for overall benefit of the organization. In the decision process Taylor's series linear approximation technique is applied to make the quadratic membership goals to its equivalent linear form. To establish the efficiency of the proposed approach a numerical example is solved.