A fuzzy goal programming technique for quadratic multiobjective multilevel programming

The purpose of this paper is to develop a fuzzy goal programming methodology for solving quadratic multiobjective multilevel programming problems in a hierarchical decision making environment. In the proposed procedure, the tolerance membership functions in fuzzy set theory are defined first for measuring the degree of satisfactions of the objectives of each decision maker at each level. Then a nonlinear fuzzy goal programming model is formulated to achieve highest degree of each of the defined membership goals at each level to the extent possible on the basis of priorities of importance of optimizing the objectives. Afterwards the nonlinear fuzzy goals are converted into linear forms by applying a linear approximation technique. The model is then solved for measuring the degree of satisfaction of the objectives of decision makers at each level by arriving at a compromise decision regarding the optimality of the sets of decision variables controlled individually by each of them. To illustrate the proposed methodology a numerical example is solved and compared the solution with existing approaches.