A fuzzy goal programming approach for solving bilevel programming problems

Abstract

This paper presents a fuzzy goal programming procedure for solving linear bilevel programming problems. The concept of tolerance membership functions for measuring the degree of satisfactions of the objectives of the decision makers at both the levels and the degree of optimality of vector of decision variables controlled by upper-level decision maker are defined first in the model formulation of the problem. Then a linear programming model by using distance function to minimize the group regret of degree of satisfactions of both the decision makers is developed. In the decision process, the linear programming model is transformed into an equivalent fuzzy goal programming model to achieve the highest degree (unity) of each of the defined membership function goals to the extent possible by minimizing their deviational variables and thereby obtaining the most satisfactory solution for both the decision makers. To demonstrate the approach, a numerical example is solved and compared the solution with the solutions of other two fuzzy programming approaches [11,12 ] studied previously.