A fuzzy programming approach for solving quadratic bilevel programming problems with fuzzy resource constraints

In this paper, a fuzzy goal programming (FGP) model is developed to solve quadratic bilevel programming problems with fuzzy resource constraints for proper distribution of decision powers to the leader and follower. In the model, formulation of the problem, concept of tolerance membership functions for measuring the degree of satisfaction of the objective of the leader and follower are defined first, under the fuzzily described system constraints. Subsequently, a quadratic programming model is constructed on the basis of degree of satisfaction of both the leader and follower. The developed model is converted into an equivalent non-linear FGP model to achieve the highest degree of satisfaction (unity) to the extent possible. In the decision process, the Taylor's series approximation technique is applied to linearise the non-linear goals and to achieve the fuzzy goal objective values of the decision-makers at both the levels, by arriving at most satisfactory solution regarding the optimality of two different sets of decision variables controlled separately by each of them. An illustrative example is solved to demonstrate the efficiency of the proposed approach and the solution is compared with the solution obtained by using an existing methodology developed by Osman et al. in 2004.