A Fuzzy Linear Programming Approach to Solve Bi-level Multi-objective Linear Programming Problems

Abstract

This paper presents a new fuzzy linear programming approach to solve bi-level multi-objective linear programming problems. First, we solve all the linear programming models on a given set of constraints. After that, we determine membership functions of the objective functions and of the decision variables at the first level. Later, we determine weights for all the membership functions, and form a fuzzy linear programming model. The solution of the model should be the best one for all decision-makers on both levels. To demonstrate the efficiency of the proposed approach, we solve a business planning problem and compare the obtained results with the ones obtained using fuzzy goal programming methodology.