Two-phase approach for asymmetric fuzzy multiobjective linear programming problem

A lot of methods for solving the fuzzy mathematical programming problem have been proposed. In many cases of them, we translate the original fuzzy problem into a crisp problem. Then, we can solve the translated crisp problem using some ordinal methods. Hence, it becomes one of the important factors how to incorporate the information of fuzzy environment in the original fuzzy problem, to the translated crisp problem. In this paper, we propose a two-phase approach for solving the multiobjective linear programming problem with fuzzy parameters. In the first phase, we solve an alpha level for the constraints and fuzzy parameters, considering the feasibility of objective functions. In the second phase, based on the optimal alpha level obtained in the first phase, we search again the ranges of objective functions' values. Then, we solve a well-balanced solution for the original multiobjective fuzzy problem.