Pareto-optimal solution for multiple objective linear programming problems with fuzzy goals

Several methods have been addressed to attain fuzzy-efficient solution for the multiple objective linear programming problems with fuzzy goals (FMOLP) in the literature. Recently, Jimenez and Bilbao showed that a fuzzy-efficient solution may not guarantee to be a Pareto-optimal solution in the case that one of fuzzy goals is fully achieved. To show this point they employ Guu and Wu's two-phase approach to obtain a fuzzy-efficient solution first, then a model like a conventional goal programming problem is proposed to find a Pareto-optimal solution. In this study, a new simplified two-phase approach is proposed to find a Pareto-optimal solution for FMOLP without relying on the results of Guu and Wu's two-phase approach. This new simplified two-phase approach not only obtains the Pareto-optimal solution but also provides more potential information for decision makers. Precisely, decision makers can find out whether the fuzzy goals of objective function are overestimated or not and the amount of overestimation can easily be computed if it exists.