An Extension of the Linear Programming Method with Fuzzy Parameters

In a recent paper, Jiménez et al. [M. Jiménez, M. Arenas, A. Bilbao, M.V. Rodríguez. Linear programming with fuzzy parameters: An interactive method resolution. European Journal of Operational Research 177(2007) 1599-1609] propose a “general” and “interactive” method for solving linear programming problems with fuzzy parameters. In this study, we propose a revision to the optimal crisp value of the objective function to eliminate the restrictive constraints imposed by Jiménez et al. (2007). The revised approach can be generalized to solve many real-world linear programming problems where the coefficients are fuzzy numbers. In contrary to the approach proposed by Jiménez et al. (2007), our method is rightfully general and interactive as it provides an optimal solution that is not subject to specific restrictive conditions and supports the interactive participation of the DM in all steps of the decision making process. We also present a counterexample to illustrate the merits of the proposed method and the drawbacks of the Jiménez et al.'s (2007) method