An extension of the linear programming method with fuzzy parameters
In a recent paper, Jiménez et al. (2007) 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 generalised 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 Decision-Maker (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 Jiménez et al.’s (2007) method.
Hatami-Marbini, Adel and Tavana, Madjid, "An extension of the linear programming method with fuzzy parameters" (2010). Business Systems and Analytics Faculty Work. 272.
Hatami-Marbini, A. and Tavana, M. (2011) ‘An Extension of the Linear Programming Method with Fuzzy Parameters,’ International Journal of Mathematics in Operational Research, Vol. 3, No. 1, pp. 44-55.