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An interactive satisfying method based on alternative tolerance is presented for the multiple objective optimization problem with fuzzy parameters. Using the alpha-level sets of the fuzzy numbers, all the objectives are modeled as the fuzzy goals, and the tolerances of the objectives are iteratively changed according to a decision maker for a satisfying solution. Via a specific attainable point programming model, the membership functions can be modified, and then, a lexicographic two-phase programming procedure is constructed correspondingly to find the final solution. In a special case, the objective constraint is added instead of changing the membership functions; therefore, the dissatisfying objectives for the decision maker can be improved step by step. The presented method not only acquires the alpha-Pareto optimal or weak alpha-Pareto optimal solution of the fuzzy multiple objective optimization, but also satisfies the progressive preference of the decision maker. A numerical example shows its power.
Date of Publication: Oct. 2008