روش تعاملی فازی برای مشکلات برنامه ریزی خطی زاویه ای بلوک چند هدفه با پارامترهای فازی

In this paper, by considering the experts’ imprecise or fuzzy understanding of the nature of the parameters in the problem-formulation process, large-scale multiobjective block-angular linear programming problems involving fuzzy parameters characterized by fuzzy numbers are formulated. Using the α-level sets of fuzzy numbers, the corresponding nonfuzzy α-programming problem is introduced. The fuzzy goals of the decision maker for the objective functions are quantified by eliciting the corresponding membership functions including nonlinear ones. Through the introduction of an extended Pareto optimality concept, if the decision maker specifies the degree α and the reference membership values, the corresponding extended Pareto optimal solution can be obtained by solving the minimax problems for which the Dantzig–Wolfe decomposition method is applicable. Then a linear programming-based interactive fuzzy satisficing method for deriving a satisficing solution for the decision maker efficiently from an extended Pareto optimal solution set is presented along with an illustrative numerical example.