An interactive fuzzy satisficing method for multiobjective block angular linear programming problems with fuzzy parameters
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 alpha-level sets of fuzzy numbers, the corresponding nonfuzzy alpha-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 alpha 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. (C) 2000 Elsevier Science B.V. All rights reserved.
decomposition methods block angular structure large-scale linear programs fuzzy programming interactive methods