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 fu zzy parameters characterized by fuzzy numbers are formulated. Using the alp ha-level sets of fuzzy numbers, the corresponding nonfuzzy alpha-programmin g problem is introduced. The fuzzy goals of the decision maker for the obje ctive functions are quantified by eliciting the corresponding membership fu nctions including nonlinear ones. Through the introduction of an extended P areto optimality concept, if the decision maker specifies the degree alpha and the reference membership values, the corresponding extended Pareto opti mal 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 solu tion for the decision maker efficiently from an extended Pareto optimal sol ution set is presented along with an illustrative numerical example. (C) 20 00 Elsevier Science B.V. All rights reserved.