An interactive fuzzy satisficing method for generalized multiobjective linear programming problems with fuzzy parameters

In a new interactive fuzzy satisficing method for multiobjective linear programming problems with fuzzy parameters, the satisficing solution of the decision maker is derived efficiently from among M-α-Pareto optimal solutions.

Abstract

A new interactive fuzzy satisficing method for multiobjective linear programming problems with fuzzy parameters is proposed. In general, two types of fuzziness of human judgements should be incorporated in multiobjective programming problems. One is the experts' ambiguous understanding of the nature of the parameters in the problem-formulation process, and the other is the fuzzy goals of the decision maker for each of the objective functions. In order to cope with both types of fuzziness, multiobjective linear programming problems with fuzzy parameters which reflect the experts' ambiguous understanding in the problem-formulation are formulated and the concept of generalized α-multiobjective linear programming and M-α-Pareto optimality is introduced. In our interactive fuzzy satisficing method, the satisficing solution of the decision maker is derived efficiently from among M-α-Pareto optimal solutions. On the basis of the proposed method, an interactive computer program is written to implement man-machine interactive procedures. Finally, an illustrative numerical example for multiobjective linear programming problems with fuzzy parameters is demonstrated along with the corresponding computer outputs.