Interactive fuzzy decision-making for multi-objective nonlinear programming using reference membership intervals

Abstract

This paper presents an interactive fuzzy decision-making method by assuming that the decision-maker (DM) has fuzzy goals for each of the objective functions in multi-objective non-linear programming problems. Through the interaction with the DM, the fuzzy goals of the DM are quantified by eliciting the corresponding membership functions. After determining the membership functions for each of the objective functions, in order to generate a candidate for the satisficing solution which is also Pareto optimal, the DM is asked to specify his reference intervals for each of the membership functions, called reference membership intervals. For the DM's reference membership intervals, the corresponding augmented weighted minimax problem is solved and the DM is supplied with the Pareto optimal solution which is in a sense close to his requirement together with the trade-off rates between the membership functions. Then by considering the current values of the membership functions as well as the trade-off rates, the DM responds by updating his reference membership intervals. In this way the satisficing solution for the DM can be derived efficiently from among a Pareto optimal solution set by updating his reference membership intervals. On the basis of the proposed method, a time-sharing computer program is written and an illustrative numerical example is demonstrated along with the corresponding computer outputs.