This paper presents an interactive fuzzy satisficing method for multiobjective nonlinear programming problems with fuzzy numbers. On the basis of the α-level sets of the fuzzy numbers, the concept of α-multiobjective nonlinear programming and (local) M-α-Pareto optimality is introduced. Through interaction with the decision maker (DM), the fuzzy goals of the DM for each of the objective functions in α-multiobjective nonlinear programming are quantified by eliciting the corresponding membership functions. After determining the membership functions, in order to generate a candidate for the satisficing solution which is also (locally) M-α-Pareto optimal, if the DM specifies the degree α of the α-level sets and the reference membership values, the augmented minimax problem is solved and the DM is supplied with the corresponding (local) M-α-Pareto optimal solution together with the trade-off rates among the values of the membership functions and the degree α. Then by considering the current values of the membership functions and α as well as the trade-off rates, the DM responds by updating his reference membership values and/or the degree α. In this way the (local) satisficing solution for the DM can be derived efficiently from among an M-α-Pareto optimal solution set. Based on the proposed method, an interactive computer program has been written and an illustrative numerical example is given along with the corresponding computer outputs.
