This paper presents a new interactive decision making method for multiobjective nonlinear programming problems with fuzzy parameters. The fuzzy parameters involved in objective functions and constraints are characterized by fuzzy numbers. The concept of α-Pareto optimality is introduced in which the usual Pareto optimality is extended based on the α-level sets of fuzzy numbers. In our interactive decision making method, if the decision maker (DM) specifies his reference objective values and the degree α of the α-level sets, the minimax problem is solved and the DM is supplied with the corresponding α-Pareto optimal solution together with the trade-off rates among the values of the objective functions and the degree α. Then by considering the current values of the objective functions and α as well as the trade-off rates, the DM responds by updating his reference objective values and/or the degree v. In this way, the satisficing solution for the DM can be derived efficiently from among an α-Pareto optimal solution set.