The authors consider fuzzy multiobjective nonlinear programming problems as a generalization of conventional multiobjective nonlinear programming problems using the \(\alpha\)-level sets of fuzzy numbers. Introducing the notion of \(\alpha\)-Pareto optimality they apply the standard solution technique for multiobjective nonlinear programming problems. An interactive decision making method is presented to derive the satisficing solution of the decision maker from among the \(\alpha\)-Pareto optimal solutions set, as a solution of a corresponding minimax problem, which expresses the decision maker's degree of preference (trade-off information between a standing objective function and each of the other objective functions as well as between the degree \(\alpha\) and the objective functions). This trade-off information is easily obtainable since it is related to the strict positive Lagrange multipliers of the minimax problem. The paper presents an interactive algorithm and a numerical example clarifying various aspects of both the solution concept and the proposed method.