MODM(multiobjective decision-making)problem is very complex system for the analysist and decision maker. Therefore, it requires suitable MODM method to solve multiobjective decision-making problem. This paper presents an interactive fuzzy decision making method for solving multiobjective nonlinear programming problems with fuzzy goals and α-cut set of fuzzy numbers. In our interactive method, if the decision maker specifies the degree ^αof the objective value and the imprecise goals, λ-mux problem is solved. To examplify the proposed method, an interactive computer programming written in FORTRAN and an illustrate numerical example along with computer outputs are presented.