Solving Fuzzy Linear Programming Problems with Fuzzy Decision Variables

The numerical method for solving the fuzzy linear programming problems with fuzzy decision variables is proposed in this paper. The difficulty for solving this kind of problem is that the decision variables are assumed to be nonnegative fuzzy numbers instead of nonnegative real numbers. In other words, the decision variables are assumed to be membership functions. One of the purposes of this paper is to derive the analytic formula of error estimation regarding the approximate optimal solution. On the other hand, the existence of optimal solutions is also studied in this paper. Finally we present two numerical examples to demonstrate the usefulness of the numerical method.