Interactive fuzzy programming for multi-level linear programs with fuzzy numbers

In the fuzzy programming for multi-level linear programming problems developed by Lai et al. (1996), since the fuzzy goals are determined for both an objective function and decision variables at the upper level, undesirable solutions are produced when these fuzzy goals are inconsistent. In order to overcome such problems, after eliminating the fuzzy goals for decision variables, interactive fuzzy programming for multi-level linear programming problems with fuzzy parameters is presented. In our interactive method, after determining the fuzzy goals of the decision makers at all levels, a satisfactory solution is derived efficiently by updating the satisfactory degrees of decision makers at the upper level with considerations of overall satisfactory balance among all levels. An illustrative numerical example for three-level linear programming problems is provided to demonstrate the feasibility of the proposed method