Interactive fuzzy stochastic two-level linear programming with simple recourse

In this paper, assuming cooperative behavior of the decision makers, two-level linear programming problems involving random variables in constraints are considered. Using the concept of simple recourse, the formulated stochastic two-level simple recourse problems are transformed into deterministic two-level programming ones. Taking into account vagueness of judgments of the decision makers, interactive fuzzy programming is presented. In the proposed interactive method, after determining the fuzzy goals of the decision makers at both levels, a satisfactory solution is derived efficiently by updating the satisfactory degree of the decision maker at the upper level with considerations of overall satisfactory balance between both levels. An illustrative numerical example is provided to demonstrate the feasibility and efficiency of the proposed method.