Interactive fuzzy programming for fuzzy random two-level linear programming problems through probability maximization with possibility

This paper considers two-level linear programming problems involving fuzzy random variables under cooperative behavior of the decision makers. Through the introduction of fuzzy goals together with possibility measures, the formulated fuzzy random two-level linear programming problem is transformed into the problem to maximize the satisfaction degree for each fuzzy goal. By adopting probability maximization, the transformed stochastic two-level programming problem can be reduced to a deterministic one. Interactive fuzzy programming to derive a satisfactory solution for the decision maker at the upper level in consideration of the cooperative relation between decision makers is presented. An illustrative numerical example demonstrates the feasibility and efficiency of the proposed method.

► Cooperative fuzzy random two-level linear programming problems are considered.
► Fuzzy goals are introduced into the formulated two-level programming problems.
► New models are proposed through possibility and stochastic programming.
► Interactive fuzzy programming to obtain a satisfactory solution is presented.
► An illustrative numerical example demonstrates the feasibility and efficiency of the proposed method.