Interactive random fuzzy two-level programming through possibility-based probability model

This paper considers interactive decision making methods for random fuzzy two-level linear programming problems. Assuming that the decision makers concern about the probabilities that their own objective function values are smaller than or equal to certain target values, fuzzy goals of the decision makers for the probabilities are introduced. Then, the possibility-based probability model to maximize the degrees of possibility with respect to the attained probability is considered. Interactive fuzzy nonlinear programming to obtain 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.