Random fuzzy bilevel linear programming through possibility-based fractile model

This paper focuses on random fuzzy noncooperative bilevel linear programming problems. Considering the probabilities that the decision makers' objective function values are smaller than or equal to target variables, fuzzy goals of the decision makers are introduced. Using the fractile model to optimize the target variables under the condition that the degrees of possibility with respect to the attained probabilities are greater than or equal to certain permissible levels, the original random fuzzy bilevel programming problems are reduced to deterministic ones. Extended concepts of Stackelberg solutions are introduced and computational methods are also presented. A numerical example is provided to illustrate the proposed method.