An Interactive Fuzzy Satisficing Method for Multiobjective Linear Programming Problems with Random Fuzzy Variables Using Possibility-based Probability Model

This paper formulates multiobjective linear programming problems where each coefficient of the objective functions is expressed by a random fuzzy variable. Assuming that the decision maker concerns about the probability that each of the objective function values is smaller than or equal to a certain target value, the fuzzy goals of the decision maker 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. For solving transformed deterministic problems efficiently, particle swarm optimization for nonlinear programming problems is introduced. An interactive fuzzy satisficing method is presented for deriving a satisficing solution for a decision maker efficiently by updating the reference probability levels. An illustrative numerical example is provided to demonstrate the feasibility and efficiency of the proposed method.