Interactive fuzzy programming through possibility measures and probability maximization for two-level linear programming problems involving fuzzy random variable coefficients

In this research, focusing on two-level linear programming problems involving fuzzy random variables, we pro pose a new decision making model through possibility measures. Taking into account vagueness of judgments of decision makers for each objective function, fuzzy goals are introduced. Noting that the degree of the possibility fluctuates stochastically, we propose a probability maximization model in stochastic programming. Through 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.