Interactive fuzzy decision making for multiobjective stochastic linear programming problems with variance-covariance matrices

In this paper, we propose an interactive fuzzy decision making method for multiobjective stochastic linear programming problems with variance-covariance matrices to obtain a satisfactory solution, in which the criteria of probability maximization and fractile optimization are considered simultaneously. In the proposed method, it is assumed that the decision maker has fuzzy goals for not only permissible objective levels of a probability maximization model but also permissible probability levels of a fractile criterion optimization model. After eliciting the corresponding membership functions for the fuzzy goals, two kinds of membership functions for permissible objective levels and permissible probability levels are integrated through the fuzzy decision, and two kinds of Pareto optimality concepts are introduced. An interactive algorithm is proposed to obtain a satisfactory solution from among a Pareto optimal solution set.