Fuzzy decision making for multiobjective stochastic programming problems

In this study, we propose a fuzzy decision making method for multiobjective stochastic linear programming problems with variance covariance matrices (MOSLPs), in which the criteria of probability maximization and fractile optimization are simultaneously considered. For a probability maximization model for an MOSLP, the decision maker is required to specify permissible objective levels. However, fewer values of permissible objective levels for minimization problems result in fewer values of the corresponding distribution function because of the conflicts between them. Similarly, for a fractile optimization model for an MOSLP, the decision maker is required to specify permissible probability levels. However, due to conflicts between the probability levels and the corresponding objective functions, larger values of permissible probability levels result in larger values of the corresponding objective function for minimization problems. In this study, it is assumed that the decision maker has fuzzy goals not only for permissible objective levels of a probability maximization model but also for permissible probability levels of a fractile optimization model, and such fuzzy goals are quantified by eliciting the corresponding membership functions. On the basis of the fuzzy decision, the satisfactory solution of the decision maker is obtained by applying a convex programming technique.