The paper considers a discrete stochastic multiple criteria decision making problem. This problem is defined by a finite set of actions A, a set of attributes X and a set of evaluations of actions with respect to attributes E. In stochastic case the evaluation of each action with respect to each attribute takes form of a probability distribution. Thus, the comparison of two actions leads to the comparison of two vectors of probability distributions. In the paper a new procedure for solving this problem is proposed. It is based on three concepts: stochastic dominance, interactive approach, and preference threshold. The idea of the procedure comes from the interactive multiple objective goal programming approach. The set of actions is progressively reduced as the decision maker specifies additional requirements. At the beginning the decision maker is asked to define preference threshold for each attribute. Next, at each iteration the decision maker is confronted with the set of considered actions. If the decision maker is able to make a final choice then the procedure ends, otherwise he/she is asked to specify aspiration level. A didactical example is presented to illustrate the proposed technique.
