Stochastic multiple criteria decision making with aspiration level based on prospect stochastic dominance

In order to solve a problem of a discrete stochastic multiple-criteria decision making (MCDM) with aspiration levels, a method on the basis of prospect stochastic dominance is proposed in this paper. The psychological behavior of decision maker, for instance, judgmental distortion, reference dependence and loss aversion, are considered. Based on the concept of prospect theory, aspiration levels are initially took to be the reference points. Definition and related analysis of prospect stochastic dominance degree (PSDD) is given to describe the degree that one alternative dominates another when the prospect stochastic dominance relation for each pair of alternatives with respect to aspiration level is determined. On the basis of the PSDD matrix of alternative pairwise comparisons regarding the aspiration level of every criterion, an overall PSDD matrix is constructed using Choquet integral. Further, according to the concept of the PROMETHEE II, an outramking method is designed to collect the alternatives ranking result. Finally, the effectiveness and applicability of the method proposed are illustrated by two given numerical examples.