For the multi-attribute and multi-identifier large group decision making problem with attribute aspirations, in the situation of considering decision making participants’ psychological behavior, attribute aspirations given by decision making participants are regarded as their reference points, and probability distributions for group gain-losses are constructed. Then, matrices of prospect stochastic dominance relations on pairwise comparisons of alternatives are established by using the prospect stochastic dominance rule, and the ranking of alternatives are determined by calculating prospect stochastic dominance degrees. Finally, a numerical example illustrates the feasibility and effectiveness of the proposed method.