A decision analysis method is proposed to solve the multiple attribute decision making problem with attribute aspirations in the form of random variable. Firstly, the decision matrix is transformed into the matrix about gains and losses relative to the attribute aspirations by calculating the gain and loss value of each attribute value relative to the attribute aspiration. Then, the using the stochastic dominance rule, stochastic dominance relations on pairwise comparisons of alternatives for each attribute are judged, and the stochastic dominance relation matrixes on pairwise comparisons of alternatives are constructed. Furthermore, the PROMETHEE II method is used to obtain the ranking of alternatives. Finally, an example for the portable hard disk purchase problem in a research institute is used to illustrate the practicability of the proposed method.