The stochastic dominance criterion has been extensively applied in stochastic multiple-attribute decision making as a robust tool for quantitatively comparing decision-makers’ preferences over alternatives. Existing research predominantly relies on first-order and second-order stochastic dominance criteria. In view of the limitations that the first-order stochastic dominance criterion imposes strict requirements on distribution conditions, while the second-order stochastic dominance criterion is only applicable to risk-averse decision-makers, this paper proposes a stochastic multiple-attribute decision making method based on fractional-order stochastic dominance criteria. First, the fractional-order stochastic dominance degree is defined, which can measure the dominance degree between two alternatives in a more accurate and flexible manner. To determine attribute weights accurately, both the Best-Worst Method and the Cumulative Residual Entropy method are adopted to derive subjective and objective weights, respectively, and these are subsequently combined through game-theoretic aggregation to obtain attribute weights combination. Then, the PROMETHEE?II method is applied to rank the alternatives and identify the optimal alternative. Numerical examples show the effectiveness and robustness of the proposed approach, highlighting its broader applicability compared with conventional methods, and offering an effective theoretical tool for alternative selection under complex uncertain environments.