With the implementation of the renewable energy quota system and the development of the green certificate market, the diversification of cross-region trading subjects has brought about the problem of complicating the competition and cooperative relationship between multiple subjects. This problem makes it difficult to balance the conflict of interests of multiple participating subjects in green certificate transactions, and reduces the enthusiasm for trading. To this end, this paper proposes a multi-participant decision model of cross-regional green certificate trading behavior that takes into account the uncertainty of renewable energy generation. In the model, in order to explore the potential full set of strategies of the participating subjects, the cooperative game theory is utilized to analyze the complex interaction between multiple participating subjects in the cross-regional transaction, and the cooperative game model based on green certificates is established. As the participating subjects' information about other participants and their knowledge of the game environment are limited, the decision-making behavior is uncertain. In order to more reasonably portray the subject's game behavior in the actual decision-making scenario and to solve the defect that the traditional evolutionary game model can not reflect the influence of uncertain factors, we use the stochastic evolutionary game theory to dynamically deduce the cooperative strategies of the participating subjects under the limited rationality, and at the same time, introduce the strategy influencing factors to explore the dependence relationship between strategies. In addition, in order to cope with the impact of power generation uncertainty on cross-regional trading and to solve the defects of distributionally robust fuzzy set construction which is subjective and only for the analysis of uncertainty in a single time section, it is proposed to use Bayesian multivariate nonlinear model and mixed-effects model to construct probability distribution fuzzy sets of wind and light power generation uncertainty on the basis of distributionally robust theory. Finally, based on the arithmetic example, the cooperative strategy of multi-participants in cross-regional transactions under finite rationality is deduced, and the impact of uncertainty factors on the cooperative strategy is analyzed.