The implication and contagion effect of emotion cannot be ignored in rumor spreading. This paper sheds light on how DMs'emotional type and intensity affect rumor spreading. Based on the theory of RDEU and evolutionary game, we construct an evolutionary game model of rumor spreading by considering emotions, which takes netizens and the government as the core subjects. Through MATLAB to simulate and reveal the influencing mechanism of DMs'emotional type and intensity on rumor spreading. The results indicate that the DMs'choice of strategy is not only affected by their own emotional preference and intensity but also affected by that of the other player in rumor spreading. Pessimism has a more significant influence on the stability of the evolutionary game than optimism, the government's emotion types are more sensitive to the game results than netizens, and the emotional intensity is proportional to the evolution speed. More importantly, some significant emotional thresholds are found, which can be used to predict the behavior of netizens, helping the government gain critical time to deal with rumors and avoid the Tacitus Trap crisis. Furthermore, the simulation results are summarized as five types: risk, opportunity, ideal, security, and opposition. We hope that this work is beneficial to the government's public governance.