In social networks, studying rumor propagation patterns is essential for curbing the spread of rumors. Given the coexistence and conflict of multiple-type rumor information, as well as users’ cognitive differences, this article presents a rumor propagation model grounded in user cognition and evolutionary game theory. First, considering the potential impact of social relationships between users on rumor propagation, the KD-Tree algorithm is employed to uncover hidden connections between users, thereby enriching the topology of the user’s social network. Second, a user behavior driving mechanism for rumor, anti-rumor, and motivation-rumor types is constructed based on evolutionary games to reflect the interactive and strategic nature of users’ responses. Moreover, the Lotka-Volterra equation is utilized to explore the dynamic game of multi-type rumor information and the cognitive process of users. Finally, to address differences in users’ cognition, this article introduces the anti-rumor trust state A and the motivation-rumor trust state M , which arise from users’ exposure to multiple types of rumor information. Based on these trust states, a rumor propagation model, SIAMR, is constructed using user cognition and evolutionary game theory. Experiments demonstrate that the model accurately captures the dynamic interactions between multi-type rumor information and the transmission process of rumor topics in social networks. The proposed model integrates cognitive psychology with a strategic interaction framework, offering a more realistic representation of rumor propagation behavior in the real world. Experimental results reveal that SIAMR improves prediction accuracy by 14.23% over baseline models in simulating the dynamics of multiple types of rumors, effectively capturing users’ cognitive influences and the mechanisms of information competition.