Abstract: Identifying critical nodes is one of the principal tasks of social network analysis, and it is essential to understand the structure and dynamic characteristics of the complex networks. However, the analysis framework of node importance mainly focuses on single-relational networks. As a typical model of the real world, the multi-relational network has become one of the hot topics in the field of network science, in which the research on node importance lacks systematic research. Focusing on the study of node importance in multi-relational social networks, we create the directed multiplex network model to describe a multi-relational network and use the representation framework based on tensor algebra to analyze it. Meanwhile, we propose a measure of node importance considered the influence of centrality, prestige, transitivity in multi-relational social networks. Considering the influence of coupling information and the difference of transmission mechanism for node importance on multi-relational networks, in this work we improve the method and propose another more efficient method called IOMEC to evaluate the node importance. Experimental results on four real networks show that the method of information fusion can effectively eliminate the influence on node importance evaluation, which is caused by the coupling information and the transmission mechanism of the multi-relational network. The IOMEC method can measure the importance of nodes more accurately and has lower time complexity. The experimental results demonstrate that centrality and prestige are the main factors to evaluate the node importance and the necessity of considering the transitivity of nodes. In this work we not only provide new ideas and methods for evaluating node importance for multi-relational networks but also expand the application of information fusion technology.