In social networks, trust relationships are the basis for interactions among decision nodes. Trust relationships are subjective and dynamic, and there are only few sample data to measure the strength of these connections. Uncertainty theory is a mathematical system that studies the belief degree of experts and provides a new method for measuring trust in social networks. In this paper, uncertainty theory is applied to the modeling of social networks. For any feature where certain information cannot be directly obtained, the recommended trust is derived based on direct trust values, and the constraints of single-path trust chains are established. To avoid secondary uncertainties caused by subjective weighting while considering multi-node, multi-path chains, two weighted trust aggregation operators are developed to accomplish a multi-trust transitive aggregation model. The belief degrees of the nodes, the trust chains and the whole network are quantified, and a social network trust measurement model based on uncertainty theory is constructed. In the case of a lack of data on the trust chain, a trust threshold constraint is used to calculate the range of the incomplete chain.