Group decision-making problems within social relationships among experts are called SN-GDM problems and have been widely considered in many fields, such as management, social science, and natural science. In SN-GDM problems, the trust relationships among experts possess uncertainty and attenuation during propagation. However, few studies have focused on the two issues at the same time. This work aims to develop a trust transitivity model for SN-GDM with intuitionistic fuzzy (IF) information. First, to model the trust relationships among experts, we present an intuitionistic fuzzy trust transitivity model that contains a trust propagation operator and an aggregation operator. Second, some concepts of IF trust network centrality analysis are defined and applied to determine expert weights. Third, a new approach is proposed to solve SN-GDM problems with IF information. Finally, comparison analysis is conducted to highlight the advantages of the proposed approach. An example is also provided to show the validity of the proposed method,