In order to solve the limitations of traditional methods in the reliability assessment of complex systems with multi-states and difficult to obtain accurate failure rates, and the problems of T-S fault tree in the system reliability analysis, such as complex calculation and inverse reasoning, etc., a reliability assessment method based on T-S fault tree and interval-valued fuzzy multi-state Bayesian network is proposed. Based on the analysis of the T-S fault tree, it is mapped into a Bayesian network. In the existing fuzzy Bayesian network reliability analysis method, the interval variable is introduced. Fuzzy processing is carried out to construct an interval-valued triangular fuzzy Bayesian network. Combining the characteristics of interval fuzzy subsets and Bayesian networks, a solution algorithm for leaf node failure probability, interval fuzzy importance, and interval fuzzy posterior probability is obtained under the condition of knowing only the root node failure status. Finally, the method is used to evaluate the reliability of the expansion system of the tunnel stacker, and it is verified that this method can accurately and effectively identify the weak links of the polymorphic system, and provide guidance for maintenance and diagnosis.