In this work, a generalized fuzzy subset (GFS) method is proposed to assess the time-varying multi-state reliability of the perturbation failure coupling measurement (PFCM) system. First, a perturbation-failure coupling mechanism is designed to define the propagation chain of perturbations so as to integrate all the possible perturbations as the inputs of the GFS method. Second, to assess the time-varying multi-state reliability, a GFS reliability model is constructed based on the composite limit state. Furthermore, the concept of the uncertain subset boundary is presented to conduct the reliability assessment via a group of embedded interval type-2 fuzzy sets. To address the deficiency of the GFS reliability model, a data-driven strategy is designed to establish the implicit relation between the limited expert knowledge and the membership function. Finally, the experimental tests are carried out to examine the superiority of the GFS method, and parametric studies are also conducted to study the reliability of the PFCM system.