Failure mode and effect analysis (FMEA) is an effective quality management technique widely used in various industries to improve the reliability and safety of systems, products, processes, and services. In traditional FMEA, the ranking of failure modes is carried out by the risk priority number (RPN), which is calculated by the product of severity (S), occurrence (O), and detection (D). Nevertheless, the normal FMEA has many inherent defects in assessing and ranking failure modes. Therefore, in this paper, we present a new FMEA model, which integrates probabilistic linguistic term sets (PLTSs) and fuzzy Petri nets (FPNs) for the risk assessment and prioritization of failure modes. Specifically, the PLTSs are used to capture the uncertainty of FMEA team members' subjective judgments, and the FPNs are established to acquire the risk priority of the identified failure modes. Besides, a technique for order preference by similarity to an ideal solution (TOPSIS)-based weighting method is proposed to determine the objective weight of each team member. Finally, a marine-ship system risk assessment example is provided to illustrate the suggested FMEA and a comparative analysis is conducted to assess its effectiveness and usefulness. The results show that the new FMEA approach can produce more reliable and reasonable risk ranking result of failure modes. INDEX TERMS Failure mode and effect analysis (FMEA), probabilistic linguistic term set (PLTS), TOPSIS method, fuzzy Petri net (FPN). The associate editor coordinating the review of this manuscript and approving it for publication was Zhiwu Li.