<p>Failure modes and effect analysis (FMEA) is a widely-used method for mitigating potential risks and enhancing reliability across various fields. However, many previous FMEA-related studies have inadequately addressed the uncertainty inherent in variable information, and they often assume that the decision-makers (DMs) are fully rational and neglect their cognitive behaviors. Besides, the existing studies often overlook the interdependencies among risk factors, resulting in compromised accuracy of risk priority. To resolve the abovementioned drawbacks, this paper develops an integrated failure analysis framework that employs variable precision rough set (VPRS) to manage uncertain failure information, incorporates the prospect theory to reflect DMs’ gain and loss preferences, applies the Choquet integral to aggregate interdependent risk factors, and adopts the Technique for Order Preference by Similarity to an Ideal Solution to prioritize failure modes. The proposed method combines the strengths of VPRS theory in effectively handling ambiguity to discern preference variations in uncertain environments, the benefits of the prospect theory in capturing diverse attitudes toward DMs’ gains and losses while accommodating their bounded rationality, and the capacity of Choquet integral in modeling interrelationships among risk factors. In practice, the proposed method is tested on the pre-screening and triage data from M Hospital. Moreover, a further comparison confirms the advantages of our approach.</p>