Risk evaluation in failure mode and effect analysis: AHP-VIKOR method with picture fuzzy rough number

One of the most commonly used reliability analysis methods is failure mode and effects analysis, which is very effective at finding, assessing, and addressing potential failure modes in a variety of commercial applications. Its wide-ranging viewpoint facilitates the investigation of potential failures, causes, and effects in designs, products, and processes. On the other hand, traditional failure mode and effects analysis is often criticized for its shortcomings in identifying the weights of the criteria, identifying the failure modes’ relative risk, and managing ambiguity in the risk assessment process. To overcome these complications, this article considers the analytic hierarchy process and the VIKOR method with picture fuzzy rough numbers. Primarily, a picture fuzzy rough number is offered to represent an expert’s expertise, compile group risk assessments, and address subjectivity and uncertainty in risk assessment. Then, an extended analytic hierarchy process based on picture fuzzy rough numbers is offered to regulate the criterion’s weights. An extended VIKOR method based on picture fuzzy rough number is used to rate the failure scenarios based on risk priority. A case study of the check valve in real life is used to validate the effectiveness of the suggested failure mechanism and effect analysis. The effectiveness of the suggested picture fuzzy rough multi-criteria group decision-making method is demonstrated by comparative studies, which also highlight its significant advantages in managing subjectivity and ambiguity during the evaluation of failure modes.