A three-way decision method with probability dominance relation in interval-valued hesitant fuzzy environment for marine steam turbine fault diagnosis

As an important measure to solve the multi-attribute decision-making (MADM) problems, the establishment of three-way decision (3WD) approach has been adopted not only stay at the theoretical level, but also applied to various practical problems. However, there exists a research gap of employing three-way decision (3WD) approach to enrich fault diagnosis based on interval-valued hesitant fuzzy environment (IVHF). To address these challenges, this paper proposes a neighborhood \((\delta , \eta )\) $(\delta ,\eta )$ three-way decision (3WD) approach to solve fault diagnosis under the IVHF environment. First, the relative loss function (RLF) is considered as a wonderful substitution for the loss function, which usually serves as a conventional tool to consider the losses more comprehensively. Furthermore, an interval-valued hesitant fuzzy weight averaging operator is detected when creating the aggregated loss function. Moreover, a neighborhood \((\delta , \eta )\) $(\delta ,\eta )$ probability dominance similarity relation is taken instead of the equivalence relation, which is regarded as an effective way to calculate the outranked class. Finally, the proposed method is verified by a marine turbine fault diagnosis case. Results of parameter analysis and comparison analysis show that the proposed approach can diagnose the fault of marine turbine rationality and stability.