Choquet-like Integrals with Rough Attribute Fuzzy Measures for Data-driven Decision-making

As nonlinear fuzzy aggregation functions, Choquet-like integrals with fuzzy measures are widely used in decision-making, rule-based classification, and information fusion. However, the fuzzy measures in the existing Choquet-like integrals are typically provided via human intervention, not driven by data, thereby significantly limiting the automation level of the resulting systems. As an effective data-driven tool, rough set theory has shown its great potential for attribute reduction while dealing with many real-world problems. Nonetheless, different reduction methods generally lead to different outcomes, while obtaining all reductions exhaustively is NP-hard. Therefore, it is an interesting challenge to induce fuzzy measures by rough sets, using corresponding Choquet-like integrals to establish a data-driven decision-making method that is applicable for practical problems. To tackle this challenge, Choquet-like integrals based on rough attribute fuzzy measures are introduced here. Also, a novel decision-making model exploits the resulting Choquet-like integrals for problems of fault diagnosis and classification. First, a form of data-driven fuzzy measure is introduced through the specificity measures of rough sets, which is named as rough attribute fuzzy measure. Second, for decision information systems, the concept of p-matching degree between two objects is defined over different domain attributes. Third, based on rough attribute fuzzy measures and p-matching degrees, a type of Choquet-like integral is established. Subsequently, the new decision-making network model and its associated computational algorithm are provided. The proposed approach is evaluated over both numerical examples and public datasets to demonstrate its efficacy.