Multigranulation variable-scale fuzzy neighborhood measures and corresponding Choquet-like integrals for feature selection

Abstract

Choquet-like integrals, a nonlinear fuzzy aggregation function, are diffusely applied in several real problems. However, the corresponding fuzzy measures in them are provided by human intervention and not by data-driven methods. As an effective knowledge representation tool, rough set models in different approximation spaces are established for data processing. Particularly, the multigranulation fuzzy β-covering approximation space has been concerned with only a single scale β∈(0,1]. However, different granulation structures should have different scales. Therefore, establishing a multigranulation approximation space with a variable scale by inducing fuzzy measures through data-driven methods and using corresponding Choquet-like integrals in practical problems is a significant challenge. To address this challenge, the notion of multigranulation variable-scale fuzzy Θ-covering group approximation space is presented here, as well as multigranulation variable-scale fuzzy neighborhood measures in it. Furthermore, Choquet-like integrals with the presented measures are constructed to solve the issue of feature selection (i.e., attribute reduction) under the new approximation spaces. Firstly, the concept of multigranulation variable-scale fuzzy Θ-covering group approximation space is presented, where different fuzzy β-coverings have different scales β∈Θ. Moreover, multigranulation variable-scale fuzzy neighborhood measures in it, as fuzzy measures, are presented. Subsequently, Choquet-like integrals with multigranulation variable-scale fuzzy neighborhood measures are constructed. A novel attribute reduction method under Choquet-like integrals with multigranulation variable-scale fuzzy neighborhood measures is proposed for any decision information table. Finally, the presented method is selected for solving problems of classification and diagnosis of rolling bearing faults. Several public data sets are used to demonstrate the effectiveness and feasibility of the presented methods mentioned above.