Optimization attribute reduction with fuzzy rough sets based on algorithm stability

Fuzzy rough sets (FRSs) theory is an important granular computing method to deal with incomplete information systems, and the attribute reduction is a basic key issue in FRSs. In this paper, we construct a novel framework for selecting the optimal reduct of FRSs with theoretical guarantees by considering the influence of granule size and incorporating the stability theory in machine learning. Firstly, a granule-based soft-margin support vector machine algorithm (GSSVM) is proposed for classification tasks by introducing the λ-conditional entropy into the hinge loss function, which takes the impact of granule size on data loss into account. Secondly, according to stability theory, the generalization error bound of the GSSVM algorithm is derived as a theoretical guarantee for selecting the optimal reduct. Finally, an optimization attribute reduction algorithm (RDROAR) based on the relative discernibility relation is presented by removing the attributes with low importance in a reduct while ensuring the generalization ability of GSSVM. Numerical experiments prove the effectiveness of the improved algorithm as well as verify the rationality and effectiveness of the optimal reduct.