Multi-fuzzy β-covering fusion based accuracy and self-information for feature subset selection

Granular structures are mathematical representations of knowledge used in granular computing. As a new type of granular structure, fuzzy β-covering has attracted widespread attention in recent years. One of the most critical related studies is measuring the uncertainty of fuzzy β-coverings. It is the foundation for studying fuzzy β-covering applications, such as classification and clustering. In this paper, we investigate the uncertainty measures of fuzzy β-coverings from the viewpoints of algebra and information theory, and propose the corresponding methods of fuzzy β-covering reduction for feature selection. Firstly, a generalized fuzzy β-neighborhood and the associated fuzzy β-covering rough sets are presented. Secondly, three types of accuracy measures of fuzzy β-coverings are constructed via fuzzy β-covering rough sets. On this basis, the self-information of fuzzy β-coverings is defined by fusing accuracy and roughness measures. Based on the proposed uncertainty measures, two heuristic methods of fuzzy β-covering reduction are put forward and the corresponding algorithms are designed for monotonic feature selection. Finally, the performance of the proposed methods is compared with several mainstream feature selection methods and experimental results demonstrate the rationality and superiority of our proposed methods.