A novel method for incremental feature selection with fuzzy β-covering

Fuzzy β-covering has attracted significant academic attention due to its enhanced capability in representing uncertain information, surpassing traditional fuzzy covering approaches. However, the initial formulation of fuzzy β-covering rough sets fails to guarantee the inclusion relation between the upper and lower approximations. In addition, unlike partitions, coverings may contain redundant elements while still satisfying the covering property, making it crucial to assess whether any redundant elements are present. Nevertheless, the incremental mechanism for the reduct of fuzzy β-covering is still unclear. To address these limitations, we first introduce generalized fuzzy β-neighborhoods and derive the corresponding fuzzy β-covering rough sets, ensuring the inclusion relation between the upper and lower approximations. On this basis, a feature selection method with fuzzy β-covering based on relative discernibility relation is proposed, which only calculates the fuzzy positive region in the process of obtaining relative discernibility relation. Furthermore, to investigate incremental mechanisms for reduct of fuzzy β-covering, we develop novel incremental feature selection algorithms for fuzzy β-covering. Experimental comparisons with both non-incremental and incremental algorithms demonstrate that our proposed methods effectively identify the reduct of fuzzy β-covering, showcasing superior computational efficiency.