Overlap function-based fuzzy β-covering relations and fuzzy β-covering rough set models

As an extension of the fuzzy covering, fuzzy β-covering has garnered significant scholarly concern. However, certain limitations impede its practical application. To address the issue of inaccurate characterization of object relationships caused by the current fuzzy β-neighborhood operator, four new operators were developed, which exhibit both symmetry and reflexivity through the utilization of established fuzzy β-neighborhood operators, overlap functions and grouping functions. Furthermore, we demonstrate that these operators satisfy the fuzzy β-covering relation, and utilize the fuzzy β-covering relations on the basis of overlap functions to propose new fuzzy β-covering rough set model. Additionally, incorporating the attribute significance, an attribute reduction algorithm is designed. Ultimately, we substantiate the rationality and superiority of our proposed algorithm by conducting a sequence of experiments. Meanwhile, we analyze the impacts of varying overlap functions and β values on the algorithm's performance.