A fuzzy β-covering rough set model for attribute reduction by composite measure

Fuzzy β-covering rough sets, the state-of-the-art theory of covering-based rough sets, have received much attention. The key step in establishing a fuzzy rough set model is to construct the fuzzy binary relation between objects. However, under the environment of multiple fuzzy β-coverings, the existing fuzzy β-neighborhoods either do not satisfy the reflexivity of relation or rely on R-implication operators. For this reason, these fuzzy β-neighborhoods are not very suitable for characterizing the similarity between objects. In order to characterize the similarity between objects under the environment of multiple fuzzy β-coverings more reasonably, this paper constructs a β-neighborhood that satisfies the reflexivity and does not depend on any fuzzy operators. On this basis, a novel fuzzy β-covering rough set model is established. Based on the proposed model, several monotonic uncertainty measures of fuzzy β-coverings are defined. Finally, an attribute reduction method is presented, and the experimental analysis demonstrates the effectiveness of our proposed method compared with the other five excellent attribute reduction methods.