Novel classes of fuzzy β-covering-based rough set over two distinct universes

For a deep study of Yang's approach of fuzzy β-covering based rough sets over two distinct universes, we propose novel classes of fuzzy β-covering-based rough set models by introducing the concepts of fuzzy β-minimal and β-maximal descriptions over two distinct universes in this paper. First of all, we propose the definitions of fuzzy β-minimal and β-maximal descriptions over two distinct universes and investigate some of their characteristics. Secondly, we propose four novel types of fuzzy β-neighborhoods over two distinct universes and investigate some of their properties. Meanwhile, we study four types of β-neighborhoods over two distinct universes. Then, we define four types of fuzzy β-covering-based rough set models over two distinct universes by using fuzzy β-neighborhoods. Moreover, some basic properties and topological characters of these novel fuzzy β-covering-based rough approximation operators are investigated. Especially, the relationship among these models are also discussed. Finally, we present some remarks and propositions to clarify the contributions and the relationship between our models and the others.