Modern classes of fuzzy $\alpha$-covering via rough sets over two distinct finite sets

Following the research of Yang and Atef proposing new classes of fuzzy $\beta$-covering via rough sets types over 2-featured universes, we present some modern classes of fuzzy $\alpha$-covering via rough sets over two distinct finite sets using fuzzy $\alpha$-neighborhoods for two distinct points over 2-distinct finite universes. Throughout this research, we present the ideas of the fuzzy $\alpha$-neighborhood system and the fuzzy $\alpha$-neighborhood for two distinct points over two distinct finite sets and investigate the relations of the fuzzy $\alpha$-neighborhood system, fuzzy $\alpha$-minimal and $\alpha$-maximal descriptions over two distinct finite sets. Moreover, some kinds of fuzzy $\alpha$-neighborhoods are proposed. In addition, some new types of fuzzy $\alpha$-coverings over two finite sets are established. Finally, numerous topological characteristics of fuzzy $\alpha$-covering via rough set types are investigated.