Novel Models of Fuzzy Rough Coverings Based on Fuzzy α-Neighborhood and its Application to Decision-Making

Recently, the concept of a fuzzy $\alpha $ - neighborhood operator with reflexivity was established and a fuzzy rough set covering based on a fuzzy $\alpha $ - neighborhood operator was defined by Zhang et al. As a generalization of Zhang et al. models, this article aims to introduce the notion of a complementary fuzzy $\alpha $ -neighborhood operator with reflexivity. Also, three new kinds of a fuzzy rough set covering based on a fuzzy $\alpha $ - neighborhood operator are constructed and some of their properties are discussed. Further, the relationships between these models are studied. Several new kinds of a fuzzy rough set covering based variable precision are put forward and the relevant properties are constructed. Finally, an application to MADM to solve realistic problems is illustrated.