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

Abstract

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.

Keywords

• α-neighborhood operator%22%2C%22default_operator%22%3A%22AND%22%7D%7D%7D"> Complementary fuzzy <italic xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">α</italic>-neighborhood operator
• fuzzy rough set covering
• fuzzy rough set covering based variable precision
• multi-attribute decision making