A novel approach to fuzzy rough sets based on a fuzzy covering

This paper proposes an approach to fuzzy rough sets in the framework of lattice theory. The new model for fuzzy rough sets is based on the concepts of both fuzzy covering and binary fuzzy logical operators (fuzzy conjunction and fuzzy implication). The conjunction and implication are connected by using the complete lattice-based adjunction theory. With this theory, fuzzy rough approximation operators are generalized and fundamental properties of these operators are investigated. Particularly, comparative studies of the generalized fuzzy rough sets to the classical fuzzy rough sets and Pawlak rough set are carried out. It is shown that the generalized fuzzy rough sets are an extension of the classical fuzzy rough sets as well as a fuzzification of the Pawlak rough set within the framework of complete lattices. A link between the generalized fuzzy rough approximation operators and fundamental morphological operators is presented in a translation-invariant additive group.