Extended Concept of Generalized Fuzzy Rough Sets on Asymmetric Fuzzy Coverings

This paper extends and generalizes fuzzy rough sets approximated on fuzzy coverings of the universe induced by a weak fuzzy similarity relation. The weak fuzzy similarity relation is considered as a generalization of fuzzy similarity relation in representing a more realistic relationship between two objects in which it has weaker symmetric and transitive properties. The generalization of fuzzy rough sets approximations is discussed based on two interpretations, object-oriented generalization and class-oriented generalization. More concepts of generalized fuzzy rough set approximations are introduced and defined representing more alternatives to provide interval-valued fuzzy sets. Some properties of the concepts are examined.