Generalized fuzzy rough approximation operators based on fuzzy coverings

This paper focuses on the generalization of covering-based rough set models via the concept of fuzzy covering. Based on a fuzzy covering of a universe of discourse, two pairs of generalized lower and upper fuzzy rough approximation operators are constructed by means of an implicator I and a triangular norm T. Basic properties of the generalized fuzzy rough approximation operators are investigated. Topological properties of the generalized fuzzy rough approximation operators and characterizations of the fuzzy T-partition by the generalized upper fuzzy rough approximation operators are further established. When fuzzy coverings are a family of R-foresets or R-aftersets of all elements of a universe of discourse with respect to a fuzzy binary relation R, the corresponding generalized fuzzy rough approximation operators degenerate into the fuzzy-neighborhood-oriented fuzzy rough approximation operators. Combining with the fuzzy-neighborhood-operator-oriented fuzzy rough approximation operators, conditions under which some or all of these approximation operators are equivalent are subsequently determined.