Generalized fuzzy rough approximation operators based on fuzzy coverings Original Research Article

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 image and a triangular norm image. 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 image 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.