Definable Subsets in Covering Approximation Spaces

Covering approximation spaces is a class of important generalization of approximation spaces. For a subset X of a covering approximation space (U, C), is X definable or rough? The answer of this question is uncertain, which depends on covering approximation operators endowed on (U, C). Note that there are many various covering approximation operators, which can be endowed on covering approximation spaces. This paper investigates covering approximation spaces endowed ten covering approximation operators respectively, and establishes some relations among definable subsets, inner definable subsets and outer definable subsets in covering approximation spaces, which deepens some results on definable subsets in approximation spaces. Keywords—Covering approximation space, covering approximation operator, definable subset, inner definable subset, outer definable subset.