Classification of coverings in the finite approximation spaces

Moreover, based on the relationship between the neighborhood and the complementary neighborhood, we find that each class of coverings has a dual class, and each pair of approximation operators has a dual pair of approximation operators. For a finite universe, considering one pair of approximation operators under one equivalence class of coverings is equivalent to considering its dual approximation operator pair under the dual class of coverings. Finally, we also present a sufficient condition under which, for any given pair of neighborhood-based lower and upper approximation operators, two coverings of the universe U generate the same pair of approximations of each X⊂U if and only if they belong to the same equivalence class.