Some twin approximation operators on covering approximation spaces

• We simplified the definitions of some known approximation operators.
• We define the twin approximation operators.
• We give some concrete examples about the twin approximation operators.
• We investigate the relationships among the given twin approximation operators.
• We reveal the topological properties of the given twin approximation operators.

Complementary neighborhood is a conception analogous to the neighborhood that we first introduced in a former paper. In this paper, we show that two different approximation operators may have a close relationship, namely, they can be defined almost in the same way except that one uses the notion of neighborhood and another uses the complementary neighborhood. We call such two approximation operators the twin approximation operators. We give some concrete examples of the twin approximation operators. Through detailed investigation on the relationship between the neighborhood and the complementary neighborhood, we further study the properties of given twin approximation operators and investigate the relationships between different twins. We also reveal the topological properties of those twin approximation operators.