New Rough Approximations Based on E‐Neighborhoods

This paper puts forward some rough approximations which are motivated from topology. Given a subset R ⊆ U × U , we can use 8 types of E ‐neighborhoods to construct approximations of an arbitrary X ⊆ U on the one hand. On the other hand, we can also construct approximations relying on a topology which is induced by an E ‐neighborhood. Properties of these approximations and relationships between them are studied. For convenience of use, we also give some useful and easy‐to‐understand examples and make a comparison between our approximations and those in the published literature.