New Rough Approximations Based on E-Neighborhoods

Abstract

This paper puts forward some rough approximations which are motivated from topology. Given a subset $R\subseteq U\times U$ , we can use 8 types of $E$ -neighborhoods to construct approximations of an arbitrary $X\subseteq U$ 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.