Nearness of Objects. Approximation Space Model Revisited

This paper is devoted to a nearness relation in an Efremovic̆proximity space. The basic approach is to consider the nearness of the upper and lower approximation of a set introduced by Z. Pawlak during the early 1980s as a foundation for rough sets. Two forms of nearness relations are considered, namely, a spatial EFand a descriptive EFrelation. This leads to a study of the nearness of objects either spatially or descriptively in the approximation of a set. The 2007 nearness approximation space model is refined and extended in this paper, leading two new forms of nearness approximation spaces. There is a natural transition from the two forms of approximation introduced in this article to nearness of information granules. This leads to the study of methods of inducing approximations of nearness relations for information granules and the benefits of this approach for approximate reasoning over granular computations.