On the Point Closure System by Tolerance

Abstract

Tolerances provide a general tool for studying indiscernibility phenomena that are ubiquitous in data analysis and knowledge system. The collections of blocks, classes and point closures form three different coverings closely related to the given tolerance. The structure and property of the induced point closure system are investigated, and axiomizations of three types of covering based rough approximation operators are discussed from the relational viewpoint, in which point closure system plays an important role.