Near approximations via general ordered topological spaces

TL;DR

This paper explores near approximation concepts within general ordered topological spaces, extending rough set theory by integrating binary relations and topology to better handle imperfect knowledge.

Contribution

It introduces a generalized framework for near approximation using ordered topological spaces, expanding the theoretical understanding of rough sets with new concepts and results.

Findings

Defined increasing and decreasing near approximations

Introduced near boundary regions and near accuracy measures

Provided proofs, implications, and illustrative examples

Abstract

Rough set theory is a new mathematical approach to imperfect knowledge. The notion of rough sets is generalized by using an arbitrary binary relation on attribute values in information systems, instead of the trivial equality relation. The topology induced by binary relations is used to generalize the basic rough set concepts. This paper studies near approximation via general ordered topological approximation spaces which may be viewed as a generalization of the study of near approximation from the topological view. The basic concepts of some increasing (decreasing) near approximations, increasing (decreasing) near boundary regions and increasing (decreasing) near accuracy were introduced and sufficiently illustrated. Moreover, proved results, implications and add examples.