Topologies and approximation operators induced by binary relations

TL;DR

This paper explores new topologies and approximation operators in rough set theory induced by binary relations, analyzing their interrelations and providing examples of lower and upper approximations.

Contribution

It introduces novel topologies and approximation operators based on binary relations and neighborhood operators, expanding the mathematical framework of rough set theory.

Findings

New topologies induced by binary relations are characterized.

Relationships among the induced topologies are analyzed.

Examples of lower and upper approximations are provided.

Abstract

Rough set theory is an important mathematical tool for dealing with uncertain or vague information. This paper studies some new topologies induced by a binary relation on universe with respect to neighborhood opera- tors. Moreover, the relations among them are studied. In additionally, lower and upper approximations of rough sets using the binary relation with respect to neighborhood operators are studied and examples are given.