New Topological Approaches to Rough Sets via Subset Neighborhoods

Abstract

This paper aims to obtain new types of approximations by using topological concepts. Firstly different kinds of topologies are generated by subset neighborhoods and relationships between them are studied. Then j-subset approximations based on these topologies are introduced and their basic properties are examined. In addition to this S-j-near open and theta beta(Sj)-open sets are defined and the connections among them are given. Later new approximations are presented with the help of the aforementioned sets and their main properties are investigated. Furthermore the proposed approximations are compared both with themselves and with the previous one. From this it is shown that the approximations based on theta beta(Sj)-open sets are more accurate than those based on S-j-open and S-j-near open sets under arbitrary binary relation and than those based on j-open sets under similarity relation. Finally a real-life problem related to COVID-19 is addressed to highlight the importance of applying the proposed approximations.