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 θ β S j -open sets are defined and the connections among them are given. Later, new approximations are presented with the help of the

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... tioned 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 θ β S j -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.