Soft points, s-relations and soft rough approximate operations

Abstract

Soft set theory is a new mathematical tool to deal with uncertain problems. Since soft sets are defined by mappings and they lack “points”, managing them is not convenient. In this paper, the concept of soft points is introduced and the relationship between soft points and soft sets is investigated. We prove that soft sets can be translated into soft point sets and may be expediently handled like ordinary sets. Moreover, we propose s-relations on soft sets. By means of soft points and these results, a pair of soft rough approximate operations is defined. Serial, reflexive, symmetric, transitive and Euclidean s-relations are characterized by using soft rough approximate operations. In addition, we research soft topologies induced by a reflexive s-relation on a special soft set and gives their structure.