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.
Highlights
Most of traditional methods for formal modeling, reasoning and computing are crisp, deterministic and precise in character
We introduce the concept of soft points, prove that soft sets can be translate into soft point sets and it is convenient to deal with soft sets as same as ordinary sets
Remark 3.12 Theorem 3.11 illustrates that the soft contain relation and the soft equal relation can be respectively translated into the contain relation and the equal relation on two soft point sets and vice versa
Summary
Most of traditional methods for formal modeling, reasoning and computing are crisp, deterministic and precise in character. There are several theories: probability theory, fuzzy set theory 27, interval mathematics, and rough set theory 22, which we can consider as mathematical tools for dealing with uncertainties. The upper and lower approximation operations are two core notions in rough set theory They can be seen as a closure operator and an interior operator of the topology induced by an equivalence relation on a universe. The organization of this paper is as follows: In Section 2,we briefly recall basic concepts about rough sets, soft sets and soft topological spaces. We briefly recall basic concepts about rough sets, soft sets and soft topological spaces. We only consider the case where both U and E are nonempty finite sets
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