Further research of single valued neutrosophic rough sets

Smarandache (1998) initiated neutrosophic sets (NSs) as a new mathematical tool for dealing with problems involving incomplete, indeterminant and inconsistent knowledge. By simplifying NSs, Smarandache (1998) and Wang et al. (2010) proposed the concept of single valued neutrosophic sets (SVNSs) and studied some properties of SVNSs. In this paper, we mainly investigate the topological structures of single valued neutrosophic rough sets which is constructed by combining SVNSs and rough sets. Firstly, we introduce the concept of single valued neutrosophic topological spaces. Then, we discuss the relationships between single valued neutrosophic approximation spaces and single valued neutrosophic topological spaces. Concretely, a reflexive and transitive single valued neutrosophic relation can induce a single valued neutrosophic topological space such that its single valued neutrosophic interior and closure operators are the lower and upper approximation operators induced by this single valued neutrosophic relation, respectively. Conversely, a single valued neutrosophic interior (closure, respectively) operator derived from a single valued neutrosophic topological space is just the single valued neutrosophic lower (upper, respectively) approximation operator derived from a single valued neutrosophic approximation space under some conditions. Finally, we show there exists a one-to-one correspondence between the set of all reflexive and transitive single valued neutrosophic relations and the set of all single valued neutrosophic rough topologies.