Affiliations: [a] College of Mathematics and Information Science, Shaanxi Normal University, Xi’an, P.R. China
| [b] Department of Computer Science, University of Regina, Regina, Canada
| [c] School of Management, Xi’an Jiaotong University, Xi’an, P.R. China
| [d] College of Economics, Northwest University of Political Science and Law, Xi’an, P.R. China
| [e] College of Science, Xi’an Shiyou University, Xi’an, P.R. China
Correspondence:
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Corresponding author. Hai-Long Yang, College of Mathematics and Information Science, Shaanxi Normal University, Xi’an 710119, P.R. China. Tel.: +86 13572106227; Fax: +86 2985310277; E-mail: yanghailong@snnu.edu.cn.
Abstract: Smarandache initiated neutrosophic sets (NSs) which can be used as a mathematical tool for dealing with indeterminate and inconsistent information. In order to apply NSs conveniently, single valued neutrosophic sets (SVNSs) were proposed by Wang et al. In this paper, we propose single valued neutrosophic relations (SVNRs) and study their properties. The notions of anti-reflexive kernel, symmetric kernel, reflexive closure, and symmetric closure of a SVNR are introduced, respectively. Their accurate calculate formulas and some properties are explored. Some examples are also given. Finally, single valued neutrosophic relation mappings and inverse single valued neutrosophic relation mappings are introduced, and some interesting properties are also obtained.
Keywords: Single valued neutrosophic sets, single valued neutrosophic relations, kernels, closures, single valued neutrosophic relation mappings, inverse single valued neutrosophic relation mappings
