On single valued neutrosophic relations

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. Finally, single valued neutrosophic relation mappings and inverse single valued neutrosophic relation mappings are introduced, and some interesting properties are also obtained.

A Novel Rough Set Model in Generalized Single Valued Neutrosophic Approximation Spaces and Its Application

“…Yang et al [24] proposed the notions of single-valued neutrosophic relations from U to V and generalized single-valued neutrosophic approximation spaces as follows.…”

“…Ye [23] proposed similarity measures between SVNSs based on the tangent function and a multi-period medical diagnosis method based on the similarity measure and the weighted aggregation of multi-period information to solve multi-period medical diagnosis problems with single-valued neutrosophic information. Yang et al [24] proposed SVNRs and studied some kinds of kernels and closures of SVNRs. Ye [25] presented a simplified neutrosophic harmonic averaging projection measure and its multiple attribute decision making method with simplified neutrosophic information.…”

On single valued neutrosophic refined rough set model and its application

“…Subsequently, Wang et al [17] raised single valued neutrosophic sets (SVNSs). Yang et al [18] discussed single valued neutrosophic relations (SVNRs) and explored their properties in detail. In order to describe more accurate information, Ye [19] introduced single valued neutrosophic refined sets in which the three neutrosophic components T, I, F are refined (divided) into T 1 [20] presented distance and similarity measure of single valued neutrosophic refined sets and applied the measure to medical diagnosis problems.…”

Generalized interval neutrosophic rough sets and its application in multi-attribute decision making

“…Yang et al [33] studied the single valued neutrosophic relations in detail. Biswas et al [2] studied TOPSIS method for multi-attribute group decision-making under single-valued neutrosophic environment.…”