Abstract
This paper aims to introduce the notion of r-single-valued neutrosophic connected sets in single-valued neutrosophic topological spaces, which is considered as a generalization of r-connected sets in Šostak’s sense and r-connected sets in intuitionistic fuzzy topological spaces. In addition, it introduces the concept of r-single-valued neutrosophic separated and obtains some of its basic properties. It also tries to show that every r-single-valued neutrosophic component in single-valued neutrosophic topological spaces is an r-single-valued neutrosophic component in the stratification of it. Finally, for the purpose of symmetry, it defines the so-called single-valued neutrosophic relations.
Highlights
IntroductionSmarandache had established a generalization of intuitionistic fuzzy sets
Under a neutrosophic environment, Smarandache had established a generalization of intuitionistic fuzzy sets
We introduce the concept of r-single-valued neutrosophic connected sets and r-single-valued neutrosophic component in single-valued neutrosophic topological spaces
Summary
Smarandache had established a generalization of intuitionistic fuzzy sets. His neutrosophic framework has a very large impact of constant applications for different fields in applied and pure sciences. In 1965, Zadeh [1] defined the so-called fuzzy sets (F S) and, later on, Atanassov [2] defined the intuitionistic fuzzy sets (IF S) in 1983. The main concept of fuzzy topology (F T ) was defined by Chang [3]. Lowen [4] gave the introduction to the concept of stratified fuzzy topology in the sense of Chang’s fuzzy topology. Lee et al and Liu et al in their papers [5,6] investigated fuzzy connectedness (F -connected) in fuzzy topological spaces
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