Connectedness and Stratification of Single-Valued Neutrosophic Topological Spaces

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.

Single-Valued Neutrosophic Roughness via Ideals

“…Others as Wang et al [4] defined the single-valued neutrosophic set concept. In (2020, 2021) Saber et al [5][6][7][8][9][10][11] introduced and studied the concepts of single-valued neutrosophic ideal, single-valued neutrosophic ideal open local function, connectedness in single-valued neutrosophic topological spaces (£, ˜ σ , ˜ ς , ˜ δ ) and compactness in single-valued neutrosophic ideal topological spaces.…”

Fuzzy (Almost, δ) Ideal Continuous Mappings

“…We must state that this subject has been researched by physicists [7,[10][11][12][13] as well as by others. El-Naschie has shown that the notion of fuzzy topology in Ŝostak sense has very important applications in quantum particle physics especially about both string theory and ε (∞) theory [8,9,12,15,16] and also Saber et al [30][31][32][33][34][35][36][37][38][39] who familiarized the concepts of single-valued neutrosophic ideal open local function and single-valued neutrosophic topological space. In this paper, we give a decomposition of fuzzy continuity, fuzzy ideal continuity and fuzzy ideal α-continuity, and we obtain several characterizations of fuzzy α-I-continuous functions.…”

On Single Valued Neutrosophic Regularity Spaces

“…Meanwhile, Kim et al [5,6] inspected the single valued neutrosophic relations (SVNRs) and symmetric closure of SVNR, respectively. Recently, Saber et al [7][8][9] introduced the concepts of single-valued neutrosophic ideal open local function and single-valued neutrosophic topological space. Many of their applications appear in the studies of Das et al [10].…”