Open Access

ARTICLE

On Single Valued Neutrosophic Regularity Spaces

by Yaser Saber^1,2, Fahad Alsharari^1,6,*, Florentin Smarandache³, Mohammed Abdel-Sattar^4,5

1 Department of Mathematics, College of Science and Human Studies, Hotat Sudair, Majmaah University, Majmaah, 11952, Saudi Arabia
2 Department of Mathematics, Faculty of Science, Al-Azhar University, Assiut, 71524, Egypt
3 Department of Mathematics, University of New Mexico, Gallup, NM 87301, USA
4 Department of Mathematics, College of Science and Arts King Khaled University, Mhayal Asier, 61913, Saudi Arabia
5 Department of Mathematics and Computer Science, Faculty of Science, Beni-Suef University, Beni-Suef, 62511, Egypt
6 Department of Mathematics, College of Science and Arts, Jouf University, Gurayat, 77455, Saudi Arabia

* Corresponding Author: Fahad Alsharari. Email:

(This article belongs to the Special Issue: Advances in Neutrosophic and Plithogenic Sets for Engineering and Sciences: Theory, Models, and Applications (ANPSESTMA))

Computer Modeling in Engineering & Sciences 2022, 130(3), 1625-1648. https://doi.org/10.32604/cmes.2022.017782

Received 06 June 2021; Accepted 03 August 2021; Issue published 30 December 2021

Abstract

This article aims to present new terms of single-valued neutrosophic notions in the Šostak sense, known as single-valued neutrosophic regularity spaces. Concepts such as r-single-valued neutrosophic semi £-open, r-single-valued neutrosophic pre-£-open, r-single valued neutrosophic regular-£-open and r-single valued neutrosophic α£-open are defined and their properties are studied as well as the relationship between them. Moreover, we introduce the concept of r-single valued neutrosophic θ£-cluster point and r-single-valued neutrosophic γ £-cluster point, r-θ£-closed, and θ£-closure operators and study some of their properties. Also, we present and investigate the notions of r-single-valued neutrosophic θ£-connectedness and r-single valued neutrosophic δ£-connectedness and investigate relationship with single-valued neutrosophic almost £-regular. We compare all these forms of connectedness and investigate their properties in single-valued neutrosophic semiregular and single-valued neutrosophic almost regular in neutrosophic ideal topological spaces in Šostak sense. The usefulness of these concepts are incorporated to multiple attribute groups of comparison within the connectedness and separateness of θ£ and δ£.

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Keywords

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