Mathematics and Statistics Vol. 12(1), pp. 16 - 23
DOI: 10.13189/ms.2024.120103
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Other New Versions of Generalized Neutrosophic Connectedness and Compactness and Their Applications

Alaa. M. F. AL. Jumaili ^*
Department of Mathematics, College of Education for Pure Sciences, University of Anbar, Iraq

ABSTRACT

The concepts of neutrosophic connectedness and compactness between neutrosophic sets find extensive applications in various fields, including sensor networks, physics, mechanical engineering, robotics and data analysis involving numerous variables. Neutrosophic set theory also plays a pivotal role in addressing complex problems in engineering, environment science, economics, and advanced mathematical disciplines. Hence, this paper aims to extend the classical definitions of neutrosophic connectedness and compactness within neutrosophic topological spaces. We introduce new classes of neutrosophic connectedness and compactness, specifically, neutrosophic δ-ß-connectedness and neutrosophic δ-ß-compactness, defined using a generalized neutrosophic open set known as "neutrosophic δ-ß-open sets". We explore several essential properties and characterizations of these spaces and introduce new notions of neutrosophic covers, which lead to the concept of neutrosophic compact spaces. Additionally, we present characterizations related to neutrosophic δ-ß-separated sets. A noteworthy feature of these concepts is their ability to model intricate connectedness networks and facilitate optimal solutions for problems involving a multitude of variables, each with degrees of acceptance, rejection, and indeterminacy. We provide relevant examples to illustrate our main findings.

KEYWORDS
Neutrosophic δ-ß-Open Sets, Neutrosophic δ-ß-Connectedness, Neutrosophic δ-ß-Compactness, Neutrosophic δ-ß-Separated-Sets

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Alaa. M. F. AL. Jumaili , "Other New Versions of Generalized Neutrosophic Connectedness and Compactness and Their Applications," Mathematics and Statistics, Vol. 12, No. 1, pp. 16 - 23, 2024. DOI: 10.13189/ms.2024.120103.

(b). APA Format:
Alaa. M. F. AL. Jumaili (2024). Other New Versions of Generalized Neutrosophic Connectedness and Compactness and Their Applications. Mathematics and Statistics, 12(1), 16 - 23. DOI: 10.13189/ms.2024.120103.