A uniform interval-valued intuitionistic fuzzy environment: topological descriptors and their application in neural networks

Ali Al Khabyah; Haseeb Ahmad; Ali Ahmad; Ali N. A. Koam; Ali Al Khabyah; Haseeb Ahmad; Ali Ahmad; Ali N. A. Koam

doi:10.3934/math.20241397

AIMS Mathematics

2024, Volume 9, Issue 10: 28792-28812. doi: 10.3934/math.20241397

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Research article

A uniform interval-valued intuitionistic fuzzy environment: topological descriptors and their application in neural networks

1.
Department of Mathematics, College of Science, King Khalid University, Abha 61413, Saudi Arabia
2.
Department of Mathematics, Lahore Leads University, Lahore, Pakistan
3.
Department of Computer Science, College of Engineering and Computer Science, Jazan University, Jazan, Saudi Arabia
4.
Department of Mathematics, College of Science, Jazan University, P.O. Box 114, Jazan 45142, Kingdom of Saudi Arabia

Received: 16 August 2024 Revised: 27 September 2024 Accepted: 09 October 2024 Published: 12 October 2024
MSC : 05C10, 05C50, 05C70, 05C90, 15A18, 15A90, 74E40, 74F25

The concept of being uniform strong interval-valued intuitionistic fuzzy (also termed as USIVIF) is an integration of two ideologies, which are called "uniformity" and "strong interval-valued intuitionistic fuzzy sets". Inspired by the study on uniform fuzzy topological indices, it is natural to introduce uniform IVIFTIs. Originally, topological indices were generalized for the fuzzy sets However, the utilization of the interval-valued intuitionistic fuzzy topological indices provides a finer approach, especially if there are multiple uncertainties based on intervals. Consequently, both theories imply that topological indices are not fixed and depend on certain situations or problems in the question. In this article, the generalized results for the uniform degree of the fuzzy sets associated with individual vertices/edges of strong interval-valued intuitionistic fuzzy graphs were presented and results for the total uniform degree of such graphs were also included. In addition, the nature of the implemented methods and models was discussed based on the cellular neural interval-valued intuitionistic fuzzy graphs of sets of membership and non-membership values.
Citation: Ali Al Khabyah, Haseeb Ahmad, Ali Ahmad, Ali N. A. Koam. A uniform interval-valued intuitionistic fuzzy environment: topological descriptors and their application in neural networks[J]. AIMS Mathematics, 2024, 9(10): 28792-28812. doi: 10.3934/math.20241397

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Abstract

The concept of being uniform strong interval-valued intuitionistic fuzzy (also termed as USIVIF) is an integration of two ideologies, which are called "uniformity" and "strong interval-valued intuitionistic fuzzy sets". Inspired by the study on uniform fuzzy topological indices, it is natural to introduce uniform IVIFTIs. Originally, topological indices were generalized for the fuzzy sets However, the utilization of the interval-valued intuitionistic fuzzy topological indices provides a finer approach, especially if there are multiple uncertainties based on intervals. Consequently, both theories imply that topological indices are not fixed and depend on certain situations or problems in the question. In this article, the generalized results for the uniform degree of the fuzzy sets associated with individual vertices/edges of strong interval-valued intuitionistic fuzzy graphs were presented and results for the total uniform degree of such graphs were also included. In addition, the nature of the implemented methods and models was discussed based on the cellular neural interval-valued intuitionistic fuzzy graphs of sets of membership and non-membership values.

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