n Power Root Fuzzy Sets and Its Topology

Tareq M. Al-shami; Hariwan Z. Ibrahim; Abdelwaheb Mhemdi; Radwan Abu-Gdairi

doi:10.5391/IJFIS.2022.22.4.350

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International Journal of Fuzzy Logic and Intelligent Systems 2022; 22(4): 350-365

Published online December 25, 2022

https://doi.org/10.5391/IJFIS.2022.22.4.350

n Power Root Fuzzy Sets and Its Topology

Tareq M. Al-shami¹, Hariwan Z. Ibrahim², Abdelwaheb Mhemdi³, and Radwan Abu-Gdairi⁴

¹Department of Mathematics, Sana’a University, Sana’a, Yemen Future University, Egypt
²Department of Mathematics, Faculty of Education, University of Zakho, Zakho, Kurdistan Region-Iraq
³Department of Mathematics, College of Sciences and Humanities in Aflaj, Prince Sattam bin Abdulaziz University, Riyadh, Saudi Arabia
⁴Department of Mathematics, Faculty of Science, Zarqa University, P.O. Box 13110 Zarqa, Jordan

Correspondence to :
Abdelwaheb Mhemdi (mhemdiabd@gmail.com)

Received: October 15, 2022; Revised: November 23, 2022; Accepted: December 12, 2022

This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0/) which permits unrestricted noncommercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

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One of the most useful expansions of fuzzy sets for coping with information uncertainties is the q-rung orthopair fuzzy sets. In such circumstances, in this article, we define a novel extension of fuzzy sets called n^th power root fuzzy set (briefly, nPR-fuzzy set) and elucidate their relationship with intuitionistic fuzzy sets, SR-fuzzy sets, CR-fuzzy sets and q-rung orthopair fuzzy sets. Then, we provide the necessary set of operations for nPR-fuzzy sets as well as study their various features. Furthermore, we familiarize the concept of nPR-fuzzy topology and investigate the basic aspects of this topology. In addition, we define separated nPR-fuzzy sets and then present the concept of disconnected nPR-fuzzy sets. Moreover, we study and characterize nPR-fuzzy continuous maps in great depth. Finally, we establish 𝕿₀ and 𝕿₁ in nPR-fuzzy topologies and discover the links between them.

Keywords: nPR-fuzzy sets, Operations, nPR-fuzzy topology, Separated nPR-FSs, Connected nPR-FS, nPR-fuzzy continuous maps, 𝕿₀, 𝕿₁

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This research has received no external funding.

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The authors declare that they have no competing interests.

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No data were used to support this study.

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TareqM. Al-shami received the M.S. and Ph.D. degrees in pure mathematics from the Department of Mathematics, Faculty of Science, Mansoura University, Egypt. He is currently an Assistant Professor with the department of Mathematics, Sana’a University, Sana’a, Yemen. He has published more than 136 research articles in international peer-reviewed SCIE and ESCI journals such as Information Sciences, Knowledge-Based Systems, Applied and Computational Mathematics, Computational and Applied Mathematics, Artificial Intelligence Review, AIMS mathematics, Soft Computing journal among others. His research interests include pure mathematics, topology and its extensions, ordered topology, soft set theory, rough set theory and fuzzy set theory with applications in decision-making, medical diagnosis, information measures, and information aggregation. Dr. Tareq received Obada-Prize for postgraduate students in Feb. 2019. Also, he obtained the first rank at Sana’a University -Yemen according to Scopus data of the region of Yemen for the period from 2018 to 2121.

Hariwan Z. Ibrahim is currently working as an assistant professor in the Department of Mathematics at the University of Zakho, Kurdistan Region-Iraq. He received his Ph.D. degree from the same university. His area of interest includes Fuzzy Topology, Topological Algebra, Ditopology, Ideal Topology and Soft Topology. He has published more than 80 research papers in international journals.

Abdelwaheb Mhemdi is a doctor in pure Mathematics. He was awarded a PhD. from the Faculty of Sciences, Tunis Elmanar University. He was an assistant professor from 2011 to 2016 in Tunis Elmanar University and Gafsa University. Since 2016, he has been teaching at Prince Sattam bin Abdulaziz University in Saudi Arabia. Now, he is an associate professor, and he is the head of the department of Mathematics in the College of Sciences and Humanities in Al Aflaj. Mhemdi produced many original articles in general Topology, especially in Separation Axioms, Soft Topological spaces, and Category of Topological Spaces.

Radwan Abu-Gdairi is an assistant professor of Mathematics at Department of Mathematics, Faculty of Science, Zarqa University, Jordan. His research interests are in the areas of pure and applied mathematics including Topology, Fuzzy topology, Rough set theory and it’s applications. He has published research articles in reputed international journals of mathematical sciences. He is referee of some mathematical journals.