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International Journal of Fuzzy Logic and Intelligent Systems 2021; 21(1): 29-37

Published online March 25, 2021

https://doi.org/10.5391/IJFIS.2021.21.1.29

© The Korean Institute of Intelligent Systems

On Soft Topological Polygroups and Their Examples

Rasoul Mousarezaei and Bijan Davvaz

Department of Mathematics, Yazd University, Yazd, Iran

Correspondence to :
Bijan Davvaz (davvaz@yazd.ac.ir)

Received: November 10, 2020; Revised: February 11, 2021; Accepted: February 22, 2021

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.

Polygroups are a special subclass of hypergroups that satisfies group-like axioms. A polygroup is a multigroup that is completely regular and reversible in itself. A topological polygroup is a polygroup P with a topology on P that satisfies certain conditions. Moreover, the concept of soft sets is a general mathematical tool for dealing with uncertainty. In this study, we investigate soft topological polygroups over a polygroup. The ideas presented in this article can be used to build more polygroups and soft topological polygroups.

Keywords: Soft set, Topological polygroup, Soft polygroup, Soft topological polygroups

No potential conflict of interest relevant to this article was reported.

Rasoul Mousarezaei is a PhD candidate at the Department of Mathematics, Yazd University, Iran. He has been working on research related to soft sets and algebraic hyperstructures.

E-mail:


Bijan Davvaz is a professor at the Department of Mathematics, Yazd University, Iran. He earned his Ph.D. in mathematics with a thesis on “Topics in Algebraic Hyperstructures” from Tarbiat Modarres University, Iran, and completed his M.Sc. in mathematics at the University of Tehran. Apart from his role as a professor, he also served as a Head of the Department of Mathematics (1998–2002), Chairman of the Faculty of Science (2004–2006), and Vice-President for Research (2006–2008) at Yazd University, Iran. His areas of interest include algebra, algebraic hyperstructures, rough sets, and fuzzy logic. A member of editorial boards for 25 mathematical journals, Prof. Davvaz has authored 5 books and over 550 research papers, especially on algebra, fuzzy logic, algebraic hyperstructures, and their applications.

E-mail: davvaz@yazd.ac.ir


Article

Original Article

International Journal of Fuzzy Logic and Intelligent Systems 2021; 21(1): 29-37

Published online March 25, 2021 https://doi.org/10.5391/IJFIS.2021.21.1.29

Copyright © The Korean Institute of Intelligent Systems.

On Soft Topological Polygroups and Their Examples

Rasoul Mousarezaei and Bijan Davvaz

Department of Mathematics, Yazd University, Yazd, Iran

Correspondence to:Bijan Davvaz (davvaz@yazd.ac.ir)

Received: November 10, 2020; Revised: February 11, 2021; Accepted: February 22, 2021

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.

Abstract

Polygroups are a special subclass of hypergroups that satisfies group-like axioms. A polygroup is a multigroup that is completely regular and reversible in itself. A topological polygroup is a polygroup P with a topology on P that satisfies certain conditions. Moreover, the concept of soft sets is a general mathematical tool for dealing with uncertainty. In this study, we investigate soft topological polygroups over a polygroup. The ideas presented in this article can be used to build more polygroups and soft topological polygroups.

Keywords: Soft set, Topological polygroup, Soft polygroup, Soft topological polygroups

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