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International Journal of Fuzzy Logic and Intelligent Systems 2024; 24(2): 141-152

Published online June 25, 2024

https://doi.org/10.5391/IJFIS.2024.24.2.141

© The Korean Institute of Intelligent Systems

Exploring Regularities of Ordered Semigroups Through Generalized Fuzzy Ideals

Young Bae Jun1, Kittisak Tinpun2, and Nareupanat Lekkoksung3

1Department of Mathematics Education, Gyeongsang National University, Jinju, Korea
2Department of Mathematics and Computer Science, Faculty of Science and Technology, Prince of Songkla University, Pattani, Thailand
3Division of Mathematics, Faculty of Engineering, Rajamangala University of Technology Isan, Khon Kaen, Thailand

Correspondence to :
Nareupanat Lekkoksung (nareupanat.le@rmuti.ac.th)

Received: February 17, 2022; Revised: August 18, 2023; Accepted: May 3, 2024

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

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We consider (α, β)-fuzzy ideals, which are a generalized version of fuzzy ideals, in ordered semigroups. A connection between (α, β)-fuzzy quasi-ideals and (α, β)-fuzzy left (right) ideals is provided. The notion of (α, β)-fuzzy ideals is characterized in terms of a particular operation. We describe regular and intra-regular ordered semigroups using the concept of (α, β)fuzzy ideals.

Keywords: (α, β)-fuzzy left ideal, (α, β)-fuzzy right ideal, Ordered semigroup, Regular, Intra-regular

Acknowledgments

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The author would like to thank Rajamangala University of Technology Isan, Khon Kaen Campus.

Conflict of Interest

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

Biographies

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Young Bae Jun is an Emeritus Professor of Gyeongsang National University, Korea. He is currently the Editor-in-Chief of two international journals and the editorial board of six international journals. He has published over 800 papers in international journals. His primary scientific interests include BCK/BCI-algebras and fuzzy (soft, rough) logical algebras. He was on the list of 2016, 2017, 2018 and 2019 Highly Cited Researchers which has been published in Clarivate Analytics.

Email: skywine@gmail.com

Kittisak Tinpun received Ph.D from University of Potsdam, Germany. He is currently working as an assistant professor at the Prince of Songkla University, Pattani Campus, Thailand. His research interests are semigroup theory, transformation semigroup theories.

Email: kittisak.ti@psu.ac.th

Nareupanat Lekkoksung received M.Sc. and Ph.D. from Khon Kaen University. He is currently an assistant professor at Rajamangala University of Technology Isan, Khon Kaen Campus, since 2019. His research interests are hypersubstitution theory, semigroup theory, and fuzzy set theory.

Email: nareupanat.le@rmuti.ac.th

Article

Original Article

International Journal of Fuzzy Logic and Intelligent Systems 2024; 24(2): 141-152

Published online June 25, 2024 https://doi.org/10.5391/IJFIS.2024.24.2.141

Copyright © The Korean Institute of Intelligent Systems.

Exploring Regularities of Ordered Semigroups Through Generalized Fuzzy Ideals

Young Bae Jun1, Kittisak Tinpun2, and Nareupanat Lekkoksung3

1Department of Mathematics Education, Gyeongsang National University, Jinju, Korea
2Department of Mathematics and Computer Science, Faculty of Science and Technology, Prince of Songkla University, Pattani, Thailand
3Division of Mathematics, Faculty of Engineering, Rajamangala University of Technology Isan, Khon Kaen, Thailand

Correspondence to:Nareupanat Lekkoksung (nareupanat.le@rmuti.ac.th)

Received: February 17, 2022; Revised: August 18, 2023; Accepted: May 3, 2024

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

We consider (α, β)-fuzzy ideals, which are a generalized version of fuzzy ideals, in ordered semigroups. A connection between (α, β)-fuzzy quasi-ideals and (α, β)-fuzzy left (right) ideals is provided. The notion of (α, β)-fuzzy ideals is characterized in terms of a particular operation. We describe regular and intra-regular ordered semigroups using the concept of (α, β)fuzzy ideals.

Keywords: (&alpha,, &beta,)-fuzzy left ideal, (&alpha,, &beta,)-fuzzy right ideal, Ordered semigroup, Regular, Intra-regular

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