Intra-regular semihypergroups characterized by Fermatean fuzzy bi-hyperideals

Warud Nakkhasen; Teerapan Jodnok; Ronnason Chinram; Warud Nakkhasen; Teerapan Jodnok; Ronnason Chinram

doi:10.3934/math.20241698

AIMS Mathematics

2024, Volume 9, Issue 12: 35800-35822. doi: 10.3934/math.20241698

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Intra-regular semihypergroups characterized by Fermatean fuzzy bi-hyperideals

1.
Department of Mathematics, Faculty of Science, Mahasarakham University, Maha Sarakham 44150, Thailand
2.
Department of Mathematics, Faculty of Science and Technology, Surindra Rajabhat University, Surin 32000, Thailand
3.
Division of Computational Science, Faculty of Science, Prince of Songkla University, Songkhla 90110, Thailand

Received: 26 September 2024 Revised: 02 December 2024 Accepted: 13 December 2024 Published: 24 December 2024
MSC : 08A72, 20M10, 20M17

The concept of Fermatean fuzzy sets was introduced by Senapati and Yager in 2019 as a generalization of fuzzy sets, intuitionistic fuzzy sets, and Pythagorean fuzzy sets. In this article, we apply the notions of Fermatean fuzzy left (resp., right) hyperideals and Fermatean fuzzy (resp., generalized) bi-hyperideals in semihypergroups to characterize intra-regular semihypergroups, such as $ S $ is an intra-regular semihypergroup if and only if $ \mathcal{L}\cap\mathcal{R}\subseteq \mathcal{L}\circ\mathcal{R} $, for every Fermatean fuzzy left hyperideal $ \mathcal{L} $ and Fermatean fuzzy right hyperideal $ \mathcal{R} $ of a semihypergroup $ S $. Moreover, we introduce the concept of Fermatean fuzzy interior hyperideals of semihypergroups and use these properties to describe the class of intra-regular semihypergroups. Next, we demonstrate that Fermatean fuzzy interior hyperideals coincide with Fermatean fuzzy hyperideals in intra-regular semihypergroups. However, in general, Fermatean fuzzy interior hyperideals do not necessarily have to be Fermatean fuzzy hyperideals in semihypergroups. Finally, we discuss some characterizations of semihypergroups when they are both regular and intra-regular by means of different types of Fermatean fuzzy hyperideals in semihypergroups.
- Fermatean fuzzy hyperideal,
- Fermatean fuzzy bi-hyperideal,
- Fermatean fuzzy interior hyperideal,
- regular semihypergroup,
- intra-regular semihypergroup
Citation: Warud Nakkhasen, Teerapan Jodnok, Ronnason Chinram. Intra-regular semihypergroups characterized by Fermatean fuzzy bi-hyperideals[J]. AIMS Mathematics, 2024, 9(12): 35800-35822. doi: 10.3934/math.20241698

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Abstract

The concept of Fermatean fuzzy sets was introduced by Senapati and Yager in 2019 as a generalization of fuzzy sets, intuitionistic fuzzy sets, and Pythagorean fuzzy sets. In this article, we apply the notions of Fermatean fuzzy left (resp., right) hyperideals and Fermatean fuzzy (resp., generalized) bi-hyperideals in semihypergroups to characterize intra-regular semihypergroups, such as $ S $ is an intra-regular semihypergroup if and only if $ \mathcal{L}\cap\mathcal{R}\subseteq \mathcal{L}\circ\mathcal{R} $, for every Fermatean fuzzy left hyperideal $ \mathcal{L} $ and Fermatean fuzzy right hyperideal $ \mathcal{R} $ of a semihypergroup $ S $. Moreover, we introduce the concept of Fermatean fuzzy interior hyperideals of semihypergroups and use these properties to describe the class of intra-regular semihypergroups. Next, we demonstrate that Fermatean fuzzy interior hyperideals coincide with Fermatean fuzzy hyperideals in intra-regular semihypergroups. However, in general, Fermatean fuzzy interior hyperideals do not necessarily have to be Fermatean fuzzy hyperideals in semihypergroups. Finally, we discuss some characterizations of semihypergroups when they are both regular and intra-regular by means of different types of Fermatean fuzzy hyperideals in semihypergroups.

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