Intra-regular semihypergroups characterized by Fermatean fuzzy bi-hyperideals
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)...
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AIMS Press
2024-12-01
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20241698 |
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| author | Warud Nakkhasen Teerapan Jodnok Ronnason Chinram |
| author_facet | Warud Nakkhasen Teerapan Jodnok Ronnason Chinram |
| author_sort | Warud Nakkhasen |
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| description | 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. |
| format | Article |
| id | doaj-art-b5013d51bb094d5a9a1030cade87c662 |
| institution | Kabale University |
| issn | 2473-6988 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | AIMS Press |
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| spelling | doaj-art-b5013d51bb094d5a9a1030cade87c6622025-01-23T07:53:25ZengAIMS PressAIMS Mathematics2473-69882024-12-01912358003582210.3934/math.20241698Intra-regular semihypergroups characterized by Fermatean fuzzy bi-hyperidealsWarud Nakkhasen0Teerapan Jodnok1Ronnason Chinram2Department of Mathematics, Faculty of Science, Mahasarakham University, Maha Sarakham 44150, ThailandDepartment of Mathematics, Faculty of Science and Technology, Surindra Rajabhat University, Surin 32000, ThailandDivision of Computational Science, Faculty of Science, Prince of Songkla University, Songkhla 90110, ThailandThe 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.https://www.aimspress.com/article/doi/10.3934/math.20241698fermatean fuzzy hyperidealfermatean fuzzy bi-hyperidealfermatean fuzzy interior hyperidealregular semihypergroupintra-regular semihypergroup |
| spellingShingle | Warud Nakkhasen Teerapan Jodnok Ronnason Chinram Intra-regular semihypergroups characterized by Fermatean fuzzy bi-hyperideals AIMS Mathematics fermatean fuzzy hyperideal fermatean fuzzy bi-hyperideal fermatean fuzzy interior hyperideal regular semihypergroup intra-regular semihypergroup |
| title | Intra-regular semihypergroups characterized by Fermatean fuzzy bi-hyperideals |
| title_full | Intra-regular semihypergroups characterized by Fermatean fuzzy bi-hyperideals |
| title_fullStr | Intra-regular semihypergroups characterized by Fermatean fuzzy bi-hyperideals |
| title_full_unstemmed | Intra-regular semihypergroups characterized by Fermatean fuzzy bi-hyperideals |
| title_short | Intra-regular semihypergroups characterized by Fermatean fuzzy bi-hyperideals |
| title_sort | intra regular semihypergroups characterized by fermatean fuzzy bi hyperideals |
| topic | fermatean fuzzy hyperideal fermatean fuzzy bi-hyperideal fermatean fuzzy interior hyperideal regular semihypergroup intra-regular semihypergroup |
| url | https://www.aimspress.com/article/doi/10.3934/math.20241698 |
| work_keys_str_mv | AT warudnakkhasen intraregularsemihypergroupscharacterizedbyfermateanfuzzybihyperideals AT teerapanjodnok intraregularsemihypergroupscharacterizedbyfermateanfuzzybihyperideals AT ronnasonchinram intraregularsemihypergroupscharacterizedbyfermateanfuzzybihyperideals |