On fuzzy sub-semi-rings of nexuses
In this paper, we first constructed a semi-ring on a nexus and then defined a fuzzy sub-semi-ring associated with a nexus $ N $. We investigated some properties and applications. Fuzzy versions of some well-known crisp concepts are provided over a nexus. We verified some applications of this fuzzy o...
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AIMS Press
2024-12-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20241715 |
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| author | Vajiheh Nazemi Niya Hojat Babaei Akbar Rezaei |
| author_facet | Vajiheh Nazemi Niya Hojat Babaei Akbar Rezaei |
| author_sort | Vajiheh Nazemi Niya |
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| description | In this paper, we first constructed a semi-ring on a nexus and then defined a fuzzy sub-semi-ring associated with a nexus $ N $. We investigated some properties and applications. Fuzzy versions of some well-known crisp concepts are provided over a nexus. We verified some applications of this fuzzy on semi-ring $ N $. We obtained some relationships between sub-semi-ring and fuzzy sub-semi-ring of $ N $. However, these relationships were not true for ideals. We put a condition on fuzzy sub-semi-ring so that these relationships were true for ideals. We defined strong fuzzy sub-semi-ring on $ N $. For strong fuzzy sub-semi-ring on $ N $ and for every $ \alpha\in[0, \mu(0)] $, the level set $ \mu^\alpha $ was an ideal of $ N $. For some strong fuzzy sub-semi-rings $ \mu $, we verified when $ \mu^\alpha $ was a prime ideal of $ N $. In the following, for a semi-ring homomorphism $ f:N\longrightarrow M $, we showed that if $ \mu\in FSUB_S(N) $, then $ f(\mu)\in FSUB_S(M) $ and if $ \mu\in FSUB_S(M) $ then $ f \circ\mu\in FSUB_S(N) $. Finally, we verified some concepts of fuzzy quotient of a nexus semi-ring. |
| format | Article |
| id | doaj-art-00cdbf9adfe64282bdb41277b8d5aa2f |
| institution | Kabale University |
| issn | 2473-6988 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj-art-00cdbf9adfe64282bdb41277b8d5aa2f2025-01-23T07:53:25ZengAIMS PressAIMS Mathematics2473-69882024-12-01912361403615710.3934/math.20241715On fuzzy sub-semi-rings of nexusesVajiheh Nazemi Niya0Hojat Babaei1Akbar Rezaei2Department of Mathematics, Islamic Azad University of Kerman, Kerman, IranDepartment of Mathematics, Islamic Azad University of Kerman, Kerman, IranDepartment of Mathematics, Payame Noor University, P.O. Box 19395-3697, Tehran, IranIn this paper, we first constructed a semi-ring on a nexus and then defined a fuzzy sub-semi-ring associated with a nexus $ N $. We investigated some properties and applications. Fuzzy versions of some well-known crisp concepts are provided over a nexus. We verified some applications of this fuzzy on semi-ring $ N $. We obtained some relationships between sub-semi-ring and fuzzy sub-semi-ring of $ N $. However, these relationships were not true for ideals. We put a condition on fuzzy sub-semi-ring so that these relationships were true for ideals. We defined strong fuzzy sub-semi-ring on $ N $. For strong fuzzy sub-semi-ring on $ N $ and for every $ \alpha\in[0, \mu(0)] $, the level set $ \mu^\alpha $ was an ideal of $ N $. For some strong fuzzy sub-semi-rings $ \mu $, we verified when $ \mu^\alpha $ was a prime ideal of $ N $. In the following, for a semi-ring homomorphism $ f:N\longrightarrow M $, we showed that if $ \mu\in FSUB_S(N) $, then $ f(\mu)\in FSUB_S(M) $ and if $ \mu\in FSUB_S(M) $ then $ f \circ\mu\in FSUB_S(N) $. Finally, we verified some concepts of fuzzy quotient of a nexus semi-ring.https://www.aimspress.com/article/doi/10.3934/math.20241715nexussemi-ringfuzzy sub-semi-ringsemi-ring homomorphismfuzzy quotient |
| spellingShingle | Vajiheh Nazemi Niya Hojat Babaei Akbar Rezaei On fuzzy sub-semi-rings of nexuses AIMS Mathematics nexus semi-ring fuzzy sub-semi-ring semi-ring homomorphism fuzzy quotient |
| title | On fuzzy sub-semi-rings of nexuses |
| title_full | On fuzzy sub-semi-rings of nexuses |
| title_fullStr | On fuzzy sub-semi-rings of nexuses |
| title_full_unstemmed | On fuzzy sub-semi-rings of nexuses |
| title_short | On fuzzy sub-semi-rings of nexuses |
| title_sort | on fuzzy sub semi rings of nexuses |
| topic | nexus semi-ring fuzzy sub-semi-ring semi-ring homomorphism fuzzy quotient |
| url | https://www.aimspress.com/article/doi/10.3934/math.20241715 |
| work_keys_str_mv | AT vajihehnazeminiya onfuzzysubsemiringsofnexuses AT hojatbabaei onfuzzysubsemiringsofnexuses AT akbarrezaei onfuzzysubsemiringsofnexuses |