Introduction to NeutroHyperGroups
NeutroSophication and AntiSophication are processes through which NeutroAlgebraic and AntiAlgebraic structures can be generated from any classical structures. Given any classical structure with m operations (laws and axioms) where m ≥ 1 we can generate (2m − 1) NeutroStructures and (3m − 2m) AntiStr...
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| Format: | Article |
| Language: | English |
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University of New Mexico
2020-11-01
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| Series: | Neutrosophic Sets and Systems |
| Subjects: | |
| Online Access: | https://fs.unm.edu/NSS/IntroductionToNeutroHyperGroups2.pdf |
| _version_ | 1797774675336495104 |
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| author | M.A. Ibrahim A.A.A. Agboola |
| author_facet | M.A. Ibrahim A.A.A. Agboola |
| author_sort | M.A. Ibrahim |
| collection | DOAJ |
| description | NeutroSophication and AntiSophication are processes through which NeutroAlgebraic and AntiAlgebraic structures can be generated from any classical structures. Given any classical structure with m operations (laws and axioms) where m ≥ 1 we can generate (2m − 1) NeutroStructures and (3m − 2m) AntiStructures. In this paper, we introduce for the first time the concept of NeutroHyperGroups. Specifically, we study a particular class of NeutroHy perGroups called [2, 3]− NeutroHyperGroups and present their basic properties and several examples. It is shown that the intersection of two [2, 3]− NeutroSubHyperGroups is not necessarily a [2, 3]−NeutroSubHypergroup but their union may produce a [2, 3]− NeutroSubhypergroup. Also, the quotient of a [2, 3]−NeutroHyperGroup factored by a [2, 3]− NeutroSubHyperGroup is shown to be a [2, 3]−NeutroHyperGroup. Examples are provided to show that in the neutro sophic environment, [2, 3]− NeutroHyperGroups are associated with dismutation reactions in some chemical reactions and biological processes. |
| first_indexed | 2024-03-12T22:24:32Z |
| format | Article |
| id | doaj.art-48341388277f46a38e1c7584002b2446 |
| institution | Directory Open Access Journal |
| issn | 2331-6055 2331-608X |
| language | English |
| last_indexed | 2024-03-12T22:24:32Z |
| publishDate | 2020-11-01 |
| publisher | University of New Mexico |
| record_format | Article |
| series | Neutrosophic Sets and Systems |
| spelling | doaj.art-48341388277f46a38e1c7584002b24462023-07-22T12:26:17ZengUniversity of New MexicoNeutrosophic Sets and Systems2331-60552331-608X2020-11-0138153210.5281/zenodo.4300363Introduction to NeutroHyperGroupsM.A. IbrahimA.A.A. AgboolaNeutroSophication and AntiSophication are processes through which NeutroAlgebraic and AntiAlgebraic structures can be generated from any classical structures. Given any classical structure with m operations (laws and axioms) where m ≥ 1 we can generate (2m − 1) NeutroStructures and (3m − 2m) AntiStructures. In this paper, we introduce for the first time the concept of NeutroHyperGroups. Specifically, we study a particular class of NeutroHy perGroups called [2, 3]− NeutroHyperGroups and present their basic properties and several examples. It is shown that the intersection of two [2, 3]− NeutroSubHyperGroups is not necessarily a [2, 3]−NeutroSubHypergroup but their union may produce a [2, 3]− NeutroSubhypergroup. Also, the quotient of a [2, 3]−NeutroHyperGroup factored by a [2, 3]− NeutroSubHyperGroup is shown to be a [2, 3]−NeutroHyperGroup. Examples are provided to show that in the neutro sophic environment, [2, 3]− NeutroHyperGroups are associated with dismutation reactions in some chemical reactions and biological processes. https://fs.unm.edu/NSS/IntroductionToNeutroHyperGroups2.pdfneutrohypergroupneutrosubhypergroupneutrohypergrouphomomorphism |
| spellingShingle | M.A. Ibrahim A.A.A. Agboola Introduction to NeutroHyperGroups Neutrosophic Sets and Systems neutrohypergroup neutrosubhypergroup neutrohypergrouphomomorphism |
| title | Introduction to NeutroHyperGroups |
| title_full | Introduction to NeutroHyperGroups |
| title_fullStr | Introduction to NeutroHyperGroups |
| title_full_unstemmed | Introduction to NeutroHyperGroups |
| title_short | Introduction to NeutroHyperGroups |
| title_sort | introduction to neutrohypergroups |
| topic | neutrohypergroup neutrosubhypergroup neutrohypergrouphomomorphism |
| url | https://fs.unm.edu/NSS/IntroductionToNeutroHyperGroups2.pdf |
| work_keys_str_mv | AT maibrahim introductiontoneutrohypergroups AT aaaagboola introductiontoneutrohypergroups |