Fuzzy Hypervector Spaces
The aim of this paper is the generalization of the notion of fuzzy vector spaces to fuzzy hypervector spaces. In this regard, by considering the notion of fuzzy hypervector spaces, we characterized a fuzzy hypervector space based on its level sub-hyperspace. The algebraic nature of fuzzy hypervector...
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| Format: | Article |
| Language: | English |
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Wiley
2008-01-01
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| Series: | Advances in Fuzzy Systems |
| Online Access: | http://dx.doi.org/10.1155/2008/295649 |
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| author | R. Ameri O. R. Dehghan |
| author_facet | R. Ameri O. R. Dehghan |
| author_sort | R. Ameri |
| collection | DOAJ |
| description | The aim of this paper is the generalization of the notion of fuzzy vector spaces to fuzzy hypervector spaces. In this regard, by considering the notion of fuzzy hypervector spaces, we characterized a fuzzy hypervector space based on its level sub-hyperspace. The algebraic nature of fuzzy hypervector space under transformations is studied. Certain conditions are obtained under which a given fuzzy hypervector space can or cannot be realized as a union of two fuzzy hypervector spaces such that none is contained in the other. The construction of a fuzzy hypervector space generated by a given fuzzy subset of a hypervector space is given. The set of all fuzzy cosets of a fuzzy hypervector space is shown to be a hypervector space. Finally, a fuzzy quotient hypervector space is defined and an analogue of a consequence of the “fundamental theorem of homomorphisms” is obtained. |
| format | Article |
| id | doaj-art-dd1f8452a8ae44ef927d2dad1bd7923d |
| institution | Kabale University |
| issn | 1687-7101 1687-711X |
| language | English |
| publishDate | 2008-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Fuzzy Systems |
| spelling | doaj-art-dd1f8452a8ae44ef927d2dad1bd7923d2025-02-03T01:32:12ZengWileyAdvances in Fuzzy Systems1687-71011687-711X2008-01-01200810.1155/2008/295649295649Fuzzy Hypervector SpacesR. Ameri0O. R. Dehghan1Department of Mathematics, Faculty of Basic Sciences, University of Mazandaran, 47415-453 Babolsar, IranDepartment of Mathematics, Faculty of Basic Sciences, University of Mazandaran, 47415-453 Babolsar, IranThe aim of this paper is the generalization of the notion of fuzzy vector spaces to fuzzy hypervector spaces. In this regard, by considering the notion of fuzzy hypervector spaces, we characterized a fuzzy hypervector space based on its level sub-hyperspace. The algebraic nature of fuzzy hypervector space under transformations is studied. Certain conditions are obtained under which a given fuzzy hypervector space can or cannot be realized as a union of two fuzzy hypervector spaces such that none is contained in the other. The construction of a fuzzy hypervector space generated by a given fuzzy subset of a hypervector space is given. The set of all fuzzy cosets of a fuzzy hypervector space is shown to be a hypervector space. Finally, a fuzzy quotient hypervector space is defined and an analogue of a consequence of the “fundamental theorem of homomorphisms” is obtained.http://dx.doi.org/10.1155/2008/295649 |
| spellingShingle | R. Ameri O. R. Dehghan Fuzzy Hypervector Spaces Advances in Fuzzy Systems |
| title | Fuzzy Hypervector Spaces |
| title_full | Fuzzy Hypervector Spaces |
| title_fullStr | Fuzzy Hypervector Spaces |
| title_full_unstemmed | Fuzzy Hypervector Spaces |
| title_short | Fuzzy Hypervector Spaces |
| title_sort | fuzzy hypervector spaces |
| url | http://dx.doi.org/10.1155/2008/295649 |
| work_keys_str_mv | AT rameri fuzzyhypervectorspaces AT ordehghan fuzzyhypervectorspaces |