Geometrical isomorphisms between categories of fuzzy coverings and fuzzy partitions
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866910427683749888 |
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| author | Cimpoeas, Mircea Neacsu, Adrian Gabriel |
| author_facet | Cimpoeas, Mircea Neacsu, Adrian Gabriel |
| contents | Let $Covering$ be the category of the category of fuzzy coverings, and $Partition$, the category of fuzzy partitions. We geometrically construct an isomorphism of categories between $Partition$ and a full subcategory of $Covering$, which can be used to derive bijections between fuzzy partitions and fuzzy coverings with finitely many sets. Also, we establish an isomorphism between $Covering[n]$, the category of coverings with $n$ fuzzy sets, and a subcategory of $Partition$, whose objects are partitions with $n$ sets which satisfy certain conditions, which can be also used to deduce another bijection between fuzzy partitions and fuzzy coverings with finitely many sets. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_07948 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Geometrical isomorphisms between categories of fuzzy coverings and fuzzy partitions Cimpoeas, Mircea Neacsu, Adrian Gabriel General Mathematics 03E72, 18B05 Let $Covering$ be the category of the category of fuzzy coverings, and $Partition$, the category of fuzzy partitions. We geometrically construct an isomorphism of categories between $Partition$ and a full subcategory of $Covering$, which can be used to derive bijections between fuzzy partitions and fuzzy coverings with finitely many sets. Also, we establish an isomorphism between $Covering[n]$, the category of coverings with $n$ fuzzy sets, and a subcategory of $Partition$, whose objects are partitions with $n$ sets which satisfy certain conditions, which can be also used to deduce another bijection between fuzzy partitions and fuzzy coverings with finitely many sets. |
| title | Geometrical isomorphisms between categories of fuzzy coverings and fuzzy partitions |
| topic | General Mathematics 03E72, 18B05 |
| url | https://arxiv.org/abs/2210.07948 |