1. Geometrical isomorphisms between categories of fuzzy coverings and fuzzy partitions
- Author
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Cimpoeas, Mircea and Neacsu, Adrian Gabriel
- Subjects
Mathematics - General Mathematics ,03E72, 18B05 - Abstract
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., Comment: 26 pages, 4 figures, accepted to Fuzzy Sets and Systems
- Published
- 2022
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