Geometrical isomorphisms between categories of fuzzy coverings and fuzzy partitions

Mircea Cimpoeas; Adrian Gabriel Neacsu

doi:10.1016/j.fss.2023.02.014

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arXiv · 2210.07948

Geometrical isomorphisms between categories of fuzzy coverings and fuzzy partitions

Mircea Cimpoeas·Adrian Gabriel Neacsu

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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.

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BibTeX RIS

Mircea Cimpoeas, Adrian Gabriel Neacsu. 2022-09-22. Geometrical isomorphisms between categories of fuzzy coverings and fuzzy partitions. https://doi.org/10.1016/j.fss.2023.02.014

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