Geometrical isomorphisms between categories of fuzzy coverings and fuzzy partitions

Mircea Cimpoeas; Adrian Gabriel Neacsu

doi:10.1016/j.fss.2023.02.014

paper

Geometrical isomorphisms between categories of fuzzy coverings and fuzzy partitions

arXiv:2210.07948 · doi:10.1016/j.fss.2023.02.014

Abstract

Let $C o v er in g$ be the category of the category of fuzzy coverings, and $P a r t i t i o n$ , the category of fuzzy partitions. We geometrically construct an isomorphism of categories between $P a r t i t i o n$ and a full subcategory of $C o v er in g$ , which can be used to derive bijections between fuzzy partitions and fuzzy coverings with finitely many sets. Also, we establish an isomorphism between $C o v er in g [n]$ , the category of coverings with $n$ fuzzy sets, and a subcategory of $P a r t i t i o n$ , 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.

26 pages, 4 figures, accepted to Fuzzy Sets and Systems