论文标题
模糊覆盖物和模糊分区类别之间的几何同构
Geometrical isomorphisms between categories of fuzzy coverings and fuzzy partitions
论文作者
论文摘要
让$ covering $是模糊覆盖物类别的类别，而$ partition $是模糊分区的类别。我们几何地构建了$分区$与$覆盖$的完整子类别之间的类别的同构，这些子类别可用于在模糊分区和模糊覆盖物之间得出两种有限的集合。此外，我们在$ cover [n] $的类别之间建立了同构，$ n $模糊套件的覆盖物类别和$ partition $的子类别，其对象是具有满足某些条件的$ n $套件的分区，可以使用这些条件，这些条件也可用于推论模糊分区和模糊分区之间的另一个培训和模糊封面之间的培训。
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.
