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Mathematics > Logic

arXiv:1812.07521 (math)
[Submitted on 27 Nov 2018 (v1), last revised 5 Feb 2021 (this version, v2)]

Title:Gradual and fuzzy subsets

Authors:Josefa M. Garcia, Pascual Jara
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Abstract:In fuzzy theory of sets and groups, the use of $\alpha$--levels is a standard to translate problems from the fuzzy to the crisp framework. Using strong $\alpha$--levels, it is possible to establish a one to one correspondence which makes possible doubly, a gradual and a functorial treatment of the fuzzy theory. The main result of this paper is to identify the class of fuzzy sets, respectively fuzzy groups, with subcategories of the functorial categories $\mathcal{S}\textit{et}^{(0,1]}$, resp. $\mathcal{G}\textit{r}^{(0,1]}$.
Comments: 32 pages
Subjects: Logic (math.LO); Category Theory (math.CT); Group Theory (math.GR)
MSC classes: 18E05, 03E72, 20N25
Cite as: arXiv:1812.07521 [math.LO]
  (or arXiv:1812.07521v2 [math.LO] for this version)
  https://doi.org/10.48550/arXiv.1812.07521

Submission history

From: Pascual Jara [view email]
[v1] Tue, 27 Nov 2018 04:36:27 UTC (26 KB)
[v2] Fri, 5 Feb 2021 10:25:05 UTC (26 KB)
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