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arXiv · 1812.07521

Gradual and fuzzy subsets

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. $\mathcal{G}\textit{r}^{(0,1]}$.

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BibTeXRIS

Josefa M. Garcia, Pascual Jara. 2018-11-27. Gradual and fuzzy subsets. https://arxiv.org/abs/1812.07521

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