Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Gradual and fuzzy subsets   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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The categories of this paper are: hep-th
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The categories of this paper are: math-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: stat
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The categories of this paper are: hep-lat
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The categories of this paper are: comp-gas
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The categories of this paper are: chao-dyn
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The categories of this paper are: cmp-lg
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The categories of this paper are: dg-ga
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The categories of this paper are: eess
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The categories of this paper are: chem-ph
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The categories of this paper are: econ
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The categories of this paper are: astro-ph
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The categories of this paper are: q-bio
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The categories of this paper are: adap-org
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The categories of this paper are: nucl-th