English

Gradual and fuzzy subsets

Logic 2021-02-08 v2 Category Theory Group Theory

Abstract

In fuzzy theory of sets and groups, the use of α\alpha--levels is a standard to translate problems from the fuzzy to the crisp framework. Using strong α\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 Set(0,1]\mathcal{S}\textit{et}^{(0,1]}, resp. Gr(0,1]\mathcal{G}\textit{r}^{(0,1]}.

Keywords

Cite

@article{arxiv.1812.07521,
  title  = {Gradual and fuzzy subsets},
  author = {Josefa M. Garcia and Pascual Jara},
  journal= {arXiv preprint arXiv:1812.07521},
  year   = {2021}
}

Comments

32 pages

R2 v1 2026-06-23T06:46:41.345Z