Gradual Sets: An Approach to Fuzzy Sets García Hernández, Josefa María Jara Martínez, Pascual In the fuzzy theory of sets and groups, the use of α-levels is a standard to translate problems from the fuzzy to the crisp framework. Using strong α-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], resp., Gr (0, 1]. In this line, the algebraic potential of this theory will be reached, in forthcoming papers. 2023-05-09T09:49:37Z 2023-05-09T09:49:37Z 2023-02-27 info:eu-repo/semantics/article Josefa M. García, Pascual Jara, "Gradual Sets: An Approach to Fuzzy Sets", Advances in Fuzzy Systems, vol. 2023, Article ID 6163672, 18 pages, 2023. [https://doi.org/10.1155/2023/6163672] https://hdl.handle.net/10481/81410 10.1155/2023/6163672 eng http://creativecommons.org/licenses/by/4.0/ info:eu-repo/semantics/openAccess Atribución 4.0 Internacional Hindawi