Gradual Sets: An Approach to Fuzzy Sets García Hernández, Josefa María Jara Martínez, Pascual This work was partially supported by the Research Group “FQM-266-Anillos y Módulos.” This work was supported by grant A-FQM-394-UGR20 from Programa Operativo FEDER 2014–2020 and Consejería de Economía, Conocimiento, Empresas y Universidad de la Junta de Andalucía (Spain) and by the “María de Maeztu” Excellence Unit IMAG, reference CEX2020-001105-M, funded by MCIN/ AEI/10.13039/501100011033/. 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. 2023-04-12T10:49:50Z 2023-04-12T10:49:50Z 2023-02-27 journal article García, J. M., & Jara, P. (2023). Gradual Sets: An Approach to Fuzzy Sets. Advances in Fuzzy Systems, 2023 [https://doi.org/10.1155/2023/6163672] https://hdl.handle.net/10481/81023 10.1155/2023/6163672 eng http://creativecommons.org/licenses/by/4.0/ open access Atribución 4.0 Internacional Hindawi