{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,19]],"date-time":"2025-12-19T09:57:35Z","timestamp":1766138255781,"version":"3.37.3"},"reference-count":15,"publisher":"Wiley","license":[{"start":{"date-parts":[[2023,2,27]],"date-time":"2023-02-27T00:00:00Z","timestamp":1677456000000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"FQM-266-Anillos y M\u00f3dulos","award":["A-FQM-394-UGR20","CEX2020-001105-M"],"award-info":[{"award-number":["A-FQM-394-UGR20","CEX2020-001105-M"]}]},{"DOI":"10.13039\/501100002924","name":"Federaci\u00f3n Espa\u00f1ola de Enfermedades Raras","doi-asserted-by":"publisher","award":["A-FQM-394-UGR20","CEX2020-001105-M"],"award-info":[{"award-number":["A-FQM-394-UGR20","CEX2020-001105-M"]}],"id":[{"id":"10.13039\/501100002924","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004837","name":"Ministerio de Ciencia e Innovaci\u00f3n","doi-asserted-by":"publisher","award":["A-FQM-394-UGR20","CEX2020-001105-M"],"award-info":[{"award-number":["A-FQM-394-UGR20","CEX2020-001105-M"]}],"id":[{"id":"10.13039\/501100004837","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Advances in Fuzzy Systems"],"published-print":{"date-parts":[[2023,2,27]]},"abstract":"<jats:p>In the fuzzy theory of sets and groups, the use of \u03b1-levels is a standard to translate problems from the fuzzy to the crisp framework. Using strong \u03b1-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]. 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