{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T06:18:43Z","timestamp":1777702723237,"version":"3.51.4"},"reference-count":0,"publisher":"SAGE Publications","issue":"1","license":[{"start":{"date-parts":[[2014,1,1]],"date-time":"2014-01-01T00:00:00Z","timestamp":1388534400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Journal of Intelligent &amp; Fuzzy Systems"],"published-print":{"date-parts":[[2014,7]]},"abstract":"<jats:p>Throughout the paper it is shown that the classical definition of a fuzzy subset carries additional structures. The concept of a fuzzy subset is regarded from an alternative point of view: namely, the characteristic function of a fuzzy subset may be reinterpreted in terms of a Sincov's functional equation in two variables. Since the solutions of a Sincov's functional equation are also closely related to the existence of representable total preorders, an special attention is paid to the relationship between fuzzy subsets and total preorders defined on a universe. Some possible applications of this approach are pointed out in the final section of the manuscript.<\/jats:p>","DOI":"10.3233\/ifs-131005","type":"journal-article","created":{"date-parts":[[2019,12,2]],"date-time":"2019-12-02T18:39:07Z","timestamp":1575311947000},"page":"367-375","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":4,"title":["Reinterpreting a fuzzy subset by means of a Sincov's functional equation"],"prefix":"10.1177","volume":"27","author":[{"given":"Mar\u00eda Jes\u00fas","family":"Campi\u00f3n","sequence":"first","affiliation":[{"name":"Departamento de Matem\u00e1ticas, Universidad P\u00fablica de Navarra, Campus Arrosad\u00eda, Pamplona, Spain"}]},{"given":"Raquel G.","family":"Catal\u00e1n","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1ticas, Universidad P\u00fablica de Navarra, Campus Arrosad\u00eda, Pamplona, Spain"}]},{"given":"Esteban","family":"Indur\u00e1in","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1ticas, Universidad P\u00fablica de Navarra, Campus Arrosad\u00eda, Pamplona, Spain"}]},{"given":"Gustavo","family":"Ochoa","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1ticas, Universidad P\u00fablica de Navarra, Campus Arrosad\u00eda, Pamplona, Spain"}]}],"member":"179","published-online":{"date-parts":[[2014,1]]},"container-title":["Journal of Intelligent &amp; Fuzzy Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/IFS-131005","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/IFS-131005","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T09:36:46Z","timestamp":1777455406000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/IFS-131005"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,1]]},"references-count":0,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2014,7]]}},"alternative-id":["10.3233\/IFS-131005"],"URL":"https:\/\/doi.org\/10.3233\/ifs-131005","relation":{},"ISSN":["1064-1246","1875-8967"],"issn-type":[{"value":"1064-1246","type":"print"},{"value":"1875-8967","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,1]]}}}