{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,11]],"date-time":"2026-06-11T10:53:09Z","timestamp":1781175189885,"version":"3.54.1"},"reference-count":46,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2024,12,31]],"date-time":"2024-12-31T00:00:00Z","timestamp":1735603200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Spanish Ministerio de Ciencia e Innovaci\u00f3n\/AEI\/EU FEDER Funds","award":["PID2021-122905NB-C22"],"award-info":[{"award-number":["PID2021-122905NB-C22"]}]},{"name":"Spanish Ministerio de Ciencia e Innovaci\u00f3n\/AEI\/EU FEDER Funds","award":["Chile\u2013USS\u2013FIN\u201324\u2013PASI\u201311"],"award-info":[{"award-number":["Chile\u2013USS\u2013FIN\u201324\u2013PASI\u201311"]}]},{"name":"Vicerrector\u00eda de Investigaci\u00f3n y Doctorados de la Universidad San Sebasti\u00e1n","award":["PID2021-122905NB-C22"],"award-info":[{"award-number":["PID2021-122905NB-C22"]}]},{"name":"Vicerrector\u00eda de Investigaci\u00f3n y Doctorados de la Universidad San Sebasti\u00e1n","award":["Chile\u2013USS\u2013FIN\u201324\u2013PASI\u201311"],"award-info":[{"award-number":["Chile\u2013USS\u2013FIN\u201324\u2013PASI\u201311"]}]},{"name":"\u201cAsociaci\u00f3n de Amigos\u201d of the University of Navarra","award":["PID2021-122905NB-C22"],"award-info":[{"award-number":["PID2021-122905NB-C22"]}]},{"name":"\u201cAsociaci\u00f3n de Amigos\u201d of the University of Navarra","award":["Chile\u2013USS\u2013FIN\u201324\u2013PASI\u201311"],"award-info":[{"award-number":["Chile\u2013USS\u2013FIN\u201324\u2013PASI\u201311"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In certain stages of the application of a type-2 fuzzy logic system, it is necessary to perform operations between input or output fuzzy variables in order to compute the union, intersection, aggregation, complement, and so forth. In this context, operators that satisfy the axioms of t-norms and t-conorms are of particular significance, as they are applied to model intersection and union, respectively. Furthermore, the existence of a range of these operators allows for the selection of the t-norm or t-conorm that offers the optimal performance, in accordance with the specific context of the system. In this paper, we obtain new t-norms and t-conorms on some important subfamilies of the set of functions from [0,1] to [0,1]. The structure of these families provides a more solid algebraic foundation for the applications. In particular, we define these new operators on the subsets of the functions that are convex, normal, and normal and convex, as well as the functions taking only the values 0 or 1 and the subset of functions whose support is a finite union of closed intervals. These t-norms and t-conorms are generalized to the type-2 fuzzy set framework.<\/jats:p>","DOI":"10.3390\/axioms14010027","type":"journal-article","created":{"date-parts":[[2024,12,31]],"date-time":"2024-12-31T10:17:40Z","timestamp":1735640260000},"page":"27","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Definition of Triangular Norms and Triangular Conorms on Subfamilies of Type-2 Fuzzy Sets"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8644-8564","authenticated-orcid":false,"given":"Pablo","family":"Hern\u00e1ndez-Varela","sequence":"first","affiliation":[{"name":"Departamento de Ciencias Exactas, Facultad de Ingenier\u00eda, Arquitectura y Dise\u00f1o, Universidad San Sebasti\u00e1n, Bellavista 7, Santiago 8420524, Chile"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7395-1999","authenticated-orcid":false,"given":"Francisco Javier","family":"Talavera","sequence":"additional","affiliation":[{"name":"Departamento de F\u00edsica y Matem\u00e1tica Aplicada, Facultad de Ciencias, Universidad de Navarra, C. Irunlarrea 1, 31008 Pamplona, Spain"},{"name":"Institute of Data Science and Artificial Intelligence (DATAI), Edificio Ismael S\u00e1nchez Bella, Campus Universitario, Universidad de Navarra, 31009 Pamplona, Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6473-6039","authenticated-orcid":false,"given":"Susana","family":"Cubillo","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1tica Aplicada, Universidad Polit\u00e9cnica de Madrid, Boadilla del Monte, 28660 Madrid, Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0340-9931","authenticated-orcid":false,"given":"Carmen","family":"Torres-Blanc","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1tica Aplicada, Universidad Polit\u00e9cnica de Madrid, Boadilla del Monte, 28660 Madrid, Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5547-1083","authenticated-orcid":false,"given":"Jorge","family":"Elorza","sequence":"additional","affiliation":[{"name":"Departamento de F\u00edsica y Matem\u00e1tica Aplicada, Facultad de Ciencias, Universidad de Navarra, C. Irunlarrea 1, 31008 Pamplona, Spain"},{"name":"Institute of Data Science and Artificial Intelligence (DATAI), Edificio Ismael S\u00e1nchez Bella, Campus Universitario, Universidad de Navarra, 31009 Pamplona, Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2024,12,31]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1016\/0020-0255(75)90036-5","article-title":"The concept of a linguistic variable and its application to approximate reasoning-I","volume":"8","author":"Zadeh","year":"1975","journal-title":"Inf. Sci."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"301","DOI":"10.1016\/0020-0255(75)90046-8","article-title":"The concept of a linguistic variable and its application to approximate reasoning-II","volume":"8","author":"Zadeh","year":"1975","journal-title":"Inf. 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