{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T08:08:21Z","timestamp":1760170101282},"reference-count":7,"publisher":"World Scientific Pub Co Pte Lt","issue":"06","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Unc. Fuzz. Knowl. Based Syst."],"published-print":{"date-parts":[[2003,12]]},"abstract":"<jats:p> Intuitionistic fuzzy sets constitute an extension of fuzzy sets: while fuzzy sets give a degree to which an element belongs to a set, intuitionistic fuzzy sets give both a membership degree and a non-membership degree. The only constraint on those two degrees is that the sum must be smaller than or equal to 1. In fuzzy set theory, an important class of triangular norms is the class of those that satisfy the residuation principle. In the fuzzy case a t-norm satisfies the residuation principle if and only if it is left-continuous. Deschrijver, Cornelis and Kerre proved that for intuitionistic fuzzy t-norms the equivalence between the residuation principle and intuitionistic fuzzy left-continuity only holds for t-representable t-norms.<jats:sup>1<\/jats:sup> In this paper we construct particular subclasses of intuitionistic fuzzy t-norms that satisfy the residuation principle but that are not t-representable and we show that a continuous intuitionistic fuzzy t-norm [Formula: see text] satisfying the residuation principle is t-representable if and only if [Formula: see text]. <\/jats:p>","DOI":"10.1142\/s021848850300248x","type":"journal-article","created":{"date-parts":[[2004,2,12]],"date-time":"2004-02-12T10:51:06Z","timestamp":1076583066000},"page":"691-709","source":"Crossref","is-referenced-by-count":49,"title":["CLASSES OF INTUITIONISTIC FUZZY T-NORMS SATISFYING THE RESIDUATION PRINCIPLE"],"prefix":"10.1142","volume":"11","author":[{"given":"GLAD","family":"DESCHRIJVER","sequence":"first","affiliation":[{"name":"Department of Mathematics and Computer Science, Ghent University,  Fuzziness and Uncertainty Modelling Research Unit, Krijgslaan 281 (S9), B-9000 Gent, Belgium"}]},{"given":"ETIENNE E.","family":"KERRE","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Computer Science, Ghent University, Fuzziness and Uncertainty Modelling, Research Unit, Krijgslaan 281 (S9), B-9000 Gent, Belgium"}]}],"member":"219","published-online":{"date-parts":[[2011,11,21]]},"reference":[{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(94)00210-X"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-0114(98)00167-5"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-0114(86)80034-3"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-7908-1870-3"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1016\/0022-247X(67)90189-8"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-0114(02)00127-6"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-017-1648-2"}],"container-title":["International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/linproxy.fan.workers.dev:443\/https\/www.worldscientific.com\/doi\/pdf\/10.1142\/S021848850300248X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T03:02:32Z","timestamp":1565146952000},"score":1,"resource":{"primary":{"URL":"https:\/\/linproxy.fan.workers.dev:443\/https\/www.worldscientific.com\/doi\/abs\/10.1142\/S021848850300248X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003,12]]},"references-count":7,"journal-issue":{"issue":"06","published-online":{"date-parts":[[2011,11,21]]},"published-print":{"date-parts":[[2003,12]]}},"alternative-id":["10.1142\/S021848850300248X"],"URL":"https:\/\/linproxy.fan.workers.dev:443\/https\/doi.org\/10.1142\/s021848850300248x","relation":{},"ISSN":["0218-4885","1793-6411"],"issn-type":[{"value":"0218-4885","type":"print"},{"value":"1793-6411","type":"electronic"}],"subject":[],"published":{"date-parts":[[2003,12]]}}}