{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,6,5]],"date-time":"2024-06-05T04:34:45Z","timestamp":1717562085887},"reference-count":11,"publisher":"World Scientific Pub Co Pte Lt","issue":"04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Unc. Fuzz. Knowl. Based Syst."],"published-print":{"date-parts":[[2005,8]]},"abstract":"<jats:p> Interval-valued fuzzy sets constitute an extension of fuzzy sets which give an interval approximating the \"real\" (but unknown) membership degree. Interval-valued fuzzy sets are equivalent to intuitionistic fuzzy sets in the sense of Atanassov which give both a membership degree and a non-membership degree, whose sum must be smaller than or equal to 1. Both are equivalent to L-fuzzy sets w.r.t. a special lattice L*. In fuzzy set theory, an important class of triangular norms is the class of those that satisfy the residuation principle. In a previous paper<jats:sup>5<\/jats:sup> we gave a construction for t-norms on L* satisfying the residuation principle which are not t-representable. In this paper we investigate the Smets-Magrez axioms and some other properties for the residual implicator generated by such t-norms. <\/jats:p>","DOI":"10.1142\/s0218488505003576","type":"journal-article","created":{"date-parts":[[2005,8,29]],"date-time":"2005-08-29T09:55:17Z","timestamp":1125309317000},"page":"453-464","source":"Crossref","is-referenced-by-count":11,"title":["SMETS-MAGREZ AXIOMS FOR R-IMPLICATORS IN INTERVAL-VALUED AND INTUITIONISTIC FUZZY SET THEORY"],"prefix":"10.1142","volume":"13","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":"rf3","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-0114(02)00127-6"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1016\/0022-247X(67)90189-8"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1142\/S021848850300248X"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-011-5300-3"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(87)90148-5"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-7908-1870-3"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1109\/TFUZZ.2003.822678"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1016\/S0888-613X(03)00072-0"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1016\/0888-613X(87)90023-5"},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4615-5217-8"},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(94)00210-X"}],"container-title":["International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218488505003576","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T17:30:48Z","timestamp":1565199048000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218488505003576"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2005,8]]},"references-count":11,"journal-issue":{"issue":"04","published-online":{"date-parts":[[2011,11,21]]},"published-print":{"date-parts":[[2005,8]]}},"alternative-id":["10.1142\/S0218488505003576"],"URL":"https:\/\/doi.org\/10.1142\/s0218488505003576","relation":{},"ISSN":["0218-4885","1793-6411"],"issn-type":[{"value":"0218-4885","type":"print"},{"value":"1793-6411","type":"electronic"}],"subject":[],"published":{"date-parts":[[2005,8]]}}}