{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,3]],"date-time":"2025-11-03T22:51:30Z","timestamp":1762210290494},"reference-count":5,"publisher":"World Scientific Pub Co Pte Lt","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Unc. Fuzz. Knowl. Based Syst."],"published-print":{"date-parts":[[1999,6]]},"abstract":"<jats:p> The purpose of this paper is to analyze the operators induced by relations and conversely the relations induced by operators in fuzzy logic. Given a t-norm * and given a non-empty universal set X, it is well known that if R is a fuzzy *-preorder on X then the operator induced by R, [Formula: see text], is a fuzzy consequence operator (FCO). In fact, [Formula: see text] is a *-coherent FCO. It is also known that if C is a *-coherent FCO then the relation induced by C, R<jats:sub>C<\/jats:sub>, is a fuzzy *-preorder. We explore the *-coherence axiom because we do not know in the literature any example of non-coherent operator. Then, several families of these operators will be shown. Moreover we prove that the equivalence between fuzzy preorders and fuzzy consequence operators is held in only one way. As a result, a characterization of the *-preorder concept using the induced operator is given. Also some characterizations which show when an operator induces a *-preorder are proved. Finally, we will show that the characterization of the operators induced by relations given for finite universes cannot be generalized for infinite universes. <\/jats:p>","DOI":"10.1142\/s0218488599000167","type":"journal-article","created":{"date-parts":[[2003,4,22]],"date-time":"2003-04-22T11:43:29Z","timestamp":1051011809000},"page":"219-234","source":"Crossref","is-referenced-by-count":11,"title":["ON THE RELATION BETWEEN FUZZY PREORDERS AND FUZZY CONSEQUENCE OPERATORS"],"prefix":"10.1142","volume":"07","author":[{"given":"J.","family":"ELORZA","sequence":"first","affiliation":[{"name":"Dep. de Matem\u00e1tica e Inform\u00e1tica, Dep. de Autom\u00e1tica y Computati\u00f3n, Universidad P\u00fablica de Navarra, Campus de Arrosad\u00eda 31006 Pamplona, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"P.","family":"BURILLO","sequence":"additional","affiliation":[{"name":"Dep. de Matem\u00e1tica e Inform\u00e1tica, Dep. de Autom\u00e1tica y Computati\u00f3n, Universidad P\u00fablica de Navarra, Campus de Arrosad\u00eda 31006 Pamplona, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,21]]},"reference":[{"key":"p_3","first-page":"989","volume":"988","year":"1989","journal-title":"Course 1."},{"key":"p_4","first-page":"8","author":"Zadeh L.A.","year":"1965","journal-title":"Information and Control"},{"key":"p_9","first-page":"3","volume":"4","author":"Ward M.","journal-title":"Annals of Mathematics"},{"key":"p_13","author":"Trillas J","journal-title":"(submit t o I J A R ) Proc."},{"key":"p_29","first-page":"4","volume":"5","year":"1993","journal-title":"Fuzzy Sets and Systems"}],"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\/S0218488599000167","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T03:02:31Z","timestamp":1565146951000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218488599000167"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1999,6]]},"references-count":5,"journal-issue":{"issue":"03","published-online":{"date-parts":[[2011,11,21]]},"published-print":{"date-parts":[[1999,6]]}},"alternative-id":["10.1142\/S0218488599000167"],"URL":"https:\/\/doi.org\/10.1142\/s0218488599000167","relation":{},"ISSN":["0218-4885","1793-6411"],"issn-type":[{"value":"0218-4885","type":"print"},{"value":"1793-6411","type":"electronic"}],"subject":[],"published":{"date-parts":[[1999,6]]}}}