{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T11:30:23Z","timestamp":1777462223366,"version":"3.51.4"},"reference-count":33,"publisher":"World Scientific Pub Co Pte Lt","issue":"05","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Unc. Fuzz. Knowl. Based Syst."],"published-print":{"date-parts":[[2013,10]]},"abstract":"<jats:p> We study necessary and sufficient conditions for the continuous Scott-Suppes representability of a semiorder through a continuous real-valued map and a strictly positive threshold. In the general case of a semiorder defined on topological space, we find several necessary conditions for the continuous representability. These necessary conditions are not sufficient, in general. As a matter of fact, the analogous of the classical Debreu's lemma for the continuous representability of total preorders is no longer valid for semiorders. However, and in a positive direction, we show that if the set is finite those conditions are indeed sufficient. In particular, we characterize the continuous Scott-Suppes representability of semiorders defined on a finite set endowed with a topology. <\/jats:p>","DOI":"10.1142\/s0218488513500323","type":"journal-article","created":{"date-parts":[[2013,10,10]],"date-time":"2013-10-10T17:15:00Z","timestamp":1381425300000},"page":"675-694","source":"Crossref","is-referenced-by-count":11,"title":["FURTHER RESULTS ON THE CONTINUOUS REPRESENTABILITY OF SEMIORDERS"],"prefix":"10.1142","volume":"21","author":[{"given":"A.","family":"ESTEVAN","sequence":"first","affiliation":[{"name":"Departamento de Matem\u00e1ticas, Universidad P\u00fablica de Navarra, Campus Arrosad\u00eda, Pamplona, 31006, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"J.","family":"GUTI\u00c9RREZ GARC\u00cdA","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1ticas, Universidad del Pa\u00eds Vasco UPV\/EHU, Apdo. 644, Bilbao, 48080, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"E.","family":"INDUR\u00c1IN","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1ticas, Universidad P\u00fablica de Navarra, Campus Arrosad\u00eda, Pamplona, 31006, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2013,10,10]]},"reference":[{"key":"p_1","doi-asserted-by":"publisher","DOI":"10.1016\/0304-4068(87)90003-6"},{"key":"p_3","doi-asserted-by":"publisher","DOI":"10.1142\/S0218488507004698"},{"key":"p_4","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmp.2006.10.005"},{"key":"p_5","doi-asserted-by":"publisher","DOI":"10.2307\/2964389"},{"key":"p_6","doi-asserted-by":"publisher","DOI":"10.1016\/0304-4068(87)90013-9"},{"key":"p_7","doi-asserted-by":"publisher","DOI":"10.1016\/0022-0531(87)90119-0"},{"key":"p_8","doi-asserted-by":"publisher","DOI":"10.1016\/0165-4896(88)90012-1"},{"key":"p_9","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmp.2007.09.006"},{"key":"p_11","doi-asserted-by":"publisher","DOI":"10.2307\/2525513"},{"key":"p_13","doi-asserted-by":"publisher","DOI":"10.1016\/0022-2496(92)90035-6"},{"key":"p_14","first-page":"441","volume":"17","author":"Wiener N.","year":"1914","journal-title":"Math. 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