{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:15:31Z","timestamp":1760242531693,"version":"build-2065373602"},"reference-count":21,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2017,10,28]],"date-time":"2017-10-28T00:00:00Z","timestamp":1509148800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>Looking at decisiveness as crucial, we discuss the existence of an order-preserving function for the nontotal crisp preference relation naturally associated to a nontotal fuzzy preference relation. We further present conditions for the existence of an upper semicontinuous order-preserving function for a fuzzy binary relation on a crisp topological space.<\/jats:p>","DOI":"10.3390\/axioms6040029","type":"journal-article","created":{"date-parts":[[2017,10,30]],"date-time":"2017-10-30T12:16:23Z","timestamp":1509365783000},"page":"29","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Existence of Order-Preserving Functions for Nontotal Fuzzy Preference Relations under Decisiveness"],"prefix":"10.3390","volume":"6","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8775-2824","authenticated-orcid":false,"given":"Paolo","family":"Bevilacqua","sequence":"first","affiliation":[{"name":"Dipartimento di Ingegneria e Architettura, Universit\u00e0 di Trieste, 34127 Trieste, Italy"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3799-4630","authenticated-orcid":false,"given":"Gianni","family":"Bosi","sequence":"additional","affiliation":[{"name":"Dipartimento di Scienze Economiche, Aziendali, Matematiche e Statistiche \"Bruno de Finetti\", Universit\u00e0 di Trieste, 34127 Trieste, Italy"}]},{"given":"Magal\u00ec","family":"Zuanon","sequence":"additional","affiliation":[{"name":"Dipartimento di Economia e Management, Universit\u00e0 di Brescia, 25122 Brescia, Italy"}]}],"member":"1968","published-online":{"date-parts":[[2017,10,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"271","DOI":"10.1016\/0165-0114(95)00114-Z","article-title":"An existence theorem or fuzzy utility functions: A new elementary proof","volume":"74","author":"Billot","year":"1995","journal-title":"Fuzzy Sets Syst."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"667","DOI":"10.1007\/s00355-006-0190-3","article-title":"Utility function of fuzzy preferences on a countable set under max-\u2217-transitivity","volume":"28","author":"Fono","year":"2007","journal-title":"Soc. 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