{"id":"https://openalex.org/W2002917235","doi":"https://doi.org/10.1142/s0218488513500323","title":"FURTHER RESULTS ON THE CONTINUOUS REPRESENTABILITY OF SEMIORDERS","display_name":"FURTHER RESULTS ON THE CONTINUOUS REPRESENTABILITY OF SEMIORDERS","publication_year":2013,"publication_date":"2013-10-01","ids":{"openalex":"https://openalex.org/W2002917235","doi":"https://doi.org/10.1142/s0218488513500323","mag":"2002917235"},"language":"en","primary_location":{"id":"doi:10.1142/s0218488513500323","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218488513500323","pdf_url":null,"source":{"id":"https://openalex.org/S69518169","display_name":"International Journal of Uncertainty Fuzziness and Knowledge-Based Systems","issn_l":"0218-4885","issn":["0218-4885","1793-6411"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5001220242","display_name":"Asier Estevan","orcid":"https://orcid.org/0000-0002-8822-2438"},"institutions":[{"id":"https://openalex.org/I175051016","display_name":"Universidad P\u00fablica de Navarra (UPNA)","ror":"https://ror.org/02z0cah89","country_code":"ES","type":"education","lineage":["https://openalex.org/I175051016"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"A. ESTEVAN","raw_affiliation_strings":["Departamento de Matem\u00e1ticas, Universidad P\u00fablica de Navarra, Campus Arrosad\u00eda, Pamplona, 31006, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00e1ticas, Universidad P\u00fablica de Navarra, Campus Arrosad\u00eda, Pamplona, 31006, Spain","institution_ids":["https://openalex.org/I175051016"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5047904055","display_name":"Javier Guti\u00e9rrez Garc\u00eda","orcid":"https://orcid.org/0000-0002-2904-7801"},"institutions":[{"id":"https://openalex.org/I169108374","display_name":"University of the Basque Country","ror":"https://ror.org/000xsnr85","country_code":"ES","type":"education","lineage":["https://openalex.org/I169108374"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"J. GUTI\u00c9RREZ GARC\u00cdA","raw_affiliation_strings":["Departamento de Matem\u00e1ticas, Universidad del Pa\u00eds Vasco UPV/EHU, Apdo. 644, Bilbao, 48080, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00e1ticas, Universidad del Pa\u00eds Vasco UPV/EHU, Apdo. 644, Bilbao, 48080, Spain","institution_ids":["https://openalex.org/I169108374"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5067214242","display_name":"Esteban Indur\u00e1in","orcid":"https://orcid.org/0000-0002-1511-5658"},"institutions":[{"id":"https://openalex.org/I175051016","display_name":"Universidad P\u00fablica de Navarra (UPNA)","ror":"https://ror.org/02z0cah89","country_code":"ES","type":"education","lineage":["https://openalex.org/I175051016"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"E. INDUR\u00c1IN","raw_affiliation_strings":["Departamento de Matem\u00e1ticas, Universidad P\u00fablica de Navarra, Campus Arrosad\u00eda, Pamplona, 31006, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00e1ticas, Universidad P\u00fablica de Navarra, Campus Arrosad\u00eda, Pamplona, 31006, Spain","institution_ids":["https://openalex.org/I175051016"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.345,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.7865519,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"21","issue":"05","first_page":"675","last_page":"694"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9970999956130981,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9970999956130981,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11596","display_name":"Constraint Satisfaction and Optimization","score":0.9932000041007996,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9775000214576721,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7033186554908752},{"id":"https://openalex.org/keywords/lemma","display_name":"Lemma (botany)","score":0.6528178453445435},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.581225574016571},{"id":"https://openalex.org/keywords/topological-space","display_name":"Topological space","score":0.5111938118934631},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.508489727973938},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.4922443926334381},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.4776964485645294},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4389247000217438},{"id":"https://openalex.org/keywords/finite-set","display_name":"Finite set","score":0.41978731751441956},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.26316148042678833},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.21770614385604858},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.15024298429489136}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7033186554908752},{"id":"https://openalex.org/C2777759810","wikidata":"https://www.wikidata.org/wiki/Q149316","display_name":"Lemma (botany)","level":3,"score":0.6528178453445435},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.581225574016571},{"id":"https://openalex.org/C81332173","wikidata":"https://www.wikidata.org/wiki/Q179899","display_name":"Topological space","level":2,"score":0.5111938118934631},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.508489727973938},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.4922443926334381},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4776964485645294},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4389247000217438},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.41978731751441956},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.26316148042678833},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.21770614385604858},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.15024298429489136},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C46757340","wikidata":"https://www.wikidata.org/wiki/Q43238","display_name":"Poaceae","level":2,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218488513500323","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218488513500323","pdf_url":null,"source":{"id":"https://openalex.org/S69518169","display_name":"International Journal of Uncertainty Fuzziness and Knowledge-Based Systems","issn_l":"0218-4885","issn":["0218-4885","1793-6411"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.49000000953674316,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320321837","display_name":"Ministerio de Econom\u00eda y Competitividad","ror":"https://ror.org/034900433"},{"id":"https://openalex.org/F4320321919","display_name":"Euskal Herriko Unibertsitatea","ror":"https://ror.org/000xsnr85"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W50569743","https://openalex.org/W1662659233","https://openalex.org/W1964105961","https://openalex.org/W1966692599","https://openalex.org/W1976477682","https://openalex.org/W1978730176","https://openalex.org/W1978998919","https://openalex.org/W1980971135","https://openalex.org/W1986132220","https://openalex.org/W1989511542","https://openalex.org/W1993134447","https://openalex.org/W2003474786","https://openalex.org/W2005135931","https://openalex.org/W2006376790","https://openalex.org/W2006831047","https://openalex.org/W2011503663","https://openalex.org/W2020218680","https://openalex.org/W2021339822","https://openalex.org/W2028391744","https://openalex.org/W2034637506","https://openalex.org/W2038039012","https://openalex.org/W2050354655","https://openalex.org/W2076308462","https://openalex.org/W2081036871","https://openalex.org/W2087833537","https://openalex.org/W2094315959","https://openalex.org/W2108143285","https://openalex.org/W2124046639","https://openalex.org/W2127373277","https://openalex.org/W2130872587","https://openalex.org/W2145897424","https://openalex.org/W2318064754"],"related_works":["https://openalex.org/W3006682748","https://openalex.org/W1097487277","https://openalex.org/W2768610039","https://openalex.org/W4308265086","https://openalex.org/W2949964783","https://openalex.org/W2106889256","https://openalex.org/W2735923117","https://openalex.org/W2115913661","https://openalex.org/W3168772390","https://openalex.org/W2142539551"],"abstract_inverted_index":{"We":[0],"study":[1],"necessary":[2,38,45],"and":[3,19,78],"sufficient":[4],"conditions":[5,39,46,92],"for":[6,40,64,75],"the":[7,25,41,57,60,65,87,100],"continuous":[8,16,42,66,101],"Scott-Suppes":[9,102],"representability":[10,67,103],"of":[11,28,55,59,68,104],"a":[12,15,20,29,53,80,108,113],"semiorder":[13,30],"through":[14],"real-valued":[17],"map":[18],"strictly":[21],"positive":[22,81],"threshold.":[23],"In":[24,96],"general":[26],"case":[27],"defined":[31,106],"on":[32,107],"topological":[33],"space,":[34],"we":[35,83,98],"find":[36],"several":[37],"representability.":[43],"These":[44],"are":[47,93],"not":[48],"sufficient,":[49],"in":[50,79],"general.":[51],"As":[52],"matter":[54],"fact,":[56],"analogous":[58],"classical":[61],"Debreu's":[62],"lemma":[63],"total":[69],"preorders":[70],"is":[71,89],"no":[72],"longer":[73],"valid":[74],"semiorders.":[76],"However,":[77],"direction,":[82],"show":[84],"that":[85],"if":[86],"set":[88,110],"finite":[90,109],"those":[91],"indeed":[94],"sufficient.":[95],"particular,":[97],"characterize":[99],"semiorders":[105],"endowed":[111],"with":[112],"topology.":[114]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
