{"id":"https://openalex.org/W1503825774","doi":"https://doi.org/10.1023/a:1006444906980","title":"A Characterization Theorem for the Canonical Basis of a Closure Operator","display_name":"A Characterization Theorem for the Canonical Basis of a Closure Operator","publication_year":1999,"publication_date":"1999-09-01","ids":{"openalex":"https://openalex.org/W1503825774","doi":"https://doi.org/10.1023/a:1006444906980","mag":"1503825774"},"language":"en","primary_location":{"id":"doi:10.1023/a:1006444906980","is_oa":false,"landing_page_url":"https://doi.org/10.1023/a:1006444906980","pdf_url":null,"source":{"id":"https://openalex.org/S121371512","display_name":"Order","issn_l":"0167-8094","issn":["0167-8094","1572-9273"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Order","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/A5045443290","display_name":"Nathalie Caspard","orcid":null},"institutions":[{"id":"https://openalex.org/I4210144804","display_name":"Laboratoire de Recherche en Informatique","ror":"https://ror.org/04e3ktk27","country_code":"FR","type":"facility","lineage":["https://openalex.org/I102197404","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I4210144804","https://openalex.org/I4210159245"]},{"id":"https://openalex.org/I102197404","display_name":"Universit\u00e9 Paris-Sud","ror":"https://ror.org/028rypz17","country_code":"FR","type":"education","lineage":["https://openalex.org/I102197404"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"N. Caspard","raw_affiliation_strings":["LRI, Universit\u00e9 Paris Sud, 91405, Orsay cedex, France","LRI, Universit\u00e9 Paris-Sud, Orsay, Cedex, France"],"affiliations":[{"raw_affiliation_string":"LRI, Universit\u00e9 Paris Sud, 91405, Orsay cedex, France","institution_ids":["https://openalex.org/I102197404","https://openalex.org/I4210144804"]},{"raw_affiliation_string":"LRI, Universit\u00e9 Paris-Sud, Orsay, Cedex, France","institution_ids":["https://openalex.org/I102197404","https://openalex.org/I4210144804"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5045443290"],"corresponding_institution_ids":["https://openalex.org/I102197404","https://openalex.org/I4210144804"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":0.3719,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.58295536,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"16","issue":"3","first_page":"227","last_page":"230"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11106","display_name":"Data Management and Algorithms","score":0.9922999739646912,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11106","display_name":"Data Management and Algorithms","score":0.9922999739646912,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/T11596","display_name":"Constraint Satisfaction and Optimization","score":0.9887999892234802,"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/T11063","display_name":"Rough Sets and Fuzzy Logic","score":0.983299970626831,"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":0.82452791929245},{"id":"https://openalex.org/keywords/closure","display_name":"Closure (psychology)","score":0.780547022819519},{"id":"https://openalex.org/keywords/closure-operator","display_name":"Closure operator","score":0.7678968906402588},{"id":"https://openalex.org/keywords/characterization","display_name":"Characterization (materials science)","score":0.6472873687744141},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.5862272381782532},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.4326211214065552},{"id":"https://openalex.org/keywords/shift-operator","display_name":"Shift operator","score":0.4292190968990326},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4240695536136627},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.41654980182647705},{"id":"https://openalex.org/keywords/compact-operator","display_name":"Compact operator","score":0.2544519901275635},{"id":"https://openalex.org/keywords/closed-set","display_name":"Closed set","score":0.20714470744132996},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.1437709927558899},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.10841485857963562}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.82452791929245},{"id":"https://openalex.org/C146834321","wikidata":"https://www.wikidata.org/wiki/Q2979672","display_name":"Closure (psychology)","level":2,"score":0.780547022819519},{"id":"https://openalex.org/C160771489","wikidata":"https://www.wikidata.org/wiki/Q10564851","display_name":"Closure operator","level":3,"score":0.7678968906402588},{"id":"https://openalex.org/C2780841128","wikidata":"https://www.wikidata.org/wiki/Q5073781","display_name":"Characterization (materials science)","level":2,"score":0.6472873687744141},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5862272381782532},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4326211214065552},{"id":"https://openalex.org/C65630602","wikidata":"https://www.wikidata.org/wiki/Q2278680","display_name":"Shift operator","level":4,"score":0.4292190968990326},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4240695536136627},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.41654980182647705},{"id":"https://openalex.org/C79013869","wikidata":"https://www.wikidata.org/wiki/Q1780743","display_name":"Compact operator","level":3,"score":0.2544519901275635},{"id":"https://openalex.org/C164953516","wikidata":"https://www.wikidata.org/wiki/Q320357","display_name":"Closed set","level":2,"score":0.20714470744132996},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.1437709927558899},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.10841485857963562},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C171250308","wikidata":"https://www.wikidata.org/wiki/Q11468","display_name":"Nanotechnology","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C34447519","wikidata":"https://www.wikidata.org/wiki/Q179522","display_name":"Market economy","level":1,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1023/a:1006444906980","is_oa":false,"landing_page_url":"https://doi.org/10.1023/a:1006444906980","pdf_url":null,"source":{"id":"https://openalex.org/S121371512","display_name":"Order","issn_l":"0167-8094","issn":["0167-8094","1572-9273"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Order","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":2,"referenced_works":["https://openalex.org/W106642128","https://openalex.org/W2059867571"],"related_works":["https://openalex.org/W2044273750","https://openalex.org/W50402501","https://openalex.org/W2592717749","https://openalex.org/W574916794","https://openalex.org/W2170250808","https://openalex.org/W1977216384","https://openalex.org/W2791369284","https://openalex.org/W1503825774","https://openalex.org/W2994612529","https://openalex.org/W2000685762"],"abstract_inverted_index":null,"counts_by_year":[{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2016-06-24T00:00:00"}