{"id":"https://openalex.org/W32395600","doi":"https://doi.org/10.1016/s1571-0653(04)00013-7","title":"The lattices of Moore families and closure operators on a finite set","display_name":"The lattices of Moore families and closure operators on a finite set","publication_year":1999,"publication_date":"1999-04-01","ids":{"openalex":"https://openalex.org/W32395600","doi":"https://doi.org/10.1016/s1571-0653(04)00013-7","mag":"32395600"},"language":"en","primary_location":{"id":"doi:10.1016/s1571-0653(04)00013-7","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s1571-0653(04)00013-7","pdf_url":null,"source":{"id":"https://openalex.org/S902237881","display_name":"Electronic Notes in Discrete Mathematics","issn_l":"1571-0653","issn":["1571-0653"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Electronic Notes in Discrete Mathematics","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":[],"countries":[],"is_corresponding":true,"raw_author_name":"Nathalie Caspard","raw_affiliation_strings":["CERMSEM, Maison des Sciences \u00c9conomiques (Universit\u00e9 Paris1), 106-112, bd de l' H\u01d2pital, 75013, Paris, France"],"affiliations":[{"raw_affiliation_string":"CERMSEM, Maison des Sciences \u00c9conomiques (Universit\u00e9 Paris1), 106-112, bd de l' H\u01d2pital, 75013, Paris, France","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5044067532","display_name":"Bernard Monjardet","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Bernard Monjardet","raw_affiliation_strings":["CERMSEM, Maison des Sciences \u00c9conomiques (Universit\u00e9 Paris1), 106-112, bd de l' H\u01d2pital, 75013, Paris, France"],"affiliations":[{"raw_affiliation_string":"CERMSEM, Maison des Sciences \u00c9conomiques (Universit\u00e9 Paris1), 106-112, bd de l' H\u01d2pital, 75013, Paris, France","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5044067532","https://openalex.org/A5045443290"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.4871,"has_fulltext":false,"cited_by_count":15,"citation_normalized_percentile":{"value":0.59721391,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"2","issue":null,"first_page":"25","last_page":"50"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9889000058174133,"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"}},"topics":[{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9889000058174133,"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"}},{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9805999994277954,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10388","display_name":"Advanced Steganography and Watermarking Techniques","score":0.9779000282287598,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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":0.7585015296936035},{"id":"https://openalex.org/keywords/closure","display_name":"Closure (psychology)","score":0.7435246109962463},{"id":"https://openalex.org/keywords/closure-operator","display_name":"Closure operator","score":0.7243688106536865},{"id":"https://openalex.org/keywords/family-of-sets","display_name":"Family of sets","score":0.7109315991401672},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.6681697368621826},{"id":"https://openalex.org/keywords/intersection","display_name":"Intersection (aeronautics)","score":0.6673409938812256},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5454240441322327},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.5452109575271606},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5378543138504028},{"id":"https://openalex.org/keywords/finite-set","display_name":"Finite set","score":0.5317589044570923},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.44188162684440613},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4214925169944763},{"id":"https://openalex.org/keywords/infinite-set","display_name":"Infinite set","score":0.4107920527458191},{"id":"https://openalex.org/keywords/closed-set","display_name":"Closed set","score":0.39515265822410583},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3655208349227905},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.30105113983154297},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.13779059052467346}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7585015296936035},{"id":"https://openalex.org/C146834321","wikidata":"https://www.wikidata.org/wiki/Q2979672","display_name":"Closure (psychology)","level":2,"score":0.7435246109962463},{"id":"https://openalex.org/C160771489","wikidata":"https://www.wikidata.org/wiki/Q10564851","display_name":"Closure operator","level":3,"score":0.7243688106536865},{"id":"https://openalex.org/C150591576","wikidata":"https://www.wikidata.org/wiki/Q739925","display_name":"Family of sets","level":3,"score":0.7109315991401672},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.6681697368621826},{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.6673409938812256},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5454240441322327},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.5452109575271606},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5378543138504028},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.5317589044570923},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.44188162684440613},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4214925169944763},{"id":"https://openalex.org/C199879729","wikidata":"https://www.wikidata.org/wiki/Q205140","display_name":"Infinite set","level":3,"score":0.4107920527458191},{"id":"https://openalex.org/C164953516","wikidata":"https://www.wikidata.org/wiki/Q320357","display_name":"Closed set","level":2,"score":0.39515265822410583},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3655208349227905},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.30105113983154297},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.13779059052467346},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/s1571-0653(04)00013-7","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s1571-0653(04)00013-7","pdf_url":null,"source":{"id":"https://openalex.org/S902237881","display_name":"Electronic Notes in Discrete Mathematics","issn_l":"1571-0653","issn":["1571-0653"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Electronic Notes in Discrete Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W145185837","https://openalex.org/W1566879902","https://openalex.org/W1608701707","https://openalex.org/W1639378237","https://openalex.org/W1704669313","https://openalex.org/W1971907618","https://openalex.org/W1986229129","https://openalex.org/W1991981232","https://openalex.org/W2013578649","https://openalex.org/W2015101732","https://openalex.org/W2021714595","https://openalex.org/W2027566468","https://openalex.org/W2037828579","https://openalex.org/W2045156123","https://openalex.org/W2045419166","https://openalex.org/W2066242927","https://openalex.org/W2108140789","https://openalex.org/W2125055259","https://openalex.org/W2127019902","https://openalex.org/W2128420091","https://openalex.org/W2134616382","https://openalex.org/W2154165923","https://openalex.org/W2318506549","https://openalex.org/W2330820318","https://openalex.org/W2334476461","https://openalex.org/W2416690344","https://openalex.org/W2613037847","https://openalex.org/W2792385346","https://openalex.org/W6605953870","https://openalex.org/W6636921462"],"related_works":["https://openalex.org/W2553531723","https://openalex.org/W3202111367","https://openalex.org/W4385211012","https://openalex.org/W2059478916","https://openalex.org/W291089565","https://openalex.org/W1570244907","https://openalex.org/W1655564273","https://openalex.org/W3130425472","https://openalex.org/W2064092959","https://openalex.org/W3108505487"],"abstract_inverted_index":null,"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}