{"id":"https://openalex.org/W1535538569","doi":"https://doi.org/10.1007/978-3-540-71200-8_22","title":"Lattice Theory for Rough Sets","display_name":"Lattice Theory for Rough Sets","publication_year":2007,"publication_date":"2007-05-21","ids":{"openalex":"https://openalex.org/W1535538569","doi":"https://doi.org/10.1007/978-3-540-71200-8_22","mag":"1535538569"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-540-71200-8_22","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-540-71200-8_22","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"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":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"book-chapter","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/A5091139212","display_name":"Jouni J\u00e4rvinen","orcid":"https://orcid.org/0000-0002-8729-8633"},"institutions":[{"id":"https://openalex.org/I183173800","display_name":"Turku Centre for Computer Science","ror":"https://ror.org/00vy7ed73","country_code":"FI","type":"facility","lineage":["https://openalex.org/I130217899","https://openalex.org/I155660961","https://openalex.org/I183173800"]},{"id":"https://openalex.org/I155660961","display_name":"University of Turku","ror":"https://ror.org/05vghhr25","country_code":"FI","type":"education","lineage":["https://openalex.org/I155660961"]}],"countries":["FI"],"is_corresponding":true,"raw_author_name":"Jouni J\u00e4rvinen","raw_affiliation_strings":["Turku Centre for Computer Science (TUCS), FI-20014 University of Turku, Finland","Turku Centre for Computer Science, University of Turku, Finland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Turku Centre for Computer Science (TUCS), FI-20014 University of Turku, Finland","institution_ids":["https://openalex.org/I183173800","https://openalex.org/I155660961"]},{"raw_affiliation_string":"Turku Centre for Computer Science, University of Turku, Finland","institution_ids":["https://openalex.org/I183173800","https://openalex.org/I155660961"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5091139212"],"corresponding_institution_ids":["https://openalex.org/I155660961","https://openalex.org/I183173800"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":7.8301,"has_fulltext":false,"cited_by_count":135,"citation_normalized_percentile":{"value":0.98343769,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":100},"biblio":{"volume":null,"issue":null,"first_page":"400","last_page":"498"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11063","display_name":"Rough Sets and Fuzzy Logic","score":0.9998999834060669,"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/T11063","display_name":"Rough Sets and Fuzzy Logic","score":0.9998999834060669,"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/T10215","display_name":"Semantic Web and Ontologies","score":0.9315999746322632,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T10538","display_name":"Data Mining Algorithms and Applications","score":0.9017999768257141,"subfield":{"id":"https://openalex.org/subfields/1710","display_name":"Information Systems"},"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/rough-set","display_name":"Rough set","score":0.8495143055915833},{"id":"https://openalex.org/keywords/distributive-lattice","display_name":"Distributive lattice","score":0.6756797432899475},{"id":"https://openalex.org/keywords/distributive-property","display_name":"Distributive property","score":0.6642940640449524},{"id":"https://openalex.org/keywords/notation","display_name":"Notation","score":0.6446925401687622},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.5742632746696472},{"id":"https://openalex.org/keywords/map-of-lattices","display_name":"Map of lattices","score":0.5634893774986267},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5479481220245361},{"id":"https://openalex.org/keywords/closure","display_name":"Closure (psychology)","score":0.5407585501670837},{"id":"https://openalex.org/keywords/closure-operator","display_name":"Closure operator","score":0.5279661417007446},{"id":"https://openalex.org/keywords/reduct","display_name":"Reduct","score":0.47202104330062866},{"id":"https://openalex.org/keywords/galois-connection","display_name":"Galois connection","score":0.45981842279434204},{"id":"https://openalex.org/keywords/congruence-lattice-problem","display_name":"Congruence lattice problem","score":0.4505579173564911},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4053114950656891},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3766101598739624},{"id":"https://openalex.org/keywords/closed-set","display_name":"Closed set","score":0.3676437735557556},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.28750771284103394},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.18748238682746887},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.12296134233474731},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09152966737747192},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.07216018438339233}],"concepts":[{"id":"https://openalex.org/C111012933","wikidata":"https://www.wikidata.org/wiki/Q3137210","display_name":"Rough set","level":2,"score":0.8495143055915833},{"id":"https://openalex.org/C192606457","wikidata":"https://www.wikidata.org/wiki/Q2363730","display_name":"Distributive lattice","level":3,"score":0.6756797432899475},{"id":"https://openalex.org/C11821877","wikidata":"https://www.wikidata.org/wiki/Q187959","display_name":"Distributive property","level":2,"score":0.6642940640449524},{"id":"https://openalex.org/C45357846","wikidata":"https://www.wikidata.org/wiki/Q2001982","display_name":"Notation","level":2,"score":0.6446925401687622},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.5742632746696472},{"id":"https://openalex.org/C128379363","wikidata":"https://www.wikidata.org/wiki/Q6753757","display_name":"Map of lattices","level":4,"score":0.5634893774986267},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5479481220245361},{"id":"https://openalex.org/C146834321","wikidata":"https://www.wikidata.org/wiki/Q2979672","display_name":"Closure (psychology)","level":2,"score":0.5407585501670837},{"id":"https://openalex.org/C160771489","wikidata":"https://www.wikidata.org/wiki/Q10564851","display_name":"Closure operator","level":3,"score":0.5279661417007446},{"id":"https://openalex.org/C69177213","wikidata":"https://www.wikidata.org/wiki/Q12880812","display_name":"Reduct","level":3,"score":0.47202104330062866},{"id":"https://openalex.org/C2777573902","wikidata":"https://www.wikidata.org/wiki/Q1491747","display_name":"Galois connection","level":2,"score":0.45981842279434204},{"id":"https://openalex.org/C84540187","wikidata":"https://www.wikidata.org/wiki/Q5160997","display_name":"Congruence lattice problem","level":4,"score":0.4505579173564911},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4053114950656891},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3766101598739624},{"id":"https://openalex.org/C164953516","wikidata":"https://www.wikidata.org/wiki/Q320357","display_name":"Closed set","level":2,"score":0.3676437735557556},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.28750771284103394},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.18748238682746887},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.12296134233474731},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09152966737747192},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.07216018438339233},{"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/C207114421","wikidata":"https://www.wikidata.org/wiki/Q133900","display_name":"Diffraction","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/C89957378","wikidata":"https://www.wikidata.org/wiki/Q164129","display_name":"Reciprocal lattice","level":3,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/978-3-540-71200-8_22","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-540-71200-8_22","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"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":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.106.4448","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.106.4448","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://staff.cs.utu.fi/jjarvine/papers/monograph.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.44999998807907104,"id":"https://metadata.un.org/sdg/13","display_name":"Climate action"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":77,"referenced_works":["https://openalex.org/W15218621","https://openalex.org/W43035074","https://openalex.org/W65566710","https://openalex.org/W83172133","https://openalex.org/W114854144","https://openalex.org/W116608051","https://openalex.org/W179988417","https://openalex.org/W203512583","https://openalex.org/W639459029","https://openalex.org/W654300311","https://openalex.org/W1500907847","https://openalex.org/W1503729935","https://openalex.org/W1504021105","https://openalex.org/W1505150927","https://openalex.org/W1522056303","https://openalex.org/W1536630500","https://openalex.org/W1536681184","https://openalex.org/W1553701556","https://openalex.org/W1557923305","https://openalex.org/W1563357211","https://openalex.org/W1582269801","https://openalex.org/W1582314147","https://openalex.org/W1591618909","https://openalex.org/W1834136269","https://openalex.org/W1857164369","https://openalex.org/W1933950199","https://openalex.org/W1965548823","https://openalex.org/W1968871074","https://openalex.org/W1978202330","https://openalex.org/W1979029381","https://openalex.org/W1992205482","https://openalex.org/W1993175210","https://openalex.org/W2002367458","https://openalex.org/W2003017965","https://openalex.org/W2003571395","https://openalex.org/W2006242427","https://openalex.org/W2008149162","https://openalex.org/W2019254124","https://openalex.org/W2021160545","https://openalex.org/W2023441160","https://openalex.org/W2023648368","https://openalex.org/W2046213250","https://openalex.org/W2050527500","https://openalex.org/W2054416947","https://openalex.org/W2054469070","https://openalex.org/W2068593785","https://openalex.org/W2073714748","https://openalex.org/W2093397547","https://openalex.org/W2116509046","https://openalex.org/W2165267798","https://openalex.org/W2185907055","https://openalex.org/W2313227953","https://openalex.org/W2315064349","https://openalex.org/W2396903734","https://openalex.org/W2491671861","https://openalex.org/W2500062327","https://openalex.org/W2912565176","https://openalex.org/W2988119170","https://openalex.org/W2990995826","https://openalex.org/W3023422795","https://openalex.org/W3039948875","https://openalex.org/W3043060850","https://openalex.org/W3047122219","https://openalex.org/W3142075490","https://openalex.org/W3159837440","https://openalex.org/W4205529794","https://openalex.org/W4211007335","https://openalex.org/W4233022570","https://openalex.org/W4246252414","https://openalex.org/W4252706706","https://openalex.org/W4253176183","https://openalex.org/W4253211478","https://openalex.org/W4255318870","https://openalex.org/W4255833381","https://openalex.org/W4256393076","https://openalex.org/W4285719527","https://openalex.org/W4293176479"],"related_works":["https://openalex.org/W2112873942","https://openalex.org/W2129953753","https://openalex.org/W4225006771","https://openalex.org/W1561592828","https://openalex.org/W2232374221","https://openalex.org/W1983739088","https://openalex.org/W2053994809","https://openalex.org/W2064877230","https://openalex.org/W1535538569","https://openalex.org/W2032826780"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":8},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":7},{"year":2018,"cited_by_count":8},{"year":2017,"cited_by_count":7},{"year":2016,"cited_by_count":9},{"year":2015,"cited_by_count":9},{"year":2014,"cited_by_count":13},{"year":2013,"cited_by_count":11},{"year":2012,"cited_by_count":10}],"updated_date":"2026-05-27T09:02:27.158192","created_date":"2025-10-10T00:00:00"}