{"id":"https://openalex.org/W2061086697","doi":"https://doi.org/10.1016/s1571-0661(04)80705-9","title":"Algebraic Structures of Rough Sets in Representative Approximation Spaces","display_name":"Algebraic Structures of Rough Sets in Representative Approximation Spaces","publication_year":2003,"publication_date":"2003-03-01","ids":{"openalex":"https://openalex.org/W2061086697","doi":"https://doi.org/10.1016/s1571-0661(04)80705-9","mag":"2061086697"},"language":"en","primary_location":{"id":"doi:10.1016/s1571-0661(04)80705-9","is_oa":true,"landing_page_url":"https://doi.org/10.1016/s1571-0661(04)80705-9","pdf_url":null,"source":{"id":"https://openalex.org/S50368787","display_name":"Electronic Notes in Theoretical Computer Science","issn_l":"1571-0661","issn":["1571-0661"],"is_oa":true,"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":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Electronic Notes in Theoretical Computer Science","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://doi.org/10.1016/s1571-0661(04)80705-9","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5046905618","display_name":"Zbigniew Bonikowski","orcid":null},"institutions":[{"id":"https://openalex.org/I4210137370","display_name":"Institute of Mathematics","ror":"https://ror.org/04hrrh248","country_code":"PL","type":"facility","lineage":["https://openalex.org/I4210137370","https://openalex.org/I99542240"]},{"id":"https://openalex.org/I170583851","display_name":"University of Opole","ror":"https://ror.org/04gbpnx96","country_code":"PL","type":"education","lineage":["https://openalex.org/I170583851"]}],"countries":["PL"],"is_corresponding":true,"raw_author_name":"Zbigniew Bonikowski","raw_affiliation_strings":["Institute of Mathematics and Informatics, University of Opole ul. Oleska 48, 45-052 Opole, Poland"],"affiliations":[{"raw_affiliation_string":"Institute of Mathematics and Informatics, University of Opole ul. Oleska 48, 45-052 Opole, Poland","institution_ids":["https://openalex.org/I170583851","https://openalex.org/I4210137370"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5046905618"],"corresponding_institution_ids":["https://openalex.org/I170583851","https://openalex.org/I4210137370"],"apc_list":null,"apc_paid":null,"fwci":0.3545,"has_fulltext":false,"cited_by_count":20,"citation_normalized_percentile":{"value":0.60400314,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"82","issue":"4","first_page":"52","last_page":"63"},"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"}}],"keywords":[{"id":"https://openalex.org/keywords/rough-set","display_name":"Rough set","score":0.844727635383606},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7555795907974243},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.6302818655967712},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.6243080496788025},{"id":"https://openalex.org/keywords/algebraic-structure","display_name":"Algebraic structure","score":0.47510087490081787},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.45528823137283325},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.38298463821411133},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3463495671749115},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1450902819633484},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.13290467858314514},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.060306668281555176}],"concepts":[{"id":"https://openalex.org/C111012933","wikidata":"https://www.wikidata.org/wiki/Q3137210","display_name":"Rough set","level":2,"score":0.844727635383606},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7555795907974243},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.6302818655967712},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.6243080496788025},{"id":"https://openalex.org/C182419690","wikidata":"https://www.wikidata.org/wiki/Q205464","display_name":"Algebraic structure","level":2,"score":0.47510087490081787},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.45528823137283325},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.38298463821411133},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3463495671749115},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1450902819633484},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.13290467858314514},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.060306668281555176},{"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/s1571-0661(04)80705-9","is_oa":true,"landing_page_url":"https://doi.org/10.1016/s1571-0661(04)80705-9","pdf_url":null,"source":{"id":"https://openalex.org/S50368787","display_name":"Electronic Notes in Theoretical Computer Science","issn_l":"1571-0661","issn":["1571-0661"],"is_oa":true,"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":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Electronic Notes in Theoretical Computer Science","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1016/s1571-0661(04)80705-9","is_oa":true,"landing_page_url":"https://doi.org/10.1016/s1571-0661(04)80705-9","pdf_url":null,"source":{"id":"https://openalex.org/S50368787","display_name":"Electronic Notes in Theoretical Computer Science","issn_l":"1571-0661","issn":["1571-0661"],"is_oa":true,"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":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Electronic Notes in Theoretical Computer Science","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W276045325","https://openalex.org/W610977968","https://openalex.org/W1550443332","https://openalex.org/W1557923305","https://openalex.org/W1565697979","https://openalex.org/W1584330960","https://openalex.org/W1584679449","https://openalex.org/W1591618909","https://openalex.org/W1602202955","https://openalex.org/W1602345113","https://openalex.org/W1887407428","https://openalex.org/W2031978194","https://openalex.org/W2036999870","https://openalex.org/W2045084061","https://openalex.org/W2165267798","https://openalex.org/W2512308151","https://openalex.org/W2990995826","https://openalex.org/W4255833381","https://openalex.org/W4285719527","https://openalex.org/W6635112373"],"related_works":["https://openalex.org/W2156697727","https://openalex.org/W2038106543","https://openalex.org/W1595596486","https://openalex.org/W3111870411","https://openalex.org/W163554217","https://openalex.org/W3209526873","https://openalex.org/W2738040829","https://openalex.org/W283664946","https://openalex.org/W2039513928","https://openalex.org/W2381016637"],"abstract_inverted_index":{"In":[0],"this":[1],"paper":[2],"a":[3,27,34],"generalized":[4],"notion":[5],"of":[6,36,50,58,71],"an":[7,13,18],"approximation":[8,14,51,73],"space":[9,15],"is":[10,26,33],"considered.":[11],"By":[12],"we":[16,46,54],"mean":[17],"ordered":[19],"pair":[20],"(U,":[21],"C":[22,32],"),":[23],"where":[24],"U":[25],"finite":[28],"nonempty":[29],"set":[30],"and":[31,44],"covering":[35],"U.":[37],"According":[38],"to":[39,87],"connections":[40],"between":[41],"rough":[42,59,78],"sets":[43,79],"concepts":[45],"define":[47],"two":[48,56],"types":[49,70],"operations.":[52],"Hence":[53],"obtain":[55],"families":[57,65],"sets.":[60,91],"We":[61],"show":[62],"that":[63],"these":[64],"form":[66],"lattices":[67,84],"in":[68,81],"special":[69],"representative":[72],"spaces.":[74],"The":[75],"operations":[76,89],"on":[77,90],"defined":[80],"the":[82],"above":[83],"are":[85],"analogous":[86],"classical":[88]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":2},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
