{"id":"https://openalex.org/W1559666492","doi":"https://doi.org/10.3233/fi-2013-895","title":"Duality in Rough Set Theory Based on the Square of Opposition","display_name":"Duality in Rough Set Theory Based on the Square of Opposition","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W1559666492","doi":"https://doi.org/10.3233/fi-2013-895","mag":"1559666492"},"language":"en","primary_location":{"id":"doi:10.3233/fi-2013-895","is_oa":false,"landing_page_url":"https://doi.org/10.3233/fi-2013-895","pdf_url":null,"source":{"id":"https://openalex.org/S39012697","display_name":"Fundamenta Informaticae","issn_l":"0169-2968","issn":["0169-2968","1875-8681"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318577","host_organization_name":"IOS Press","host_organization_lineage":["https://openalex.org/P4310318577"],"host_organization_lineage_names":["IOS Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Fundamenta Informaticae","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/A5063696855","display_name":"Yiyu Yao","orcid":"https://orcid.org/0000-0001-6502-6226"},"institutions":[{"id":"https://openalex.org/I194028371","display_name":"University of Regina","ror":"https://ror.org/03dzc0485","country_code":"CA","type":"education","lineage":["https://openalex.org/I194028371"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Yiyu Yao","raw_affiliation_strings":["Department of Computer Science, University of Regina, Regina, Canada. yyao@cs.uregina.ca"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Regina, Regina, Canada. yyao@cs.uregina.ca","institution_ids":["https://openalex.org/I194028371"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5063696855"],"corresponding_institution_ids":["https://openalex.org/I194028371"],"apc_list":null,"apc_paid":null,"fwci":3.2807,"has_fulltext":false,"cited_by_count":25,"citation_normalized_percentile":{"value":0.91542857,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"127","issue":"1-4","first_page":"49","last_page":"64"},"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/T10538","display_name":"Data Mining Algorithms and Applications","score":0.9287999868392944,"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":0.7342613935470581},{"id":"https://openalex.org/keywords/opposition","display_name":"Opposition (politics)","score":0.6526453495025635},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6279307007789612},{"id":"https://openalex.org/keywords/square","display_name":"Square (algebra)","score":0.43754372000694275},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.357077419757843},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3415201008319855},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2498202621936798},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.19247472286224365},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.10815483331680298},{"id":"https://openalex.org/keywords/political-science","display_name":"Political science","score":0.10013765096664429},{"id":"https://openalex.org/keywords/politics","display_name":"Politics","score":0.05008581280708313}],"concepts":[{"id":"https://openalex.org/C111012933","wikidata":"https://www.wikidata.org/wiki/Q3137210","display_name":"Rough set","level":2,"score":0.7342613935470581},{"id":"https://openalex.org/C2780668109","wikidata":"https://www.wikidata.org/wiki/Q192852","display_name":"Opposition (politics)","level":3,"score":0.6526453495025635},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6279307007789612},{"id":"https://openalex.org/C135692309","wikidata":"https://www.wikidata.org/wiki/Q111124","display_name":"Square (algebra)","level":2,"score":0.43754372000694275},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.357077419757843},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3415201008319855},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2498202621936798},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.19247472286224365},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.10815483331680298},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.10013765096664429},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.05008581280708313},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3233/fi-2013-895","is_oa":false,"landing_page_url":"https://doi.org/10.3233/fi-2013-895","pdf_url":null,"source":{"id":"https://openalex.org/S39012697","display_name":"Fundamenta Informaticae","issn_l":"0169-2968","issn":["0169-2968","1875-8681"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318577","host_organization_name":"IOS Press","host_organization_lineage":["https://openalex.org/P4310318577"],"host_organization_lineage_names":["IOS Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Fundamenta Informaticae","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.5299999713897705,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":36,"referenced_works":["https://openalex.org/W96192410","https://openalex.org/W101345952","https://openalex.org/W151443787","https://openalex.org/W266226170","https://openalex.org/W642576935","https://openalex.org/W859855686","https://openalex.org/W1500029195","https://openalex.org/W1505150927","https://openalex.org/W1516673478","https://openalex.org/W1535538569","https://openalex.org/W1539577632","https://openalex.org/W1539846681","https://openalex.org/W1553701556","https://openalex.org/W1557923305","https://openalex.org/W1578729506","https://openalex.org/W1617290740","https://openalex.org/W1857164369","https://openalex.org/W1966710300","https://openalex.org/W1987251161","https://openalex.org/W1997456116","https://openalex.org/W2023441160","https://openalex.org/W2040834628","https://openalex.org/W2055266411","https://openalex.org/W2070813883","https://openalex.org/W2082266564","https://openalex.org/W2089923511","https://openalex.org/W2099121934","https://openalex.org/W2140982545","https://openalex.org/W2143040521","https://openalex.org/W2143451122","https://openalex.org/W2148443116","https://openalex.org/W2155348479","https://openalex.org/W2465328146","https://openalex.org/W2494934527","https://openalex.org/W2523313693","https://openalex.org/W2914295596"],"related_works":["https://openalex.org/W182058443","https://openalex.org/W2392963705","https://openalex.org/W2490768301","https://openalex.org/W2107349454","https://openalex.org/W3171504412","https://openalex.org/W2490610300","https://openalex.org/W2382278777","https://openalex.org/W2167403502","https://openalex.org/W1964260090","https://openalex.org/W2353240132"],"abstract_inverted_index":{"In":[0],"rough":[1,70],"set":[2,71],"theory,":[3],"one":[4],"typically":[5],"considers":[6],"pairs":[7],"of":[8,15,22,29,31,46,48,52,63,104],"dual":[9],"entities":[10],"such":[11],"as":[12,44],"a":[13,20,27,41,55,91,123],"pair":[14,21,28],"lower":[16],"and":[17,24,33,36,107,120,134],"upper":[18],"approximations,":[19],"indiscernibility":[23],"discernibility":[25],"relations,":[26],"sets":[30],"core":[32],"non-useful":[34],"attributes,":[35],"several":[37],"more.":[38],"By":[39],"adopting":[40],"framework":[42,93],"known":[43],"hypercubes":[45],"duality,":[47],"which":[49],"the":[50,61,84],"square":[51],"opposition":[53],"is":[54,75],"special":[56],"case,":[57],"this":[58],"paper":[59],"investigates":[60],"role":[62],"duality":[64],"for":[65],"interpreting":[66],"fundamental":[67],"concepts":[68,86,106,114],"in":[69,90,116,122,138],"analysis.":[72],"The":[73],"objective":[74],"not":[76],"to":[77,82,130],"introduce":[78],"new":[79],"concepts,":[80],"but":[81],"revisit":[83],"existing":[85],"by":[87],"casting":[88],"them":[89],"common":[92,124],"so":[94],"that":[95,112],"we":[96],"can":[97],"obtain":[98],"more":[99],"insights":[100],"into":[101],"an":[102],"understanding":[103],"these":[105,113],"their":[108],"relationships.":[109],"We":[110],"demonstrate":[111],"can,":[115],"fact,":[117],"be":[118,131],"defined":[119],"explained":[121],"framework,":[125],"although":[126],"they":[127],"first":[128],"appear":[129],"very":[132],"different":[133],"have":[135],"been":[136],"studied":[137],"somewhat":[139],"isolated":[140],"ways.":[141]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":2},{"year":2018,"cited_by_count":6},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":2}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}