{"id":"https://openalex.org/W2938986960","doi":"https://doi.org/10.3233/fi-2019-1803","title":"An Uncertainty Measure Based on Lower and Upper Approximations for Generalized Rough set Models","display_name":"An Uncertainty Measure Based on Lower and Upper Approximations for Generalized Rough set Models","publication_year":2019,"publication_date":"2019-04-17","ids":{"openalex":"https://openalex.org/W2938986960","doi":"https://doi.org/10.3233/fi-2019-1803","mag":"2938986960"},"language":"en","primary_location":{"id":"doi:10.3233/fi-2019-1803","is_oa":false,"landing_page_url":"https://doi.org/10.3233/fi-2019-1803","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/A5103064030","display_name":"Zhaohao Wang","orcid":"https://orcid.org/0000-0003-1385-0947"},"institutions":[{"id":"https://openalex.org/I94310126","display_name":"Shanxi Normal University","ror":"https://ror.org/03zd3ta61","country_code":"CN","type":"education","lineage":["https://openalex.org/I94310126"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Zhaohao Wang","raw_affiliation_strings":["School of Mathematics and Computer Science, Shanxi Normal University, Shanxi, Linfen, 041000, P.R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Computer Science, Shanxi Normal University, Shanxi, Linfen, 041000, P.R. China","institution_ids":["https://openalex.org/I94310126"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5032492003","display_name":"Huifang Yue","orcid":null},"institutions":[{"id":"https://openalex.org/I94310126","display_name":"Shanxi Normal University","ror":"https://ror.org/03zd3ta61","country_code":"CN","type":"education","lineage":["https://openalex.org/I94310126"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Huifang Yue","raw_affiliation_strings":["School of Mathematics and Computer Science, Shanxi Normal University, Shanxi, Linfen, 041000, P.R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Computer Science, Shanxi Normal University, Shanxi, Linfen, 041000, P.R. China","institution_ids":["https://openalex.org/I94310126"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5015202607","display_name":"Jianping Deng","orcid":null},"institutions":[{"id":"https://openalex.org/I94310126","display_name":"Shanxi Normal University","ror":"https://ror.org/03zd3ta61","country_code":"CN","type":"education","lineage":["https://openalex.org/I94310126"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jianping Deng","raw_affiliation_strings":["School of Mathematics and Computer Science, Shanxi Normal University, Shanxi, Linfen, 041000, P.R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Computer Science, Shanxi Normal University, Shanxi, Linfen, 041000, P.R. China","institution_ids":["https://openalex.org/I94310126"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5103064030"],"corresponding_institution_ids":["https://openalex.org/I94310126"],"apc_list":null,"apc_paid":null,"fwci":0.8086,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.74655607,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"166","issue":"3","first_page":"273","last_page":"296"},"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/T14351","display_name":"Statistical and Computational Modeling","score":0.942300021648407,"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":0.9025999903678894,"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":0.8705888986587524},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7756434679031372},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.6893916130065918},{"id":"https://openalex.org/keywords/conditional-entropy","display_name":"Conditional entropy","score":0.6445481181144714},{"id":"https://openalex.org/keywords/dominance-based-rough-set-approach","display_name":"Dominance-based rough set approach","score":0.6257467865943909},{"id":"https://openalex.org/keywords/joint-entropy","display_name":"Joint entropy","score":0.6212552785873413},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5411074161529541},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.35638585686683655},{"id":"https://openalex.org/keywords/principle-of-maximum-entropy","display_name":"Principle of maximum entropy","score":0.28930485248565674},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.2742152810096741},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.19332608580589294},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.18216025829315186},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1470712125301361}],"concepts":[{"id":"https://openalex.org/C111012933","wikidata":"https://www.wikidata.org/wiki/Q3137210","display_name":"Rough set","level":2,"score":0.8705888986587524},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7756434679031372},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.6893916130065918},{"id":"https://openalex.org/C101721835","wikidata":"https://www.wikidata.org/wiki/Q813908","display_name":"Conditional entropy","level":3,"score":0.6445481181144714},{"id":"https://openalex.org/C39105242","wikidata":"https://www.wikidata.org/wiki/Q5290286","display_name":"Dominance-based rough set approach","level":3,"score":0.6257467865943909},{"id":"https://openalex.org/C106752470","wikidata":"https://www.wikidata.org/wiki/Q1364826","display_name":"Joint entropy","level":3,"score":0.6212552785873413},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5411074161529541},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.35638585686683655},{"id":"https://openalex.org/C9679016","wikidata":"https://www.wikidata.org/wiki/Q1417473","display_name":"Principle of maximum entropy","level":2,"score":0.28930485248565674},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.2742152810096741},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.19332608580589294},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.18216025829315186},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1470712125301361},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3233/fi-2019-1803","is_oa":false,"landing_page_url":"https://doi.org/10.3233/fi-2019-1803","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":[{"display_name":"Climate action","score":0.41999998688697815,"id":"https://metadata.un.org/sdg/13"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W436841052","https://openalex.org/W1523763698","https://openalex.org/W1584845053","https://openalex.org/W1995875735","https://openalex.org/W1999612973","https://openalex.org/W2007262119","https://openalex.org/W2007810691","https://openalex.org/W2009653394","https://openalex.org/W2013378801","https://openalex.org/W2014127819","https://openalex.org/W2018817163","https://openalex.org/W2023441160","https://openalex.org/W2035567190","https://openalex.org/W2053289194","https://openalex.org/W2059228994","https://openalex.org/W2076034971","https://openalex.org/W2078975878","https://openalex.org/W2092179332","https://openalex.org/W2095290023","https://openalex.org/W2101924850","https://openalex.org/W2143451122","https://openalex.org/W2276298621","https://openalex.org/W2318901577","https://openalex.org/W2365382545","https://openalex.org/W2394147154","https://openalex.org/W2395763878"],"related_works":["https://openalex.org/W2397494716","https://openalex.org/W2473601878","https://openalex.org/W2123662875","https://openalex.org/W2379884433","https://openalex.org/W2087213536","https://openalex.org/W4214891796","https://openalex.org/W2382975841","https://openalex.org/W2963142056","https://openalex.org/W1966444938","https://openalex.org/W2154788453"],"abstract_inverted_index":{"Uncertainty":[0],"measures":[1,158,165],"are":[2,51,159,166],"an":[3,33],"important":[4,34,154],"tool":[5],"for":[6,36],"analyzing":[7],"data.":[8],"There":[9],"is":[10,31,74,193],"the":[11,27,56,67,78,91,94,104,109,122,125,131,134,138,143,171,175,190],"uncertainty":[12,28,57,102,173],"of":[13,70,93,124,133,156],"a":[14,71,149],"rough":[15,23,37,46,61,72,84,106,111,115,127,177],"set":[16,24,38,47,62,73,85,116],"caused":[17],"by":[18],"its":[19],"boundary":[20,68],"region":[21,69],"in":[22,59,83,113],"models.":[25,63,86,117],"Thus":[26],"measurement":[29],"issue":[30],"also":[32],"topic":[35],"theory.":[39,48],"Shannon":[40],"entropy":[41,107,141,178,192],"has":[42,179],"been":[43],"introduced":[44],"into":[45],"However,":[49],"there":[50],"relatively":[52],"few":[53],"studies":[54],"on":[55,121],"measure":[58],"generalized":[60,114],"We":[64],"know":[65],"that":[66,189],"closely":[75],"related":[76],"to":[77,148],"upper":[79,95,105,126,135,139,176],"and":[80,96,108,129,142,185],"lower":[81,97,110],"approximations":[82],"In":[87],"this":[88],"paper,":[89],"from":[90],"viewpoint":[92],"approximations,":[98],"we":[99,119],"propose":[100],"new":[101],"measures,":[103,174],"entropy,":[112,128,137],"Then":[118],"focus":[120],"investigations":[123],"give":[130],"concepts":[132],"joint":[136],"conditional":[140],"mutual":[144],"information":[145],"with":[146,170],"respect":[147],"general":[150],"binary":[151],"relation.":[152],"Some":[153],"properties":[155],"these":[157,164],"obtained.":[160],"The":[161],"connections":[162],"among":[163],"given.":[167],"Furthermore,":[168],"comparing":[169],"existing":[172,198],"high":[180],"distinguishing":[181],"degree.":[182],"Theoretical":[183],"analysis":[184],"experimental":[186],"results":[187],"show":[188],"proposed":[191],"better":[194],"effective":[195],"than":[196],"some":[197],"measures.":[199]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
