{"id":"https://openalex.org/W3191182911","doi":"https://doi.org/10.1080/03081079.2021.1942868","title":"Relationships between fuzzy probabilistic approximation spaces and their entropy measurement","display_name":"Relationships between fuzzy probabilistic approximation spaces and their entropy measurement","publication_year":2021,"publication_date":"2021-07-05","ids":{"openalex":"https://openalex.org/W3191182911","doi":"https://doi.org/10.1080/03081079.2021.1942868","mag":"3191182911"},"language":"en","primary_location":{"id":"doi:10.1080/03081079.2021.1942868","is_oa":false,"landing_page_url":"https://doi.org/10.1080/03081079.2021.1942868","pdf_url":null,"source":{"id":"https://openalex.org/S145553572","display_name":"International Journal of General Systems","issn_l":"0308-1079","issn":["0308-1079","1026-7492","1563-5104"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of General Systems","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/A5086034088","display_name":"Zhaowen Li","orcid":"https://orcid.org/0000-0002-4437-9214"},"institutions":[{"id":"https://openalex.org/I27462735","display_name":"Yulin Normal University","ror":"https://ror.org/00445hv47","country_code":"CN","type":"education","lineage":["https://openalex.org/I27462735"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhaowen Li","raw_affiliation_strings":["Key Laboratory of Complex System Optimization and Big Data Processing in Department of Guangxi Education, Yulin Normal University, Yulin, People's Republic of China"],"affiliations":[{"raw_affiliation_string":"Key Laboratory of Complex System Optimization and Big Data Processing in Department of Guangxi Education, Yulin Normal University, Yulin, People's Republic of China","institution_ids":["https://openalex.org/I27462735"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5074332958","display_name":"Damei Luo","orcid":null},"institutions":[{"id":"https://openalex.org/I150807315","display_name":"Guangxi University","ror":"https://ror.org/02c9qn167","country_code":"CN","type":"education","lineage":["https://openalex.org/I150807315"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Damei Luo","raw_affiliation_strings":["School of Mathematics and Information Science, Guangxi University, Nanning, People's Republic of China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Information Science, Guangxi University, Nanning, People's Republic of China","institution_ids":["https://openalex.org/I150807315"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5066097892","display_name":"Gangqiang Zhang","orcid":"https://orcid.org/0000-0001-5424-6389"},"institutions":[{"id":"https://openalex.org/I167274908","display_name":"Guangxi University for Nationalities","ror":"https://ror.org/0495efn48","country_code":"CN","type":"education","lineage":["https://openalex.org/I167274908"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Gangqiang Zhang","raw_affiliation_strings":["School of Artificial Intelligence, Guangxi University for Nationalities, Nanning, People's Republic of China"],"affiliations":[{"raw_affiliation_string":"School of Artificial Intelligence, Guangxi University for Nationalities, Nanning, People's Republic of China","institution_ids":["https://openalex.org/I167274908"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5001618198","display_name":"Liangdong Qu","orcid":"https://orcid.org/0000-0002-3838-4594"},"institutions":[{"id":"https://openalex.org/I167274908","display_name":"Guangxi University for Nationalities","ror":"https://ror.org/0495efn48","country_code":"CN","type":"education","lineage":["https://openalex.org/I167274908"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Liangdong Qu","raw_affiliation_strings":["School of Artificial Intelligence, Guangxi University for Nationalities, Nanning, People's Republic of China"],"affiliations":[{"raw_affiliation_string":"School of Artificial Intelligence, Guangxi University for Nationalities, Nanning, People's Republic of China","institution_ids":["https://openalex.org/I167274908"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5110610097","display_name":"Ningxin Xie","orcid":null},"institutions":[{"id":"https://openalex.org/I167274908","display_name":"Guangxi University for Nationalities","ror":"https://ror.org/0495efn48","country_code":"CN","type":"education","lineage":["https://openalex.org/I167274908"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ningxin Xie","raw_affiliation_strings":["School of Artificial Intelligence, Guangxi University for Nationalities, Nanning, People's Republic of China"],"affiliations":[{"raw_affiliation_string":"School of Artificial Intelligence, Guangxi University for Nationalities, Nanning, People's Republic of China","institution_ids":["https://openalex.org/I167274908"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5066097892"],"corresponding_institution_ids":["https://openalex.org/I167274908"],"apc_list":null,"apc_paid":null,"fwci":0.148,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.51316212,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"50","issue":"6","first_page":"638","last_page":"671"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11063","display_name":"Rough Sets and Fuzzy Logic","score":0.9997000098228455,"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":0.9997000098228455,"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9731000065803528,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/probabilistic-logic","display_name":"Probabilistic logic","score":0.6777688264846802},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5970032215118408},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.49187564849853516},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.48055484890937805},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.396244078874588},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3423696756362915},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.340842068195343},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.2530452013015747},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.21804401278495789},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.13116449117660522},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.10090106725692749}],"concepts":[{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.6777688264846802},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5970032215118408},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.49187564849853516},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.48055484890937805},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.396244078874588},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3423696756362915},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.340842068195343},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2530452013015747},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.21804401278495789},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.13116449117660522},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.10090106725692749}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/03081079.2021.1942868","is_oa":false,"landing_page_url":"https://doi.org/10.1080/03081079.2021.1942868","pdf_url":null,"source":{"id":"https://openalex.org/S145553572","display_name":"International Journal of General Systems","issn_l":"0308-1079","issn":["0308-1079","1026-7492","1563-5104"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of General Systems","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10","score":0.4099999964237213}],"awards":[{"id":"https://openalex.org/G5646180409","display_name":null,"funder_award_id":"AD19245102, 2018GXNSFDA294003, 2018GXNSFDA281028, 2018GXNSFAA294134","funder_id":"https://openalex.org/F4320322768","funder_display_name":"Natural Science Foundation of Guangxi Province"},{"id":"https://openalex.org/G5688209403","display_name":null,"funder_award_id":"11971420","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320322768","display_name":"Natural Science Foundation of Guangxi Province","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":35,"referenced_works":["https://openalex.org/W1963626514","https://openalex.org/W1981299568","https://openalex.org/W1983583104","https://openalex.org/W1995875735","https://openalex.org/W2002115460","https://openalex.org/W2005291044","https://openalex.org/W2027654459","https://openalex.org/W2028956919","https://openalex.org/W2036869842","https://openalex.org/W2038190934","https://openalex.org/W2052604633","https://openalex.org/W2056299038","https://openalex.org/W2065071658","https://openalex.org/W2069222657","https://openalex.org/W2071765874","https://openalex.org/W2082173396","https://openalex.org/W2096082386","https://openalex.org/W2098093602","https://openalex.org/W2123509054","https://openalex.org/W2134517799","https://openalex.org/W2151326023","https://openalex.org/W2321058091","https://openalex.org/W2345227376","https://openalex.org/W2803728986","https://openalex.org/W2885557962","https://openalex.org/W2888076169","https://openalex.org/W2895848020","https://openalex.org/W2904832268","https://openalex.org/W2913852222","https://openalex.org/W2941518349","https://openalex.org/W2966120476","https://openalex.org/W3015430264","https://openalex.org/W3158746607","https://openalex.org/W4248339361","https://openalex.org/W4255833381"],"related_works":["https://openalex.org/W2494523064","https://openalex.org/W2943623134","https://openalex.org/W2030292806","https://openalex.org/W2215759665","https://openalex.org/W2960358116","https://openalex.org/W3041172967","https://openalex.org/W2749065928","https://openalex.org/W2147155098","https://openalex.org/W4287727129","https://openalex.org/W2180033908"],"abstract_inverted_index":{"A":[0],"fuzzy":[1,31,49,62,121],"probability":[2,27,58,124],"approximation":[3,8,32],"space":[4,9,33],"(FPA-space)":[5],"is":[6,23,92,100,112],"a":[7,30,60,151],"(A-space)":[10],"where":[11],"three":[12],"types":[13,47],"of":[14,48,104,117,139,153],"uncertainty":[15,96],"(probability,":[16],"fuzziness":[17],"and":[18,41,42,68,81,126],"roughness)":[19],"are":[20,52,73,85,130],"combined,":[21],"which":[22],"obtained":[24,137],"by":[25,55,102],"putting":[26],"distribution":[28],"into":[29,59],"(FA-space).":[34],"This":[35],"paper":[36,141],"studies":[37],"relationships":[38],"between":[39,83,90],"FPA-spaces":[40,84,91],"their":[43],"entropy":[44,111],"measurement.":[45],"Two":[46],"relation":[50,63],"matrices":[51],"first":[53],"defined":[54],"introducing":[56],"the":[57,88,95,108,115,136],"given":[61],"matrix":[64],"in":[65,114,133],"two":[66,76],"ways,":[67],"on":[69],"this":[70,140],"basis,":[71],"they":[72],"extended":[74],"to":[75],"FA-spaces.":[77],"Then,":[78],"equality,":[79],"dependence":[80],"independence":[82],"studied.":[86],"Next,":[87],"distance":[89],"discussed.":[93],"Moreover,":[94],"for":[97,145],"an":[98,134],"FPA-space":[99],"measured":[101],"means":[103],"information":[105,110],"entropy.":[106],"Finally,":[107],"proposed":[109],"applied":[113],"selection":[116],"classifier":[118],"systems.":[119],"Since":[120],"set":[122,128],"theory,":[123],"theory":[125,129],"rough":[127],"aggregated":[131],"together":[132],"FPA-space,":[135],"results":[138],"may":[142],"be":[143],"helpful":[144],"dealing":[146],"with":[147,150],"practice":[148],"problems":[149],"sort":[152],"uncertainty.":[154]},"counts_by_year":[{"year":2022,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
