{"id":"https://openalex.org/W2097498222","doi":"https://doi.org/10.1080/03081070600687668","title":"Information entropy, rough entropy and knowledge granulation in incomplete information systems","display_name":"Information entropy, rough entropy and knowledge granulation in incomplete information systems","publication_year":2006,"publication_date":"2006-11-06","ids":{"openalex":"https://openalex.org/W2097498222","doi":"https://doi.org/10.1080/03081070600687668","mag":"2097498222"},"language":"en","primary_location":{"id":"doi:10.1080/03081070600687668","is_oa":false,"landing_page_url":"https://doi.org/10.1080/03081070600687668","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/A5106626932","display_name":"Jiye Liang","orcid":"https://orcid.org/0000-0001-5887-9327"},"institutions":[{"id":"https://openalex.org/I4210090176","display_name":"Institute of Computing Technology","ror":"https://ror.org/0090r4d87","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210090176"]},{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"funder","lineage":["https://openalex.org/I19820366"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"J. Liang","raw_affiliation_strings":["Key Laboratory of Ministry of Education for Computation Intelligence and Chinese Information Processing, School of Computer and Information Technology, Shanxi University , Taiyuan, 030006, People's Republic of China ; Key Laboratory of Intelligent Information Processing , Institute of Computing Technology, The Chinese Academy of Sciences , Beijing, 100080, People's Republic of China","Chinese Academy of Sciences, Beijing, China"],"affiliations":[{"raw_affiliation_string":"Key Laboratory of Ministry of Education for Computation Intelligence and Chinese Information Processing, School of Computer and Information Technology, Shanxi University , Taiyuan, 030006, People's Republic of China ; Key Laboratory of Intelligent Information Processing , Institute of Computing Technology, The Chinese Academy of Sciences , Beijing, 100080, People's Republic of China","institution_ids":["https://openalex.org/I4210090176"]},{"raw_affiliation_string":"Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I19820366"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101604117","display_name":"Zhicai Shi","orcid":"https://orcid.org/0000-0003-3062-2700"},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"funder","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210090176","display_name":"Institute of Computing Technology","ror":"https://ror.org/0090r4d87","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210090176"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Z. Shi","raw_affiliation_strings":["Key Laboratory of Intelligent Information Processing , Institute of Computing Technology, The Chinese Academy of Sciences , Beijing, 100080, People's Republic of China","Key Laboratory of Intelligent Information Processing, Institute of Computing Technology, The Chinese Academy of Sciences,  Beijing, 100080, People's Republic of China"],"affiliations":[{"raw_affiliation_string":"Key Laboratory of Intelligent Information Processing , Institute of Computing Technology, The Chinese Academy of Sciences , Beijing, 100080, People's Republic of China","institution_ids":["https://openalex.org/I4210090176","https://openalex.org/I19820366"]},{"raw_affiliation_string":"Key Laboratory of Intelligent Information Processing, Institute of Computing Technology, The Chinese Academy of Sciences,  Beijing, 100080, People's Republic of China","institution_ids":["https://openalex.org/I19820366"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100698996","display_name":"Deyu Li","orcid":"https://orcid.org/0000-0003-2489-9404"},"institutions":[{"id":"https://openalex.org/I181877577","display_name":"Shanxi University","ror":"https://ror.org/03y3e3s17","country_code":"CN","type":"education","lineage":["https://openalex.org/I181877577"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"D. Li","raw_affiliation_strings":["Key Laboratory of Ministry of Education for Computation Intelligence and Chinese Information Processing, School of Computer and Information Technology, Shanxi University , Taiyuan, 030006, People's Republic of China"],"affiliations":[{"raw_affiliation_string":"Key Laboratory of Ministry of Education for Computation Intelligence and Chinese Information Processing, School of Computer and Information Technology, Shanxi University , Taiyuan, 030006, People's Republic of China","institution_ids":["https://openalex.org/I181877577"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5086771702","display_name":"Mark J. Wierman","orcid":null},"institutions":[{"id":"https://openalex.org/I114493937","display_name":"Creighton University","ror":"https://ror.org/05wf30g94","country_code":"US","type":"education","lineage":["https://openalex.org/I114493937"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"M. J. Wierman","raw_affiliation_strings":["Creighton University , Omaha, NE, 68005, USA"],"affiliations":[{"raw_affiliation_string":"Creighton University , Omaha, NE, 68005, USA","institution_ids":["https://openalex.org/I114493937"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5106626932"],"corresponding_institution_ids":["https://openalex.org/I19820366","https://openalex.org/I4210090176"],"apc_list":null,"apc_paid":null,"fwci":9.8738,"has_fulltext":false,"cited_by_count":317,"citation_normalized_percentile":{"value":0.98598421,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":99,"max":100},"biblio":{"volume":"35","issue":"6","first_page":"641","last_page":"654"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11063","display_name":"Rough Sets and Fuzzy Logic","score":1.0,"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":1.0,"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/T10050","display_name":"Multi-Criteria Decision Making","score":0.9882000088691711,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11652","display_name":"Imbalanced Data Classification Techniques","score":0.9135000109672546,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/rough-set","display_name":"Rough set","score":0.9104598760604858},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.6374189853668213},{"id":"https://openalex.org/keywords/vagueness","display_name":"Vagueness","score":0.5562663674354553},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5337425470352173},{"id":"https://openalex.org/keywords/information-diagram","display_name":"Information diagram","score":0.5330753326416016},{"id":"https://openalex.org/keywords/granularity","display_name":"Granularity","score":0.513995349407196},{"id":"https://openalex.org/keywords/reduct","display_name":"Reduct","score":0.49180033802986145},{"id":"https://openalex.org/keywords/information-system","display_name":"Information system","score":0.4552769064903259},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4548145532608032},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.4505978226661682},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.2667178511619568},{"id":"https://openalex.org/keywords/principle-of-maximum-entropy","display_name":"Principle of maximum entropy","score":0.20085754990577698},{"id":"https://openalex.org/keywords/binary-entropy-function","display_name":"Binary entropy function","score":0.18267714977264404},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.13193929195404053},{"id":"https://openalex.org/keywords/maximum-entropy-thermodynamics","display_name":"Maximum entropy thermodynamics","score":0.11882460117340088}],"concepts":[{"id":"https://openalex.org/C111012933","wikidata":"https://www.wikidata.org/wiki/Q3137210","display_name":"Rough set","level":2,"score":0.9104598760604858},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.6374189853668213},{"id":"https://openalex.org/C2776825360","wikidata":"https://www.wikidata.org/wiki/Q1411921","display_name":"Vagueness","level":3,"score":0.5562663674354553},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5337425470352173},{"id":"https://openalex.org/C67935508","wikidata":"https://www.wikidata.org/wiki/Q17078448","display_name":"Information diagram","level":5,"score":0.5330753326416016},{"id":"https://openalex.org/C177774035","wikidata":"https://www.wikidata.org/wiki/Q1246948","display_name":"Granularity","level":2,"score":0.513995349407196},{"id":"https://openalex.org/C69177213","wikidata":"https://www.wikidata.org/wiki/Q12880812","display_name":"Reduct","level":3,"score":0.49180033802986145},{"id":"https://openalex.org/C180198813","wikidata":"https://www.wikidata.org/wiki/Q121182","display_name":"Information system","level":2,"score":0.4552769064903259},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4548145532608032},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.4505978226661682},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2667178511619568},{"id":"https://openalex.org/C9679016","wikidata":"https://www.wikidata.org/wiki/Q1417473","display_name":"Principle of maximum entropy","level":2,"score":0.20085754990577698},{"id":"https://openalex.org/C44415725","wikidata":"https://www.wikidata.org/wiki/Q4913893","display_name":"Binary entropy function","level":3,"score":0.18267714977264404},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.13193929195404053},{"id":"https://openalex.org/C49775889","wikidata":"https://www.wikidata.org/wiki/Q6795896","display_name":"Maximum entropy thermodynamics","level":4,"score":0.11882460117340088},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/03081070600687668","is_oa":false,"landing_page_url":"https://doi.org/10.1080/03081070600687668","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":"Peace, Justice and strong institutions","score":0.6000000238418579,"id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W1557923305","https://openalex.org/W1600047650","https://openalex.org/W1992639932","https://openalex.org/W1995875735","https://openalex.org/W1998015481","https://openalex.org/W1999612973","https://openalex.org/W2000158142","https://openalex.org/W2014127819","https://openalex.org/W2035567190","https://openalex.org/W2041404167","https://openalex.org/W2046857474","https://openalex.org/W2077183117","https://openalex.org/W2092179332","https://openalex.org/W2095290023","https://openalex.org/W2103514965","https://openalex.org/W2340020088","https://openalex.org/W2499524267","https://openalex.org/W4232953319"],"related_works":["https://openalex.org/W2369301332","https://openalex.org/W2101726329","https://openalex.org/W2376860763","https://openalex.org/W2163171169","https://openalex.org/W1975980892","https://openalex.org/W2077183117","https://openalex.org/W1973689533","https://openalex.org/W3119649673","https://openalex.org/W1880013533","https://openalex.org/W2393055956"],"abstract_inverted_index":{"Rough":[0,23],"set":[1,24,146],"theory":[2,25],"is":[3,35],"a":[4,27,221,230],"relatively":[5],"new":[6],"mathematical":[7],"tool":[8],"for":[9,204],"use":[10],"in":[11,14,60,125,144,169,220,233],"computer":[12],"applications":[13],"circumstances":[15],"that":[16],"are":[17,67,75,166,196],"characterized":[18],"by":[19],"vagueness":[20],"and":[21,33,57,69,84,106,127,132,141,153,180,193,225],"uncertainty.":[22],"uses":[26],"table":[28],"called":[29],"an":[30,40,214],"information":[31,41,51,62,81,137,235],"system,":[32],"knowledge":[34,55,86,90,113,142],"defined":[36],"as":[37,95,118],"classifications":[38],"of":[39,50,89,112,150,160,208,213,229],"system.":[42],"In":[43],"this":[44,170],"paper,":[45],"we":[46],"introduce":[47],"the":[48,70,80,85,99,102,107,188,206,211,217,227],"concepts":[49,74],"entropy,":[52,54,138],"rough":[53,108,139,145],"granulation":[56,87,143],"granularity":[58,103],"measure":[59,104],"incomplete":[61,234],"systems,":[63],"their":[64],"important":[65],"properties":[66],"given,":[68],"relationships":[71],"among":[72],"these":[73],"established.":[76],"The":[77,123,136],"relationship":[78,100],"between":[79,101],"entropy":[82,109,140],"E(A)":[83],"GK(A)":[88,177],"A":[91,114],"can":[92,115],"be":[93,116,201],"expressed":[94,117],"E(A)+GK(A)":[96],"=":[97,121],"1,":[98],"G(A)":[105,179],"E":[110,181,192,194],"r(A)":[111,120,182],"G(A)+E":[119],"log2|U|.":[122],"conclusions":[124],"Liang":[126],"Shi":[128],"(2004":[129],"Liang,":[130],"J.Y.":[131],"Shi,":[133],"Z.Z.":[134],"2004.":[135],"theory.":[147],"International":[148],"Journal":[149],"Uncertainty,":[151],"Fuzziness":[152],"Knowledge-Based":[154],"Systems,":[155],"12(1):":[156],"37\u201346.":[157],"[Crossref],":[158],"[Web":[159],"Science":[161],"\u00ae]":[162],",":[163],"[Google":[164],"Scholar])":[165],"special":[167],"instances":[168],"paper.":[171],"Furthermore,":[172],"two":[173],"inequalities":[174],"\u2212":[175,185],"log2":[176],"\u2264":[178,183],"log2(|U|(1":[184],"E(A)))":[186],"about":[187],"measures":[189],"GK,":[190],"G,":[191],"r":[195],"obtained.":[197],"These":[198],"results":[199],"will":[200],"very":[202],"helpful":[203],"understanding":[205],"essence":[207],"uncertainty":[209],"measurement,":[210],"significance":[212],"attribute,":[215],"constructing":[216],"heuristic":[218,222],"function":[219],"reduct":[223],"algorithm":[224],"measuring":[226],"quality":[228],"decision":[231],"rule":[232],"systems.":[236]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":18},{"year":2024,"cited_by_count":14},{"year":2023,"cited_by_count":15},{"year":2022,"cited_by_count":23},{"year":2021,"cited_by_count":25},{"year":2020,"cited_by_count":20},{"year":2019,"cited_by_count":21},{"year":2018,"cited_by_count":37},{"year":2017,"cited_by_count":15},{"year":2016,"cited_by_count":11},{"year":2015,"cited_by_count":18},{"year":2014,"cited_by_count":14},{"year":2013,"cited_by_count":13},{"year":2012,"cited_by_count":14}],"updated_date":"2026-04-02T15:55:50.835912","created_date":"2025-10-10T00:00:00"}
