{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,8]],"date-time":"2026-04-08T18:40:27Z","timestamp":1775673627429,"version":"3.50.1"},"reference-count":75,"publisher":"Institute of Electrical and Electronics Engineers (IEEE)","license":[{"start":{"date-parts":[[2019,1,1]],"date-time":"2019-01-01T00:00:00Z","timestamp":1546300800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/ieeexplore.ieee.org\/Xplorehelp\/downloads\/license-information\/OAPA.html"}],"funder":[{"DOI":"10.13039\/501100004735","name":"Natural Science Foundation of\u00a0Hunan Province","doi-asserted-by":"publisher","award":["2017JJ2130"],"award-info":[{"award-number":["2017JJ2130"]}],"id":[{"id":"10.13039\/501100004735","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Social Science Foundation of Hunan Province","award":["16YBA243"],"award-info":[{"award-number":["16YBA243"]}]},{"name":"Key Project of Education Department for Hunan Province","award":["17A116"],"award-info":[{"award-number":["17A116"]}]},{"name":"High Level Innovation Team Program from Guangxi Higher Education Institutions of China","award":["[2018] 35"],"award-info":[{"award-number":["[2018] 35"]}]},{"DOI":"10.13039\/501100004607","name":"Natural Science Foundation of Guangxi Province","doi-asserted-by":"publisher","award":["2018GXNSFDA294003"],"award-info":[{"award-number":["2018GXNSFDA294003"]}],"id":[{"id":"10.13039\/501100004607","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004607","name":"Natural Science Foundation of Guangxi Province","doi-asserted-by":"publisher","award":["2018GXNSFDA281028"],"award-info":[{"award-number":["2018GXNSFDA281028"]}],"id":[{"id":"10.13039\/501100004607","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004607","name":"Natural Science Foundation of Guangxi Province","doi-asserted-by":"publisher","award":["2018GXNSFAA294134"],"award-info":[{"award-number":["2018GXNSFAA294134"]}],"id":[{"id":"10.13039\/501100004607","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004703","name":"Guangxi University for Nationalities","doi-asserted-by":"publisher","award":["2018-18XJSY-03"],"award-info":[{"award-number":["2018-18XJSY-03"]}],"id":[{"id":"10.13039\/501100004703","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Engineering Project of Undergraduate Teaching Reform of Higher Education in Guangxi","award":["2017JGA179"],"award-info":[{"award-number":["2017JGA179"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IEEE Access"],"published-print":{"date-parts":[[2019]]},"DOI":"10.1109\/access.2019.2897752","type":"journal-article","created":{"date-parts":[[2019,2,12]],"date-time":"2019-02-12T00:36:06Z","timestamp":1549931766000},"page":"27501-27514","source":"Crossref","is-referenced-by-count":23,"title":["Information Structures and Uncertainty Measures in an Incomplete Probabilistic Set-Valued Information System"],"prefix":"10.1109","volume":"7","author":[{"given":"Xiaoliang","family":"Xie","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4437-9214","authenticated-orcid":false,"given":"Zhaowen","family":"Li","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Pengfei","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Gangqiang","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"263","reference":[{"key":"ref73","first-page":"73","article-title":"A new direction in AI: Toward a computational theory of perceptions","volume":"22","author":"zadeh","year":"2001","journal-title":"AI Mag"},{"key":"ref72","doi-asserted-by":"publisher","DOI":"10.1007\/s005000050030"},{"key":"ref71","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-0114(97)00077-8"},{"key":"ref70","doi-asserted-by":"publisher","DOI":"10.1109\/91.493904"},{"key":"ref74","author":"zhang","year":"2005","journal-title":"Uncertain Decision Making Based on Rough Sets"},{"key":"ref39","article-title":"Hellinger distance","author":"nikulin","year":"2001","journal-title":"Encyclopaedia of Mathematics"},{"key":"ref75","author":"zhang","year":"2007","journal-title":"Theory and Application of Problem Solving-Theory and Application of Granular Computing in Quotient Spaces"},{"key":"ref38","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2007.07.008"},{"key":"ref33","doi-asserted-by":"publisher","DOI":"10.1142\/S0218488504002631"},{"key":"ref32","first-page":"418","article-title":"Information measures of roughness of knowledge and rough sets for incomplete information systems [J]","volume":"10","author":"liang","year":"2001","journal-title":"J Syst Sci Syst Eng"},{"key":"ref31","doi-asserted-by":"publisher","DOI":"10.1016\/j.knosys.2015.07.036"},{"key":"ref30","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-7908-1873-4_9"},{"key":"ref37","doi-asserted-by":"publisher","DOI":"10.1080\/03081070512331318329"},{"key":"ref36","first-page":"2603","article-title":"On representing and generating kernels by fuzzy equivalence relations","volume":"7","author":"moser","year":"2006","journal-title":"J Mach Learn Res"},{"key":"ref35","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2006.01.007"},{"key":"ref34","doi-asserted-by":"publisher","DOI":"10.1080\/03081070600687668"},{"key":"ref60","doi-asserted-by":"publisher","DOI":"10.1007\/s00500-015-1954-4"},{"key":"ref62","doi-asserted-by":"crossref","first-page":"1244","DOI":"10.1016\/j.asoc.2009.03.007","article-title":"Knowledge granulation, knowledge entropy and knowledge uncertainty measure in ordered information systems","volume":"9","author":"xu","year":"2009","journal-title":"Appl Soft Comput"},{"key":"ref61","doi-asserted-by":"publisher","DOI":"10.1007\/s11277-014-1748-5"},{"key":"ref63","doi-asserted-by":"publisher","DOI":"10.1016\/S0020-0255(98)10006-3"},{"key":"ref28","first-page":"107","article-title":"Granular computing on binary relations I: Data mining and neighborhood systems","author":"lin","year":"1998","journal-title":"Rough Sets in Knowledge Discovery"},{"key":"ref64","doi-asserted-by":"publisher","DOI":"10.1002\/1098-111X(200101)16:1<87::AID-INT7>3.0.CO;2-S"},{"key":"ref27","first-page":"194","article-title":"Rough set approach to incomplete information systems","author":"kryszkiewicz","year":"1995","journal-title":"Proc 2nd Annu Joint Conf Inf Sci"},{"key":"ref65","doi-asserted-by":"publisher","DOI":"10.1111\/1468-0394.00253"},{"key":"ref66","doi-asserted-by":"publisher","DOI":"10.1109\/GRC.2005.1547239"},{"key":"ref29","first-page":"121","article-title":"Granular computing on binary relations II: rough set representations and belief functions","author":"lin","year":"1998","journal-title":"Rough Sets in Knowledge Discovery"},{"key":"ref67","first-page":"10","article-title":"A unified model for set-based computations","author":"yao","year":"1994","journal-title":"Proc 3rd Int Workshop Rough Sets Soft Comput"},{"key":"ref68","doi-asserted-by":"publisher","DOI":"10.1109\/TNN.2007.894042"},{"key":"ref69","doi-asserted-by":"publisher","DOI":"10.1016\/S0019-9958(65)90241-X"},{"key":"ref2","first-page":"77","article-title":"Entropies and Co-entropies of coverings with application to incomplete information systems","volume":"75","author":"bianucci","year":"2007","journal-title":"Fundamenta Informaticae"},{"key":"ref1","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1007\/978-3-642-03281-3_2","article-title":"Information entropy and granulation Co-entropy of partitions and coverings: A summary","author":"bianucci","year":"2009","journal-title":"Transactions on Rough Sets X"},{"key":"ref20","doi-asserted-by":"publisher","DOI":"10.1016\/j.patcog.2007.03.017"},{"key":"ref22","doi-asserted-by":"publisher","DOI":"10.1109\/TKDE.2004.96"},{"key":"ref21","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijar.2010.01.004"},{"key":"ref24","doi-asserted-by":"publisher","DOI":"10.1109\/TCOM.1967.1089532"},{"key":"ref23","doi-asserted-by":"publisher","DOI":"10.1109\/TFUZZ.2008.924209"},{"key":"ref26","doi-asserted-by":"publisher","DOI":"10.1016\/S0020-0255(98)10019-1"},{"key":"ref25","doi-asserted-by":"publisher","DOI":"10.1016\/S0020-0255(98)10065-8"},{"key":"ref50","doi-asserted-by":"publisher","DOI":"10.1109\/TFUZZ.2010.2095461"},{"key":"ref51","author":"rudin","year":"1987","journal-title":"Real and Complex Analysis"},{"key":"ref59","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2007.04.010"},{"key":"ref58","doi-asserted-by":"publisher","DOI":"10.1109\/TKDE.2008.223"},{"key":"ref57","doi-asserted-by":"publisher","DOI":"10.1080\/03081079908935239"},{"key":"ref56","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.asoc.2008.05.006","article-title":"Dimensionality reduction based on rough set theory: A review","volume":"9","author":"thangavel","year":"2009","journal-title":"Appl Soft Comput"},{"key":"ref55","doi-asserted-by":"publisher","DOI":"10.1109\/69.842271"},{"key":"ref54","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-8655(02)00196-4"},{"key":"ref53","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511809682"},{"key":"ref52","doi-asserted-by":"publisher","DOI":"10.1002\/j.1538-7305.1948.tb01338.x"},{"key":"ref10","doi-asserted-by":"publisher","DOI":"10.1016\/j.envsoft.2015.12.011"},{"key":"ref11","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2013.03.045"},{"key":"ref40","doi-asserted-by":"publisher","DOI":"10.1016\/j.asoc.2016.05.019"},{"key":"ref12","first-page":"368","article-title":"On the unknown attribute values in learning from examples","author":"grzymala-busse","year":"1991","journal-title":"Proc Int Symp Methodol Intell Syst"},{"key":"ref13","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-27794-1_3"},{"key":"ref14","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2005.12.007"},{"key":"ref15","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijar.2005.06.014"},{"key":"ref16","doi-asserted-by":"publisher","DOI":"10.1016\/j.neunet.2015.03.013"},{"key":"ref17","doi-asserted-by":"publisher","DOI":"10.1016\/j.knosys.2017.02.002"},{"key":"ref18","doi-asserted-by":"crossref","first-page":"137","DOI":"10.1109\/TSMCB.2009.2024166","article-title":"Selecting discrete and continuous features based on neighborhood decision error minimization","volume":"40","author":"hu","year":"2010","journal-title":"IEEE Trans Syst Man Cybern B Cybern"},{"key":"ref19","doi-asserted-by":"publisher","DOI":"10.1016\/j.eswa.2015.10.023"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1016\/S0020-0255(98)00019-X"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1098-111X(200005)15:5<389::AID-INT2>3.0.CO;2-8"},{"key":"ref6","doi-asserted-by":"crossref","first-page":"223","DOI":"10.3233\/FI-2011-421","article-title":"Rough sets, coverings and incomplete information","volume":"108","author":"couso","year":"2011","journal-title":"Fundamenta Informaticae"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2010.10.030"},{"key":"ref8","doi-asserted-by":"publisher","DOI":"10.1016\/j.patcog.2013.09.003"},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2009.09.008"},{"key":"ref49","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijar.2008.08.004"},{"key":"ref9","doi-asserted-by":"publisher","DOI":"10.1080\/03081079008935107"},{"key":"ref46","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2006.06.003"},{"key":"ref45","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2006.06.006"},{"key":"ref48","doi-asserted-by":"publisher","DOI":"10.1016\/j.artint.2010.04.018"},{"key":"ref47","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2009.04.007"},{"key":"ref42","doi-asserted-by":"publisher","DOI":"10.1007\/BF01001956"},{"key":"ref41","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1016\/0304-3975(84)90010-0","article-title":"Representation of nondeterministic information","volume":"29","author":"ewa","year":"1984","journal-title":"Theor Comput Sci"},{"key":"ref44","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2006.06.007"},{"key":"ref43","author":"pawlak","year":"1991","journal-title":"Rough Sets Theoretical Aspects of Reasoning about Data"}],"container-title":["IEEE Access"],"original-title":[],"link":[{"URL":"http:\/\/xplorestaging.ieee.org\/ielx7\/6287639\/8600701\/08638506.pdf?arnumber=8638506","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,1,27]],"date-time":"2022-01-27T03:40:58Z","timestamp":1643254858000},"score":1,"resource":{"primary":{"URL":"https:\/\/ieeexplore.ieee.org\/document\/8638506\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019]]},"references-count":75,"URL":"https:\/\/doi.org\/10.1109\/access.2019.2897752","relation":{},"ISSN":["2169-3536"],"issn-type":[{"value":"2169-3536","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019]]}}}