{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T07:04:18Z","timestamp":1777705458211,"version":"3.51.4"},"reference-count":42,"publisher":"SAGE Publications","issue":"6","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IFS"],"published-print":{"date-parts":[[2021,12,16]]},"abstract":"<jats:p>The rough set theory and the evidence theory are two important methods used to deal with uncertainty. The relationships between the rough set theory and the evidence theory have been discussed. In covering rough set theory, several pairs of covering approximation operators are characterized by belief and plausibility functions. The purpose of this paper is to review and examine interpretations of belief functions in covering approximation operators. Firstly, properties of the belief structures induced by two pairs of covering approximation operators are presented. Then, for a belief structure with the properties, there exists a probability space with a covering such that the belief and plausibility functions defined by the given belief structure are, respectively, the belief and plausibility functions induced by one of the two pairs of covering approximation operators. Moreover, two necessary and sufficient conditions for a belief structure to be the belief structure induced by one of the two pairs of covering approximation operators are presented.<\/jats:p>","DOI":"10.3233\/jifs-201887","type":"journal-article","created":{"date-parts":[[2021,11,26]],"date-time":"2021-11-26T11:32:37Z","timestamp":1637926357000},"page":"5903-5913","source":"Crossref","is-referenced-by-count":0,"title":["Interpretations of belief functions in approximation operators by covering"],"prefix":"10.1177","volume":"41","author":[{"given":"Yan-Lan","family":"Zhang","sequence":"first","affiliation":[{"name":"College of Computer, Minnan Normal University, Zhang\u2019zhou, Fu\u2019jian, China"},{"name":"Key Laboratory of Data Science and Intelligence Application, Fujian Province University, Zhangzhou, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chang-Qing","family":"Li","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Minnan Normal University, Zhang\u2019zhou, Fu\u2019jian, China"},{"name":"Key Laboratory of Granular Computing, Minnan Normal University, Zhangzhou, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","reference":[{"key":"10.3233\/JIFS-201887_ref1","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1016\/S0020-0255(97)10046-9","article-title":"Wybraniec-Skardowska U Extensions and intentions in the rough set theory","volume":"107","author":"Bonikowski","year":"1998","journal-title":"Inf Sci"},{"issue":"16","key":"10.3233\/JIFS-201887_ref2","first-page":"71","article-title":"A calculus of rough sets of the first order","volume":"36","author":"Bryniarski","year":"1989","journal-title":"Bull Pol Acad Sci"},{"key":"10.3233\/JIFS-201887_ref3","doi-asserted-by":"crossref","first-page":"2297","DOI":"10.1007\/s13042-018-0868-8","article-title":"Attributes set reduction in multigranulationapproximation space of a multi-source decision information system","volume":"10","author":"Che","year":"2019","journal-title":"Int J Mach Learn Cyber"},{"key":"10.3233\/JIFS-201887_ref4","doi-asserted-by":"crossref","first-page":"908","DOI":"10.1016\/j.ijar.2013.10.003","article-title":"Evidencetheory-basednumerical algorithms of attribute reduction withneighborhood-covering rough sets","volume":"55","author":"Chen","year":"2014","journal-title":"Int J Approximate Reason"},{"issue":"2015","key":"10.3233\/JIFS-201887_ref5","first-page":"329","article-title":"On measurements of covering rough setsbased on granules and evidence theory","volume":"317","author":"Chen","journal-title":"Inf Sci"},{"key":"10.3233\/JIFS-201887_ref6","doi-asserted-by":"crossref","first-page":"3500","DOI":"10.1016\/j.ins.2007.02.041","article-title":"A new approach to attribute reduction ofconsistent and inconsistent covering decision systems with coveringrough sets","volume":"177","author":"Chen","year":"2007","journal-title":"Inf Sci"},{"issue":"2","key":"10.3233\/JIFS-201887_ref7","doi-asserted-by":"crossref","first-page":"325","DOI":"10.1214\/aoms\/1177698950","article-title":"Upper and lower probabilities induced by amultivalued mapping","volume":"38","author":"Dempster","year":"1967","journal-title":"Ann Math Sta"},{"key":"10.3233\/JIFS-201887_ref8","doi-asserted-by":"crossref","first-page":"941","DOI":"10.1002\/int.4550091003","article-title":"On modal logic interpretationof Dempster Shafer theory of evidence","volume":"9","author":"Harmanec","year":"1994","journal-title":"Int J lntell Syst"},{"key":"10.3233\/JIFS-201887_ref9","first-page":"184","article-title":"An information fusion approach bycombining multigranulation rough sets and evidence theory","volume":"314","author":"Lin","year":"2015","journal-title":"InfSci"},{"key":"10.3233\/JIFS-201887_ref10","first-page":"122","volume":"18","author":"Lin","year":"1998","journal-title":"Heidelberg"},{"key":"10.3233\/JIFS-201887_ref11","doi-asserted-by":"crossref","first-page":"178","DOI":"10.1016\/j.ins.2013.07.019","article-title":"The relationship among different covering approximations","volume":"250","author":"Liu","year":"2013","journal-title":"Inf Sci"},{"issue":"2019","key":"10.3233\/JIFS-201887_ref12","first-page":"194","article-title":"Belief and plausibility functionsof type-2 fuzzy rough sets","volume":"105","author":"Lu","journal-title":"Int J Approximate Reason"},{"key":"10.3233\/JIFS-201887_ref13","doi-asserted-by":"crossref","first-page":"341","DOI":"10.1007\/BF01001956","article-title":"Rough sets","volume":"11","author":"Pawlak","year":"1982","journal-title":"Int J Comput Inf Sci"},{"issue":"9-10","key":"10.3233\/JIFS-201887_ref14","first-page":"653","article-title":"Approximation operations in approximation space","volume":"35","author":"Pomykala","year":"1987","journal-title":"Bull Pol Acad Sci"},{"issue":"2007","key":"10.3233\/JIFS-201887_ref15","doi-asserted-by":"crossref","first-page":"34","DOI":"10.1007\/978-3-540-72458-2_4","article-title":"On covering rough sets. 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