{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T14:18:42Z","timestamp":1777645122505,"version":"3.51.4"},"reference-count":0,"publisher":"SAGE Publications","issue":"2","license":[{"start":{"date-parts":[[2019,3,5]],"date-time":"2019-03-05T00:00:00Z","timestamp":1551744000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Fundamenta Informaticae"],"published-print":{"date-parts":[[2019,3,5]]},"abstract":"<jats:p>Rough membership functions in covering approximation space not only give numerical characterizations of covering-based rough set approximations, but also establish the relationship between covering-based rough sets and fuzzy covering-based rough sets. In this paper, we give a new method to discuss three-way decisions with rough membership functions in covering approximation space. Firstly, we introduce three new types of rough membership functions and study their properties. And then, relationship between a covering and its derived fuzzy \u03b2-covering is investigated by using rough membership functions. In addition, we study the relationship among the four types of rough membership functions. Finally, a novel type of graded covering-based rough set model is proposed on the basis of rough membership function. And, as an application, its corresponding three-way decisions in incomplete decision systems are investigated.<\/jats:p>","DOI":"10.3233\/fi-2019-1780","type":"journal-article","created":{"date-parts":[[2019,3,5]],"date-time":"2019-03-05T11:35:54Z","timestamp":1551785754000},"page":"157-191","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":7,"title":["Three-way Decisions with Rough Membership Functions in Covering Approximation Space"],"prefix":"10.1177","volume":"165","author":[{"given":"Bin","family":"Yang","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Wuhan University, Wuhan 430072, PR China, , , ,"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bao Qing","family":"Hu","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Wuhan University, Wuhan 430072, PR China, , , ,"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Junsheng","family":"Qiao","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Wuhan University, Wuhan 430072, PR China, , , ,"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2019,3,5]]},"container-title":["Fundamenta Informaticae"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/FI-2019-1780","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/FI-2019-1780","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T06:31:25Z","timestamp":1777444285000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/FI-2019-1780"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,3,5]]},"references-count":0,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2019,3,5]]}},"alternative-id":["10.3233\/FI-2019-1780"],"URL":"https:\/\/doi.org\/10.3233\/fi-2019-1780","relation":{},"ISSN":["0169-2968","1875-8681"],"issn-type":[{"value":"0169-2968","type":"print"},{"value":"1875-8681","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,3,5]]}}}