{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,21]],"date-time":"2026-02-21T11:33:33Z","timestamp":1771673613817,"version":"3.50.1"},"reference-count":26,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2021,3,2]],"date-time":"2021-03-02T00:00:00Z","timestamp":1614643200000},"content-version":"vor","delay-in-days":60,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11771263"],"award-info":[{"award-number":["11771263"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61967001"],"award-info":[{"award-number":["61967001"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Complexity"],"published-print":{"date-parts":[[2021,1]]},"abstract":"<jats:p>This paper puts forward some rough approximations which are motivated from topology. Given a subset <jats:italic>R<\/jats:italic>\u2286<jats:italic>U<\/jats:italic> \u00d7 <jats:italic>U<\/jats:italic>, we can use 8 types of <jats:italic>E<\/jats:italic>\u2010neighborhoods to construct approximations of an arbitrary <jats:italic>X<\/jats:italic>\u2286<jats:italic>U<\/jats:italic> on the one hand. On the other hand, we can also construct approximations relying on a topology which is induced by an <jats:italic>E<\/jats:italic>\u2010neighborhood. Properties of these approximations and relationships between them are studied. For convenience of use, we also give some useful and easy\u2010to\u2010understand examples and make a comparison between our approximations and those in the published literature.<\/jats:p>","DOI":"10.1155\/2021\/6666853","type":"journal-article","created":{"date-parts":[[2021,3,3]],"date-time":"2021-03-03T01:50:07Z","timestamp":1614736207000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":35,"title":["New Rough Approximations Based on <i>E<\/i>\u2010Neighborhoods"],"prefix":"10.1155","volume":"2021","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8074-1102","authenticated-orcid":false,"given":"Tareq M.","family":"Al-shami","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8962-2556","authenticated-orcid":false,"given":"Wen Qing","family":"Fu","sequence":"additional","affiliation":[]},{"given":"E. 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