{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,14]],"date-time":"2026-03-14T23:35:47Z","timestamp":1773531347077,"version":"3.50.1"},"reference-count":41,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2022,1,7]],"date-time":"2022-01-07T00:00:00Z","timestamp":1641513600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The rough set principle was proposed as a methodology to cope with vagueness or uncertainty of data in the information systems. Day by day, this theory has proven its efficiency in handling and modeling many real-life problems. To contribute to this area, we present new topological approaches as a generalization of Pawlak\u2019s theory by using j-adhesion neighborhoods and elucidate the relationship between them and some other types of approximations with the aid of examples. Topologically, we give another generalized rough approximation using near open sets. Also, we generate generalized approximations created from the topological models of j-adhesion approximations. Eventually, we compare the approaches given herein with previous ones to obtain a more affirmative solution for decision-making problems.<\/jats:p>","DOI":"10.3390\/sym14010095","type":"journal-article","created":{"date-parts":[[2022,1,9]],"date-time":"2022-01-09T23:35:09Z","timestamp":1641771309000},"page":"95","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":30,"title":["Some Topological Approaches for Generalized Rough Sets and Their Decision-Making Applications"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1962-1280","authenticated-orcid":false,"given":"Radwan","family":"Abu-Gdairi","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Zarqa University, Zarqa P.O. Box 13110, Jordan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4446-5101","authenticated-orcid":false,"given":"Mostafa A.","family":"El-Gayar","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Helwan University, Helwan P.O. Box 11795, Egypt"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8074-1102","authenticated-orcid":false,"given":"Tareq M.","family":"Al-shami","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Sana\u2019a University, Sana\u2019a P.O. Box 1247, Yemen"}]},{"given":"Ashraf S.","family":"Nawar","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Computer Science, Faculty of Science, Menoufia University, Shiben El-Kom P.O. Box 51123, Egypt"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7779-2443","authenticated-orcid":false,"given":"Mostafa K.","family":"El-Bably","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Tanta University, Tanta P.O. Box 31111, Egypt"}]}],"member":"1968","published-online":{"date-parts":[[2022,1,7]]},"reference":[{"key":"ref_1","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. Inf. Comput. Sci."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Pawlak, Z. (1991). 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