{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:46:56Z","timestamp":1760060816211,"version":"build-2065373602"},"reference-count":41,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2025,9,24]],"date-time":"2025-09-24T00:00:00Z","timestamp":1758672000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Ningxia Scientific and Technological Leading Talent Project","award":["2022GKLRLX08"],"award-info":[{"award-number":["2022GKLRLX08"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In order to approximate an undefinable set of objects by using the extensions in OE-concept lattices, this study combines three-way concept analysis with covering-based rough set and introduces an innovative approach for managing uncertain information and decision-making. This approach employs the minimal neighborhood of the maximal description, which is determined by meet-irreducible elements, to define the lower and upper of an undefinable set. On this basis, we formalize the concepts of lower and upper approximation OE-concepts and propose a three-way approximation optimization algorithm. Experimental results demonstrate the effectiveness and efficiency of our algorithm.<\/jats:p>","DOI":"10.3390\/axioms14100721","type":"journal-article","created":{"date-parts":[[2025,9,24]],"date-time":"2025-09-24T08:19:45Z","timestamp":1758701985000},"page":"721","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Three-Way Approximations with Covering-Based Rough Set"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9845-8698","authenticated-orcid":false,"given":"Mei","family":"Li","sequence":"first","affiliation":[{"name":"College of Mathematics and Information Science, North Minzu University, Yinchuan 750021, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Renxia","family":"Wan","sequence":"additional","affiliation":[{"name":"College of Mathematics and Information Science, North Minzu University, Yinchuan 750021, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,9,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"341","DOI":"10.1007\/BF01001956","article-title":"Rough set","volume":"11","author":"Pawlak","year":"1982","journal-title":"Int. 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