{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,29]],"date-time":"2026-09-29T15:54:29Z","timestamp":1790697269625,"version":"4.1.0"},"reference-count":28,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2019,12,19]],"date-time":"2019-12-19T00:00:00Z","timestamp":1576713600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11871259"],"award-info":[{"award-number":["11871259"]}],"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":["61379021"],"award-info":[{"award-number":["61379021"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Information"],"abstract":"<jats:p>Since fuzzy    \u03b2   -covering was proposed, few papers have focused on how to calculate the reduct in fuzzy    \u03b2   -covering and how to update the reduct while adding and deleting some objects of the universe. Here, we propose a matrix-based approach for computing the reduct in a fuzzy    \u03b2   -covering and updating it dynamically using a matrix. First, matrix forms for computing the reduct in a fuzzy    \u03b2   -covering are proposed. Second, properties of the matrix-based approaches are studied while adding and deleting objects. Then, matrix-based algorithms for updating the reduct in a fuzzy    \u03b2   -covering are proposed. Finally, the efficiency and validity of the designed algorithms are verified by experiments.<\/jats:p>","DOI":"10.3390\/info11010003","type":"journal-article","created":{"date-parts":[[2019,12,20]],"date-time":"2019-12-20T09:50:33Z","timestamp":1576835433000},"page":"3","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Updating the Reduct in Fuzzy \u03b2-Covering via Matrix Approaches While Adding and Deleting Some Objects of the Universe"],"prefix":"10.3390","volume":"11","author":[{"given":"Jianxin","family":"Huang","sequence":"first","affiliation":[{"name":"Fujian Province Key Laboratory of Computer Science, School of Mathematics Science, Huaqiao University, Quanzhou 362021, China"},{"name":"School of Mathematics Science, Huaqiao University, Quanzhou 362021, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Peiqiu","family":"Yu","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statics, Minnan normal University, Zhangzhou 363000, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Weikang","family":"Li","sequence":"additional","affiliation":[{"name":"School of Mathematics Science, Huaqiao University, Quanzhou 362021, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2019,12,19]]},"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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