{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,29]],"date-time":"2026-01-29T18:27:13Z","timestamp":1769711233245,"version":"3.49.0"},"reference-count":46,"publisher":"SAGE Publications","issue":"2","license":[{"start":{"date-parts":[[2022,10,18]],"date-time":"2022-10-18T00:00:00Z","timestamp":1666051200000},"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":["Journal of Intelligent &amp; Fuzzy Systems"],"published-print":{"date-parts":[[2023,1,30]]},"abstract":"<jats:p>\n                    Let\n                    <jats:italic>L<\/jats:italic>\n                    be a commutative unital quantale. For every\n                    <jats:italic>L<\/jats:italic>\n                    -fuzzy relation\n                    <jats:italic>E<\/jats:italic>\n                    on a nonempty set\n                    <jats:italic>X<\/jats:italic>\n                    , we define an upper rough approximation operator on\n                    <jats:italic>L<\/jats:italic>\n                    <jats:sup>\n                      <jats:italic>X<\/jats:italic>\n                    <\/jats:sup>\n                    , which is a fuzzy extension of the classical Pawlak upper rough approximation operator. We show that this operator has close relation with the subsethood operator on\n                    <jats:italic>X<\/jats:italic>\n                    . Conversely, by an\n                    <jats:italic>L<\/jats:italic>\n                    -fuzzy closure operator on\n                    <jats:italic>X<\/jats:italic>\n                    , we can easily get an\n                    <jats:italic>L<\/jats:italic>\n                    -fuzzy relation. We show that this relation can be characterized by more smooth ways. Without the help of the lower approximation operator,\n                    <jats:italic>L<\/jats:italic>\n                    -fuzzy rough sets can still be studied by means of constructive and axiomatic approaches, and\n                    <jats:italic>L<\/jats:italic>\n                    -fuzzy similarities and\n                    <jats:italic>L<\/jats:italic>\n                    -fuzzy closure operators are one-to-one corresponding. We also show that, the\n                    <jats:italic>L<\/jats:italic>\n                    -topology induced by the upper rough approximation operator is stratified and Alexandrov.\n                  <\/jats:p>","DOI":"10.3233\/jifs-221896","type":"journal-article","created":{"date-parts":[[2022,10,18]],"date-time":"2022-10-18T11:41:09Z","timestamp":1666093269000},"page":"1575-1584","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":0,"title":["Upper rough approximation operators of quantale-valued similarities related to fuzzy orderings"],"prefix":"10.1177","volume":"44","author":[{"given":"Bei","family":"Zhang","sequence":"first","affiliation":[{"name":"School of Sciences, Hebei University of Science and Technology, Shijiazhuang, China"}]},{"given":"Chang-Jie","family":"Zhou","sequence":"additional","affiliation":[{"name":"School of Sciences, Hebei University of Science and Technology, Shijiazhuang, China"}]},{"given":"Wei","family":"Yao","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing, China"}]}],"member":"179","published-online":{"date-parts":[[2022,10,18]]},"reference":[{"key":"e_1_3_2_2_2","doi-asserted-by":"publisher","DOI":"10.1109\/TFUZZ.2015.2426204"},{"key":"e_1_3_2_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2017.07.016"},{"key":"e_1_3_2_4_2","doi-asserted-by":"publisher","DOI":"10.3233\/FI-1991-14406"},{"key":"e_1_3_2_5_2","doi-asserted-by":"publisher","DOI":"10.1080\/03081079008935107"},{"key":"e_1_3_2_6_2","doi-asserted-by":"publisher","DOI":"10.1016\/0022-247X(67)90189-8"},{"key":"e_1_3_2_7_2","doi-asserted-by":"crossref","unstructured":"LinT.Y. 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