{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T06:25:24Z","timestamp":1777703124934,"version":"3.51.4"},"reference-count":28,"publisher":"SAGE Publications","issue":"3","license":[{"start":{"date-parts":[[2016,7,14]],"date-time":"2016-07-14T00:00:00Z","timestamp":1468454400000},"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":[[2016,9]]},"abstract":"<jats:p>\n                    Consider\n                    <jats:italic>L<\/jats:italic>\n                    \u00a0=\u00a0(\n                    <jats:italic>L<\/jats:italic>\n                    , \u2217\u00a0, 1) be a complete residuated lattice. For an arbitrary function\n                    <jats:italic>\u03c6<\/jats:italic>\n                    defined from the set of all singletons to that of all\n                    <jats:italic>L<\/jats:italic>\n                    -sets, Chen and Li introduced a type of\n                    <jats:italic>L<\/jats:italic>\n                    -fuzzy rough sets in 2007, called\n                    <jats:italic>\u03c6<\/jats:italic>\n                    -fuzzy rough sets in this paper. The well-known\n                    <jats:italic>R<\/jats:italic>\n                    -fuzzy rough sets, where\n                    <jats:italic>R<\/jats:italic>\n                    is an\n                    <jats:italic>L<\/jats:italic>\n                    -fuzzy relation, can be regarded as a special\n                    <jats:italic>\u03c6<\/jats:italic>\n                    -fuzzy rough sets. In this paper, we prove that\n                    <jats:italic>\u03c6<\/jats:italic>\n                    -fuzzy rough sets can be represented by a family of\n                    <jats:italic>R<\/jats:italic>\n                    -fuzzy rough sets. Then we define some special\n                    <jats:italic>\u03c6<\/jats:italic>\n                    of being serial, reflexive, symmetric, transitive and Euclidean, and discuss the corresponding\n                    <jats:italic>\u03c6<\/jats:italic>\n                    -fuzzy rough sets, respectively. At last, we study the induced\n                    <jats:italic>L<\/jats:italic>\n                    -topology by\n                    <jats:italic>\u03c6<\/jats:italic>\n                    when it is reflexive or reflexive and transitive.\n                  <\/jats:p>","DOI":"10.3233\/ifs-162206","type":"journal-article","created":{"date-parts":[[2016,7,15]],"date-time":"2016-07-15T12:23:56Z","timestamp":1468585436000},"page":"1397-1406","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":0,"title":["On\n                    <i>\u03c6<\/i>\n                    -fuzzy rough sets: Representation, special cases and induced topology"],"prefix":"10.1177","volume":"31","author":[{"given":"Hongxia","family":"Han","sequence":"first","affiliation":[{"name":"College of Mathematics and Econometrics, Hunan University, Changsha, P.R. China"},{"name":"Department of Applied Mathematics, Yuncheng University, Yuncheng, P.R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qingguo","family":"Li","sequence":"additional","affiliation":[{"name":"College of Mathematics and Econometrics, Hunan University, Changsha, P.R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2016,7,14]]},"reference":[{"key":"e_1_3_2_2_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4615-0633-1"},{"key":"e_1_3_2_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2007.05.016"},{"key":"e_1_3_2_4_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2006.12.104"},{"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\/j.fss.2011.03.009"},{"key":"e_1_3_2_7_2","doi-asserted-by":"crossref","unstructured":"H\u00e1jekP. Metamathematics of Fuzzy Logic Kluwer Academic Publishers Dordrecht 1998.","DOI":"10.1007\/978-94-011-5300-3"},{"key":"e_1_3_2_8_2","doi-asserted-by":"publisher","DOI":"10.3233\/FUN-2002-53203"},{"key":"e_1_3_2_9_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2006.10.001"},{"key":"e_1_3_2_10_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0020-0255(98)10065-8"},{"key":"e_1_3_2_11_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijar.2004.11.007"},{"key":"e_1_3_2_12_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2006.02.013"},{"key":"e_1_3_2_13_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2012.02.012"},{"key":"e_1_3_2_14_2","doi-asserted-by":"publisher","DOI":"10.3233\/IFS-141522"},{"key":"e_1_3_2_15_2","doi-asserted-by":"crossref","unstructured":"Dost Senol A textural view of soft fuzzy rough sets Journal of Intelligent and Fuzzy Systems (2015). 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