{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,5]],"date-time":"2026-02-05T09:29:58Z","timestamp":1770283798399,"version":"3.49.0"},"reference-count":22,"publisher":"SAGE Publications","issue":"1","license":[{"start":{"date-parts":[[2019,1,2]],"date-time":"2019-01-02T00:00:00Z","timestamp":1546387200000},"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":[[2019,2,16]]},"abstract":"<jats:p>\n                    In this paper, the notions of\n                    <jats:italic>M<\/jats:italic>\n                    -fuzzifying derived sets and\n                    <jats:italic>M<\/jats:italic>\n                    -fuzzifying derived operators are introduced, when\n                    <jats:italic>M<\/jats:italic>\n                    is a fuzzy lattice. Then their characterizations are given. What\u2019s more, it is shown that the category of\n                    <jats:italic>M<\/jats:italic>\n                    -fuzzifying topological spaces, the category of\n                    <jats:italic>M<\/jats:italic>\n                    -fuzzifying closure spaces and the category of\n                    <jats:italic>M<\/jats:italic>\n                    -fuzzifying neighborhood spaces are all isomorphic to the category of\n                    <jats:italic>M<\/jats:italic>\n                    -fuzzifying derived spaces. Besides, we prove that the\n                    <jats:italic>M<\/jats:italic>\n                    -fuzzifying derived operators induced by\n                    <jats:italic>M<\/jats:italic>\n                    -fuzzifying neighborhood systems are equivalent to those in the sense of Ying.\n                  <\/jats:p>","DOI":"10.3233\/jifs-17465","type":"journal-article","created":{"date-parts":[[2019,1,4]],"date-time":"2019-01-04T10:34:17Z","timestamp":1546598057000},"page":"79-89","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":6,"title":["<i>M<\/i>\n                    -fuzzifying derived spaces"],"prefix":"10.1177","volume":"36","author":[{"given":"Fan-Hong","family":"Chen","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Beijing Institute of Technology, Beijing, P.R. China"},{"name":"School of Civil Engineering and Architecture, Yanching Institute of Technology, Hebei, P.R. China"}]},{"given":"Yu","family":"Zhong","sequence":"additional","affiliation":[{"name":"College of Science, North China University of Technology, Beijing, P.R. China"}]},{"given":"Fu-Gui","family":"Shi","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Beijing Institute of Technology, Beijing, P.R. China"}]}],"member":"179","published-online":{"date-parts":[[2019,1,2]]},"reference":[{"key":"e_1_3_2_2_2","first-page":"583","article-title":"Fuzzifying topological derived operator axioms","volume":"4","author":"An F.B.","year":"2005","unstructured":"AnF.B. and FangJ.M., Fuzzifying topological derived operator axioms, Journal of Ocean University of Qingdao 4 (2005), 583\u2013586.","journal-title":"Journal of Ocean University of Qingdao"},{"key":"e_1_3_2_3_2","first-page":"8","article-title":"The N-derived operator in L-fuzzy topological spaces, Journal of Shanxi Normal University","volume":"18","author":"Bai Y.C.","year":"1990","unstructured":"BaiY.C., The N-derived operator in L-fuzzy topological spaces, Journal of Shanxi Normal University, (Natural Science Edition) 18 (1990), 8\u201311.","journal-title":"(Natural Science Edition)"},{"key":"e_1_3_2_4_2","doi-asserted-by":"publisher","DOI":"10.1016\/1385-7258(82)90034-8"},{"key":"e_1_3_2_5_2","unstructured":"EngelkingR. 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