{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T16:08:02Z","timestamp":1772294882841,"version":"3.50.1"},"reference-count":40,"publisher":"World Scientific Pub Co Pte Ltd","issue":"10","funder":[{"DOI":"10.13039\/501100001809","name":"the National Natural Science Foundation of China","doi-asserted-by":"crossref","award":["11601449, 11401495, 11501391"],"award-info":[{"award-number":["11601449, 11401495, 11501391"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"name":"the Opening Project of Artificial Intelligence Key Laboratory of Sichuan Province","award":["2015RZJ01"],"award-info":[{"award-number":["2015RZJ01"]}]},{"name":"the scientific research starting project of Southwest Petroleum University","award":["2015QHZ029"],"award-info":[{"award-number":["2015QHZ029"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2017,9]]},"abstract":"<jats:p> In this paper, some characterizations are obtained on the transitivity, mildly mixing property, a-transitivity, equicontinuity, uniform rigidity and proximality of Zadeh\u2019s extensions restricted on some invariant closed subsets of all upper semi-continuous fuzzy sets in the level-wise metric. In particular, it is proved that a dynamical system is weakly mixing (resp., mildly mixing, weakly mixing and a-transitive, equicontinuous, uniformly rigid) if and only if the corresponding Zadeh\u2019s extension is transitive (resp., mildly mixing, a-transitive, equicontinuous, uniformly rigid). <\/jats:p>","DOI":"10.1142\/s0218127417501656","type":"journal-article","created":{"date-parts":[[2017,10,12]],"date-time":"2017-10-12T23:03:49Z","timestamp":1507849429000},"page":"1750165","source":"Crossref","is-referenced-by-count":35,"title":["Topological Dynamics of Zadeh\u2019s Extension on Upper Semi-Continuous Fuzzy Sets"],"prefix":"10.1142","volume":"27","author":[{"given":"Xinxing","family":"Wu","sequence":"first","affiliation":[{"name":"School of Sciences, Southwest Petroleum University, Chengdu, Sichuan 610500, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xianfeng","family":"Ding","sequence":"additional","affiliation":[{"name":"School of Sciences, Southwest Petroleum University, Chengdu, Sichuan 610500, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8806-9656","authenticated-orcid":false,"given":"Tianxiu","family":"Lu","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Sichuan University of Science and Engineering, Zigong, Sichuan 643000, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jianjun","family":"Wang","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics, Sichuan Agricultural University, Ya\u2019an, Sichuan 625014, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2017,10,12]]},"reference":[{"key":"S0218127417501656BIB001","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-2668-8"},{"key":"S0218127417501656BIB002","doi-asserted-by":"publisher","DOI":"10.1080\/00029890.1992.11995856"},{"key":"S0218127417501656BIB003","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2004.11.089"},{"key":"S0218127417501656BIB004","doi-asserted-by":"publisher","DOI":"10.1007\/BF01585664"},{"key":"S0218127417501656BIB005","doi-asserted-by":"publisher","DOI":"10.1090\/tran\/6615"},{"key":"S0218127417501656BIB006","doi-asserted-by":"publisher","DOI":"10.1007\/s11425-014-4797-z"},{"key":"S0218127417501656BIB007","series-title":"Addison-Wesley Studies in Nonlinearity","volume-title":"An Introduction to Chaotic Dynamical Systems","author":"Devaney R. L.","year":"1989","edition":"2"},{"key":"S0218127417501656BIB008","doi-asserted-by":"publisher","DOI":"10.1515\/9781400855162"},{"key":"S0218127417501656BIB009","doi-asserted-by":"publisher","DOI":"10.1017\/S0143385700004983"},{"key":"S0218127417501656BIB010","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2005.10.041"},{"key":"S0218127417501656BIB011","doi-asserted-by":"publisher","DOI":"10.1016\/0097-3165(74)90023-5"},{"key":"S0218127417501656BIB012","doi-asserted-by":"publisher","DOI":"10.1016\/S0166-8641(01)00025-6"},{"key":"S0218127417501656BIB013","doi-asserted-by":"publisher","DOI":"10.1017\/S0143385703000543"},{"key":"S0218127417501656BIB014","series-title":"Monographs and Textbooks in Pure and Applied Mathematics","volume-title":"Hyperspaces","volume":"216","author":"Illanes A.","year":"1999"},{"key":"S0218127417501656BIB015","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2011.04.006"},{"key":"S0218127417501656BIB016","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2011.02.024"},{"key":"S0218127417501656BIB017","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2014.04.017"},{"key":"S0218127417501656BIB018","doi-asserted-by":"publisher","DOI":"10.1017\/S0143385711000599"},{"key":"S0218127417501656BIB019","doi-asserted-by":"publisher","DOI":"10.1155\/2012\/875381"},{"key":"S0218127417501656BIB020","doi-asserted-by":"publisher","DOI":"10.1080\/00029890.1975.11994008"},{"key":"S0218127417501656BIB021","first-page":"93","volume":"44","author":"Li J.","year":"2014","journal-title":"J. Univ. Sci. Technol. China"},{"key":"S0218127417501656BIB022","first-page":"1","author":"Li J.","year":"2017","journal-title":"Ergod. Th. Dyn. Syst."},{"key":"S0218127417501656BIB023","doi-asserted-by":"publisher","DOI":"10.1007\/s11425-004-5234-5"},{"key":"S0218127417501656BIB024","first-page":"985","volume":"82","author":"Liu H.","year":"2009","journal-title":"Nonlin. Anal."},{"key":"S0218127417501656BIB025","doi-asserted-by":"publisher","DOI":"10.4064\/cm120-1-9"},{"key":"S0218127417501656BIB026","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2006.05.036"},{"key":"S0218127417501656BIB027","first-page":"61","volume":"16","author":"Sharkovsky A. N.","year":"1964","journal-title":"Ukrain. Mat. Zh."},{"key":"S0218127417501656BIB028","doi-asserted-by":"publisher","DOI":"10.1016\/j.topol.2010.05.002"},{"key":"S0218127417501656BIB029","doi-asserted-by":"publisher","DOI":"10.1016\/j.topol.2008.10.014"},{"key":"S0218127417501656BIB030","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2015.04.009"},{"key":"S0218127417501656BIB031","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127416502278"},{"key":"S0218127417501656BIB032","doi-asserted-by":"publisher","DOI":"10.1016\/j.cnsns.2015.06.030"},{"key":"S0218127417501656BIB033","doi-asserted-by":"publisher","DOI":"10.1088\/0951-7715\/29\/7\/1942"},{"key":"S0218127417501656BIB034","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127416500541"},{"key":"S0218127417501656BIB035","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127417501073"},{"key":"S0218127417501656BIB036","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2017.02.042"},{"key":"S0218127417501656BIB037","doi-asserted-by":"publisher","DOI":"10.1215\/20088752-3802705"},{"key":"S0218127417501656BIB038","author":"Wu X.","year":"2017","journal-title":"Iran. J. Fuzzy Syst."},{"key":"S0218127417501656BIB039","author":"Wu X.","year":"2017","journal-title":"Qual. Th. Dyn. Syst."},{"key":"S0218127417501656BIB040","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127417501279"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127417501656","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T13:12:11Z","timestamp":1565183531000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127417501656"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,9]]},"references-count":40,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2017,10,12]]},"published-print":{"date-parts":[[2017,9]]}},"alternative-id":["10.1142\/S0218127417501656"],"URL":"https:\/\/doi.org\/10.1142\/s0218127417501656","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,9]]}}}