{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T10:42:27Z","timestamp":1740134547872,"version":"3.37.3"},"reference-count":28,"publisher":"Wiley","license":[{"start":{"date-parts":[[2014,1,1]],"date-time":"2014-01-01T00:00:00Z","timestamp":1388534400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11226268","KJ131219","Xm201328","KJTD201321"],"award-info":[{"award-number":["11226268","KJ131219","Xm201328","KJTD201321"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100007957","name":"Chongqing Municipality Education Commission","doi-asserted-by":"crossref","award":["11226268","KJ131219","Xm201328","KJTD201321"],"award-info":[{"award-number":["11226268","KJ131219","Xm201328","KJTD201321"]}],"id":[{"id":"10.13039\/501100007957","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100002858","name":"China Postdoctoral Science Foundation","doi-asserted-by":"publisher","award":["11226268","KJ131219","Xm201328","KJTD201321"],"award-info":[{"award-number":["11226268","KJ131219","Xm201328","KJTD201321"]}],"id":[{"id":"10.13039\/501100002858","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Institutions of Higher Education in Chongqing","award":["11226268","KJ131219","Xm201328","KJTD201321"],"award-info":[{"award-number":["11226268","KJ131219","Xm201328","KJTD201321"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2014]]},"abstract":"<jats:p>Let<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:mrow><mml:mi>X<\/mml:mi><\/mml:mrow><\/mml:math>denote a compact metric space and let<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M2\"><mml:mi>f<\/mml:mi><mml:mi>\u00a0<\/mml:mi><mml:mo>:<\/mml:mo><mml:mi>\u00a0<\/mml:mi><mml:mi>X<\/mml:mi><mml:mo>\u2192<\/mml:mo><mml:mi>X<\/mml:mi><\/mml:math>be a continuous map. It is known that a discrete dynamical system (<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M3\"><mml:mi>X<\/mml:mi><mml:mo>,<\/mml:mo><mml:mi>f<\/mml:mi><\/mml:math>) naturally induces its fuzzified counterpart, that is, a discrete dynamical system on the space of fuzzy compact subsets of<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M4\"><mml:mrow><mml:mi>X<\/mml:mi><\/mml:mrow><\/mml:math>. In 2011, a new generalized form of Zadeh\u2019s extension principle, so-called<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M5\"><mml:mrow><mml:mi>g<\/mml:mi><\/mml:mrow><\/mml:math>-fuzzification, had been introduced by Kupka 2011. In this paper, we study the relations between Martelli\u2019s chaotic properties of the original and<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M6\"><mml:mrow><mml:mi>g<\/mml:mi><\/mml:mrow><\/mml:math>-fuzzified system. More specifically, we study the transitivity, sensitivity, and stability of the orbits in system (<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M7\"><mml:mi>X<\/mml:mi><mml:mo>,<\/mml:mo><mml:mi>f<\/mml:mi><\/mml:math>) and its connections with the same ones in its<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M8\"><mml:mrow><mml:mi>g<\/mml:mi><\/mml:mrow><\/mml:math>-fuzzified system.<\/jats:p>","DOI":"10.1155\/2014\/956467","type":"journal-article","created":{"date-parts":[[2014,3,31]],"date-time":"2014-03-31T17:20:51Z","timestamp":1396286451000},"page":"1-6","source":"Crossref","is-referenced-by-count":1,"title":["Martelli Chaotic Properties of a Generalized Form of Zadeh\u2019s Extension Principle"],"prefix":"10.1155","volume":"2014","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9729-4871","authenticated-orcid":true,"given":"Yaoyao","family":"Lan","sequence":"first","affiliation":[{"name":"College of Computer Science, Chongqing University, Chongqing 401331, China"},{"name":"Key Laboratory of Data Analyzing and Image Processing, Department of Mathematics and Finance, Chongqing University of Arts and Sciences, Yongchuan 402160, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chunlai","family":"Mu","sequence":"additional","affiliation":[{"name":"College of Mathematics and Statistics, Chongqing University, Chongqing 401331, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","reference":[{"key":"1","doi-asserted-by":"publisher","DOI":"10.1016\/S0960-0779(02)00406-X"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2004.11.006"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2004.12.039"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2004.11.089"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2004.06.039"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2005.10.041"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1016\/j.na.2009.08.042"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2010.10.020"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2012.05.011"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2011.08.004"},{"key":"12","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2005.05.026"},{"year":"1989","key":"13"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2006.05.036"},{"key":"15","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2011.04.006"},{"key":"16","doi-asserted-by":"publisher","DOI":"10.1155\/2012\/875381"},{"key":"17","first-page":"338","volume":"8","year":"1965","journal-title":"Information and Computation"},{"key":"18","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(94)90170-8"},{"key":"19","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2011.02.024"},{"key":"21","doi-asserted-by":"publisher","DOI":"10.1016\/S0166-8641(01)00025-6"},{"issue":"1","key":"22","first-page":"119","volume":"72","year":"2003","journal-title":"Acta Mathematica Universitatis Comenianae"},{"key":"23","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-04-07514-8"},{"key":"24","doi-asserted-by":"publisher","DOI":"10.1007\/s00010-005-2771-0"},{"key":"25","doi-asserted-by":"publisher","DOI":"10.2307\/2691012"},{"year":"1999","key":"26"},{"year":"1991","key":"27"},{"key":"28","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(89)90045-6"},{"key":"29","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(85)90006-5"},{"key":"30","doi-asserted-by":"publisher","DOI":"10.1016\/j.na.2009.06.003"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/956467.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/956467.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/956467.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2016,7,29]],"date-time":"2016-07-29T07:45:30Z","timestamp":1469778330000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/jam\/2014\/956467\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014]]},"references-count":28,"alternative-id":["956467","956467"],"URL":"https:\/\/doi.org\/10.1155\/2014\/956467","relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"type":"print","value":"1110-757X"},{"type":"electronic","value":"1687-0042"}],"subject":[],"published":{"date-parts":[[2014]]}}}