{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T06:32:45Z","timestamp":1777703565081,"version":"3.51.4"},"reference-count":12,"publisher":"SAGE Publications","issue":"2","license":[{"start":{"date-parts":[[2019,7,9]],"date-time":"2019-07-09T00:00:00Z","timestamp":1562630400000},"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 & Fuzzy Systems"],"published-print":{"date-parts":[[2019,9,9]]},"abstract":"\n \u00a0In this paper, we consider a type of fuzzy harmonic oscillator described by a differential equation of the form\n x<\/jats:italic>\n \u2033\u00a0+\u00a0\n a<\/jats:italic>\n 2<\/jats:sup>\n x<\/jats:italic>\n \u00a0=\u00a00 with initial conditions given by fuzzy numbers. Here, we assume that\n x<\/jats:italic>\n \u2033\u00a0(\n t<\/jats:italic>\n ) and\n a<\/jats:italic>\n 2<\/jats:sup>\n x<\/jats:italic>\n \u00a0(\n t<\/jats:italic>\n ) are linearly correlated fuzzy numbers for\n \n \n t<\/mml:mi>\n \u2208<\/mml:mo>\n \n \n \u211d<\/mml:mi>\n <\/mml:mstyle>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:inline-formula>\n and\n \n \n a<\/mml:mi>\n \u2208<\/mml:mo>\n \n \n \u211d<\/mml:mi>\n <\/mml:mstyle>\n <\/mml:mrow>\n ,<\/mml:mo>\n a<\/mml:mi>\n \u2260<\/mml:mo>\n 0<\/mml:mn>\n <\/mml:math>\n <\/jats:inline-formula>\n . In general, this assumption is necessary for the equality\n x<\/jats:italic>\n \u2033\u00a0+\u00a0\n a<\/jats:italic>\n 2<\/jats:sup>\n x<\/jats:italic>\n \u00a0=\u00a00 to make sense. Using this interactive relation, we obtain a solution for this problem using a fuzzy Laplace transform method.\n <\/jats:p>","DOI":"10.3233\/jifs-182761","type":"journal-article","created":{"date-parts":[[2019,7,12]],"date-time":"2019-07-12T14:01:00Z","timestamp":1562940060000},"page":"2495-2501","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":8,"title":["Solution of a fuzzy differential equation with interactivity via Laplace transform"],"prefix":"10.1177","volume":"37","author":[{"given":"Silvio Ant\u00f4nio Bueno","family":"Salgado","sequence":"first","affiliation":[{"name":"Institute of Applied Social Sciences, Federal University of Alfenas, Varginha, Minas Gerais, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"La\u00e9cio Carvalho","family":"de Barros","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics, University of Campinas, Campinas, S\u00e3o Paulo, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Estev\u00e3o","family":"Esmi","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics, University of Campinas, Campinas, S\u00e3o Paulo, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Daniel","family":"Eduardo S\u00e1nchez","sequence":"additional","affiliation":[{"name":"Patagonia Campus, University Austral of Chile, Coyhaique, Ays\u00e9n, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2019,7,9]]},"reference":[{"key":"e_1_3_2_2_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2003.08.004"},{"key":"e_1_3_2_3_2","first-page":"535","article-title":"Additions of completely correlated fuzzy numbers","author":"Carlsson C.","year":"2004","unstructured":"CarlssonC., Full\u00e9rR. and MajlanderP., Additions of completely correlated fuzzy numbers, In Proc IEEE Inter Conference (2004), pp. 535\u2013539.","journal-title":"Proc IEEE Inter Conference"},{"key":"e_1_3_2_4_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0020-0255(98)00016-4"},{"key":"e_1_3_2_5_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2016.04.002"},{"key":"e_1_3_2_6_2","unstructured":"BarrosL.C. BassaneziR.C. and LodwickW.A. A First Course in Fuzzy Logic Fuzzy Dynamical Systems and Biomathematics Springer-Verlag Berlin Heidelberg 2017."},{"key":"e_1_3_2_7_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.physa.2011.07.023"},{"key":"e_1_3_2_8_2","doi-asserted-by":"publisher","DOI":"10.1016\/0022-247X(83)90169-5"},{"key":"e_1_3_2_9_2","volume-title":"Fundamentals of Differential Equations","author":"Nagle R.K.","year":"2017","unstructured":"NagleR.K., SaffE.B. and SniderA.D., Fundamentals of Differential Equations, Addison-Wesley, 2017."},{"key":"e_1_3_2_10_2","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(87)90030-3"},{"key":"e_1_3_2_11_2","first-page":"103","volume":"11","author":"Salgado S.A.B.","year":"2018","unstructured":"SalgadoS.A.B., BarrosL.C. and EsmiE., Solution of fuzzy differential equation with interactivy via fuzzy Laplace transform, in: Data Science and Knowlegde Engineering for Sensing Decision Support, World Scientific Proceedings Series, vol. 11, (2018), pp. 103\u2013109.","journal-title":"Data Science and Knowlegde Engineering for Sensing Decision Support, World Scientific Proceedings Series"},{"key":"e_1_3_2_12_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00500-008-0397-6"},{"key":"e_1_3_2_13_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00500-012-0907-4"}],"container-title":["Journal of Intelligent & Fuzzy Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/JIFS-182761","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/full-xml\/10.3233\/JIFS-182761","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/JIFS-182761","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T09:38:59Z","timestamp":1777455539000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/JIFS-182761"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,7,9]]},"references-count":12,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2019,9,9]]}},"alternative-id":["10.3233\/JIFS-182761"],"URL":"https:\/\/doi.org\/10.3233\/jifs-182761","relation":{},"ISSN":["1064-1246","1875-8967"],"issn-type":[{"value":"1064-1246","type":"print"},{"value":"1875-8967","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,7,9]]}}}