On fuzzy solutions for partial differential equations

dc.creatorBertone, AM
dc.creatorJafelice, RM
dc.creatorde Barros, LC
dc.creatorBassanezi, RC
dc.date2013
dc.dateMAY 16
dc.date2014-07-30T17:47:07Z
dc.date2015-11-26T16:50:46Z
dc.date2014-07-30T17:47:07Z
dc.date2015-11-26T16:50:46Z
dc.date.accessioned2018-03-28T23:37:32Z
dc.date.available2018-03-28T23:37:32Z
dc.identifierFuzzy Sets And Systems. Elsevier Science Bv, v. 219, n. 68, n. 80, 2013.
dc.identifier0165-0114
dc.identifierWOS:000317635800004
dc.identifier10.1016/j.fss.2012.12.002
dc.identifierhttp://www.repositorio.unicamp.br/jspui/handle/REPOSIP/67630
dc.identifierhttp://repositorio.unicamp.br/jspui/handle/REPOSIP/67630
dc.identifier.urihttp://repositorioslatinoamericanos.uchile.cl/handle/2250/1275813
dc.descriptionConselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)
dc.descriptionIn this study we investigate heat, wave and Poisson equations as classical models of partial differential equations (PDEs) with uncertain parameters, considering the parameters as fuzzy numbers. The fuzzy solution is built from fuzzification of the deterministic solution. The continuity of the Zadeh extension is used to obtain qualitative properties on regular alpha-cuts of the fuzzy solution. We prove the stability with respect to the initial boundary data, and show that as time goes to zero, the diameter of the fuzzy solution converges to zero and, as a consequence, to the cylindrical surface determined by the curve of the degree of membership. Numerical simulations are used to obtain a graphical representation of the fuzzy solution and a defuzzification of this solution is obtained using the center of gravity method. We theoretically show that the surface obtained by defuzzification with the plane determined by fixing time is indeed the solution of the same initial boundary problem for this time-point for the heat and Poisson equations and, in a particular case, for the wave equation. The deterministic solution and the defuzzified surface intercept are numerically compared using the Euclidean distance. (C) 2013 Elsevier B.V. All rights reserved.
dc.description219
dc.description68
dc.description80
dc.descriptionConselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)
dc.descriptionBrazilian National Research Council [477918/2010-7, 306872/2009-9]
dc.descriptionConselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)
dc.descriptionBrazilian National Research Council [477918/2010-7, 306872/2009-9]
dc.languageen
dc.publisherElsevier Science Bv
dc.publisherAmsterdam
dc.publisherHolanda
dc.relationFuzzy Sets And Systems
dc.relationFuzzy Sets Syst.
dc.rightsfechado
dc.rightshttp://www.elsevier.com/about/open-access/open-access-policies/article-posting-policy
dc.sourceWeb of Science
dc.subjectFuzzy numbers
dc.subjectPartial differential equations
dc.subjectAnalysis
dc.subjectNumber
dc.subjectSets
dc.titleOn fuzzy solutions for partial differential equations
dc.typeArtículos de revistas


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