| Full text | |
| Author(s): |
Esmi, Estevao
[1]
;
Sanchez, Daniel Eduardo
[1, 2]
;
Wasques, Vinicius Francisco
[1]
;
de Barros, Laecio Carvalho
[1]
Total Authors: 4
|
| Affiliation: | [1] Univ Estadual Campinas, Dept Appl Math, IMECC, Campinas - Brazil
[2] Univ Austral Chile, Ctr Basic Sci Teaching Engn, Valdivia, Los Rios - Chile
Total Affiliations: 2
|
| Document type: | Journal article |
| Source: | FUZZY SETS AND SYSTEMS; v. 419, n. SI, p. 122-140, AUG 30 2021. |
| Web of Science Citations: | 3 |
| Abstract | |
In this study, we consider higher order linear differential equations with additional conditions (initial and/or boundary) given by interactive fuzzy numbers. The concept of interactivity arises from the notion of a joint possibility distribution (J). The proposed method for solving fuzzy differential equations is based on an extension of the classical solution via sup-J extension, which is a generalization of Zadeh \& rsquo;s extension principle. We prove that under certain conditions, the solution via Zadeh \& rsquo;s extension principle is equal to the convex hull of the solutions produced by the sup-J extension. We also show that the solutions based on the Fr \& eacute;chet derivatives of fuzzy functions coincide with the solutions obtained via the sup-J extension. All of the results are illustrated based on a 3rd order fuzzy boundary value problem. (c) 2020 Elsevier B.V. All rights reserved. (AU) | |
| FAPESP's process: | 16/26040-7 - Differential and integral calculus based on arithmetic of interactive fuzzy numbers |
| Grantee: | Estevão Esmi Laureano |
| Support Opportunities: | Regular Research Grants |