Fuzzy differential equations and the extension principle

M. T. Mizukoshi; L. C. Barros; Y. Chalco-Cano; H. Román-Flores; R. C. Bassanezi

doi:10.1016/j.ins.2007.02.039

Fuzzy differential equations and the extension principle

M. T. Mizukoshi
, L. C. Barros
, Y. Chalco-Cano
, H. Román-Flores
, R. C. Bassanezi

Department of Mathematics

Universidade Federal de Goiás
Universidade Estadual de Campinas
Universidad de Tarapacá

Research output: Contribution to journal › Article › peer-review

179 Scopus citations

Abstract

We study the Cauchy problem for differential equations, considering its parameters and/or initial conditions given by fuzzy sets. These fuzzy differential equations are approached in two different ways: (a) by using a family of differential inclusions; and (b) the Zadeh extension principle for the solution of the model. We conclude that the solutions of the Cauchy problem obtained by both are the same. We also provide some illustrative examples.

Original language	English
Pages (from-to)	3627-3635
Number of pages	9
Journal	Information Sciences
Volume	177
Issue number	17
DOIs	https://doi.org/10.1016/j.ins.2007.02.039
State	Published - 1 Sep 2007

Keywords

Differential inclusions
Extension principle
Fuzzy differential equation
Fuzzy sets

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10.1016/j.ins.2007.02.039

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AU - Barros, L. C.

AU - Chalco-Cano, Y.

AU - Román-Flores, H.

AU - Bassanezi, R. C.

PY - 2007/9/1

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N2 - We study the Cauchy problem for differential equations, considering its parameters and/or initial conditions given by fuzzy sets. These fuzzy differential equations are approached in two different ways: (a) by using a family of differential inclusions; and (b) the Zadeh extension principle for the solution of the model. We conclude that the solutions of the Cauchy problem obtained by both are the same. We also provide some illustrative examples.

AB - We study the Cauchy problem for differential equations, considering its parameters and/or initial conditions given by fuzzy sets. These fuzzy differential equations are approached in two different ways: (a) by using a family of differential inclusions; and (b) the Zadeh extension principle for the solution of the model. We conclude that the solutions of the Cauchy problem obtained by both are the same. We also provide some illustrative examples.

KW - Differential inclusions

KW - Extension principle

KW - Fuzzy differential equation

KW - Fuzzy sets

UR - https://www.scopus.com/pages/publications/34250379505

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DO - 10.1016/j.ins.2007.02.039

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Fuzzy differential equations and the extension principle

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Keywords

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