Comparation between some approaches to solve fuzzy differential equations
type: Item
instance of: scholarly article
title: Comparation between some approaches to solve fuzzy differential equations
zbMATH Open document ID: 1198.34005
published in: Fuzzy Sets and Systems
publication date: 2009-11-17T00:00:00Z
review text: The authors study differential equations, where a fuzzy function \(f\) is obtained by applying Zadeh's extension principle to a function \(g\). They obtain a fuzzy solution for this class of fuzzy differential equations by applying Zadeh's extension principle to the deterministic solution associated with the fuzzy problem and show that the fuzzy solution is coincident with the solution obtained by fuzzy differential inclusions. Also, in the case that \(f\) is monotone, the authors show that the fuzzy solution coincides with the solution obtained by considering the generalized derivative. They present a numerical procedure to obtain the fuzzy solution. The paper contains many examples.
reviewed by: Andrej V. Plotnikov
Mathematics Subject Classification ID: 34A07
Mathematics Subject Classification ID: 34A12
zbMATH DE Number: 5634455
zbMATH Keywords: extension principle
zbMATH Keywords: fuzzy differential equation
author: Yurilev Chalco-Cano
author: Heriberto E. Román-Flores
MaRDI profile type: Publication
full work available at URL: j.fss.2008.10.002
OpenAlex ID: W1985864380
cites work: Tuning of reachable set in one dimensional fuzzy differential inclusions
cites work: Numerical methods for fuzzy differential inclusions
cites work: Numerical solution of fuzzy differential equations by predictor-corrector method
cites work: Note on ``Numerical solution of fuzzy differential equations by predictor-corrector method''
cites work: Generalizations of the differentiability of fuzzy-number-valued functions with applications to fuzzy differential equations
cites work: First order linear fuzzy differential equations under generalized differentiability
cites work: Fuzzy differential equations
cites work: On fuzzy differential equations
cites work: On new solutions of fuzzy differential equations
cites work: \(M\)-convex fuzzy mappings and fuzzy integral mean
cites work: The extension principle and a decomposition of fuzzy sets
cites work: Q5446064
cites work: Brief note on the variation of constants formula for fuzzy differential equations
cites work: Q4871309
cites work: Existence of solutions of fuzzy differential equations with parameters
cites work: Revisiting fuzzy differential equations
cites work: Impulsive functional differential inclusions and fuzzy population models
cites work: The oscillation of delay differential inclusions and fuzzy biodynamics models
cites work: Q5465585
cites work: An Approach to Modelling and Simulation of Uncertain Dynamical Systems
cites work: NUMERICAL METHODS FOR FUZZY INITIAL VALUE PROBLEMS
cites work: Simulating continuous fuzzy systems
cites work: A note on fuzzy differential equations
cites work: Q4650359
cites work: Fuzzy differential equations and the extension principle
cites work: The Cauchy problem for continuous fuzzy differential equations
cites work: Bounded solutions for fuzzy differential and integral equations
cites work: Q3527104
cites work: LINEAR FIRST-ORDER FUZZY DIFFERENTIAL EQUATIONS
cites work: Differential Equations With Fuzzy Parameters
cites work: Runge-Kutta methods for fuzzy differential equations
cites work: The Runge-Kutta method for hybrid fuzzy differential equations
cites work: Differentials of fuzzy functions
cites work: Comparison results for fuzzy differential equations
cites work: Monotone method for fuzzy differential equations
cites work: A note on Zadeh's extensions
cites work: Embedding of level-continuous fuzzy sets on Banach spaces
cites work: Global existence of solutions to fuzzy differential equations
cites work: Existence and uniqueness of solutions to Cauchy problem of fuzzy differential equations
cites work: Existence theorems to the Cauchy problem for fuzzy differential equations under compactness-type conditions
cites work: On the structure of solutions for fuzzy initial value problem
cites work: A class of linear differential dynamical systems with fuzzy initial condition
cites work: The concept of a linguistic variable and its application to approximate reasoning. I
DOI: 10.1016/J.FSS.2008.10.002
description: scientific article; zbMATH DE number 5634455