Stability analysis of fuzzy linear differential equations
type: Item
instance of: scholarly article
title: Stability analysis of fuzzy linear differential equations
zbMATH Open document ID: 1203.34002
author: Yuanguo Zhu
published in: Fuzzy Optimization and Decision Making
publication date: 2010-06-09T00:00:00Z
review text: Using the concept of credibility measure and the credibility theory founded by Liu [\textit{Baodin Liu}, Uncertainty theory. 2nd ed. Studies in Fuzziness and Soft Computing 154. Berlin: Springer. (2007; Zbl 1141.28001)], the author considers the stability theory for a fuzzy linear differential equation, involving a fuzzy process called the standard Liu process. This formulation involves a new notion of fuzzy differential and fuzzy integral (called Liu integral). The fundamental stability concepts, such as Lyapunov stability, uniform stability, asymptotic stability, uniformly asymptotic stability, global asymtotic stability and stability of exponent \(p\) are introduced for the linear fuzzy Liu differential equation. Some sufficient and necessary conditions for different stability notions of the zero equilibrium point of the linear Liu differential equation are obtained. A few examples are also presented.
reviewed by: Gnana Bhaskar Tenali
Mathematics Subject Classification ID: 34A07
Mathematics Subject Classification ID: 34D20
Mathematics Subject Classification ID: 34A30
zbMATH DE Number: 5719113
zbMATH Keywords: Credibility measure
zbMATH Keywords: Liu process
zbMATH Keywords: fuzzy differential equation
zbMATH Keywords: stability
MaRDI profile type: Publication
full work available at URL: s10700-010-9080-3
OpenAlex ID: W2151755084
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DOI: 10.1007/S10700-010-9080-3
description: scientific article; zbMATH DE number 5719113