Analytical and numerical solutions of fuzzy differential equations

M. Z. Ahmad, Mohammad Khatim Hasan, B. De Baets

Research output: Contribution to journalArticle

33 Citations (Scopus)

Abstract

In this paper, we study analytical and numerical solutions of fuzzy differential equations based on the extension principle. For linear fuzzy differential equations, we state some results on the behaviour of the solutions and study their relationship with the generalised Hukuhara derivative. In order to approximate the solutions of linear and non-linear fuzzy differential equations, we propose a new fuzzification of the classical Euler method and then incorporate an unconstrained optimisation technique. This combination offers a powerful tool to tackle uncertainty in any numerical method. An efficient computational algorithm is also provided to guarantee the convexity of fuzzy solutions on the time domain. Several illustrative examples are given.

Original languageEnglish
Pages (from-to)156-167
Number of pages12
JournalInformation Sciences
Volume236
DOIs
Publication statusPublished - 1 Jul 2013

Fingerprint

Fuzzy Differential Equations
Analytical Solution
Differential equations
Numerical Solution
Generalized Derivatives
Extension Principle
Euler's method
Computational Algorithm
Unconstrained Optimization
Linear differential equation
Optimization Techniques
Nonlinear Differential Equations
Convexity
Time Domain
Numerical methods
Efficient Algorithms
Numerical Methods
Derivatives
Uncertainty
Numerical solution

Keywords

  • Dependency problem
  • Fuzzy derivative
  • Fuzzy differential equation
  • Numerical method

ASJC Scopus subject areas

  • Artificial Intelligence
  • Software
  • Control and Systems Engineering
  • Theoretical Computer Science
  • Computer Science Applications
  • Information Systems and Management

Cite this

Analytical and numerical solutions of fuzzy differential equations. / Ahmad, M. Z.; Hasan, Mohammad Khatim; De Baets, B.

In: Information Sciences, Vol. 236, 01.07.2013, p. 156-167.

Research output: Contribution to journalArticle

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