First order linear fuzzy differential equations under generalized differentiability

Barnabás Bede, I. Rudas, Attila L. Bencsik

Research output: Contribution to journalArticle

245 Citations (Scopus)

Abstract

First order linear fuzzy differential equations are investigated. We interpret a fuzzy differential equation by using the strongly generalized differentiability concept, because under this interpretation, we may obtain solutions which have a decreasing length of their support (which means a decreasing uncertainty). In several applications the behaviour of these solutions better reflects the behaviour of some real-world systems. Derivatives of the H-difference and the product of two functions are obtained and we provide solutions of first order linear fuzzy differential equations, using different versions of the variation of constants formula. Some examples show the rich behaviour of the solutions obtained.

Original languageEnglish
Pages (from-to)1648-1662
Number of pages15
JournalInformation Sciences
Volume177
Issue number7
DOIs
Publication statusPublished - Apr 1 2007

Fingerprint

Fuzzy Differential Equations
Differentiability
Linear differential equation
Differential equations
First-order
Variation of Constants Formula
Behavior of Solutions
Uncertainty
Derivative
Derivatives

Keywords

  • Fuzzy differential equations
  • Generalized differentiability
  • Variation of constants formula

ASJC Scopus subject areas

  • Statistics and Probability
  • Electrical and Electronic Engineering
  • Statistics, Probability and Uncertainty
  • Information Systems and Management
  • Information Systems
  • Computer Science Applications
  • Artificial Intelligence

Cite this

First order linear fuzzy differential equations under generalized differentiability. / Bede, Barnabás; Rudas, I.; Bencsik, Attila L.

In: Information Sciences, Vol. 177, No. 7, 01.04.2007, p. 1648-1662.

Research output: Contribution to journalArticle

Bede, Barnabás ; Rudas, I. ; Bencsik, Attila L. / First order linear fuzzy differential equations under generalized differentiability. In: Information Sciences. 2007 ; Vol. 177, No. 7. pp. 1648-1662.
@article{41ddfeda2f914806916ff2452dfe4783,
title = "First order linear fuzzy differential equations under generalized differentiability",
abstract = "First order linear fuzzy differential equations are investigated. We interpret a fuzzy differential equation by using the strongly generalized differentiability concept, because under this interpretation, we may obtain solutions which have a decreasing length of their support (which means a decreasing uncertainty). In several applications the behaviour of these solutions better reflects the behaviour of some real-world systems. Derivatives of the H-difference and the product of two functions are obtained and we provide solutions of first order linear fuzzy differential equations, using different versions of the variation of constants formula. Some examples show the rich behaviour of the solutions obtained.",
keywords = "Fuzzy differential equations, Generalized differentiability, Variation of constants formula",
author = "Barnab{\'a}s Bede and I. Rudas and Bencsik, {Attila L.}",
year = "2007",
month = "4",
day = "1",
doi = "10.1016/j.ins.2006.08.021",
language = "English",
volume = "177",
pages = "1648--1662",
journal = "Information Sciences",
issn = "0020-0255",
publisher = "Elsevier Inc.",
number = "7",

}

TY - JOUR

T1 - First order linear fuzzy differential equations under generalized differentiability

AU - Bede, Barnabás

AU - Rudas, I.

AU - Bencsik, Attila L.

PY - 2007/4/1

Y1 - 2007/4/1

N2 - First order linear fuzzy differential equations are investigated. We interpret a fuzzy differential equation by using the strongly generalized differentiability concept, because under this interpretation, we may obtain solutions which have a decreasing length of their support (which means a decreasing uncertainty). In several applications the behaviour of these solutions better reflects the behaviour of some real-world systems. Derivatives of the H-difference and the product of two functions are obtained and we provide solutions of first order linear fuzzy differential equations, using different versions of the variation of constants formula. Some examples show the rich behaviour of the solutions obtained.

AB - First order linear fuzzy differential equations are investigated. We interpret a fuzzy differential equation by using the strongly generalized differentiability concept, because under this interpretation, we may obtain solutions which have a decreasing length of their support (which means a decreasing uncertainty). In several applications the behaviour of these solutions better reflects the behaviour of some real-world systems. Derivatives of the H-difference and the product of two functions are obtained and we provide solutions of first order linear fuzzy differential equations, using different versions of the variation of constants formula. Some examples show the rich behaviour of the solutions obtained.

KW - Fuzzy differential equations

KW - Generalized differentiability

KW - Variation of constants formula

UR - http://www.scopus.com/inward/record.url?scp=33846224330&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33846224330&partnerID=8YFLogxK

U2 - 10.1016/j.ins.2006.08.021

DO - 10.1016/j.ins.2006.08.021

M3 - Article

VL - 177

SP - 1648

EP - 1662

JO - Information Sciences

JF - Information Sciences

SN - 0020-0255

IS - 7

ER -