A new approach to fuzzy initial value problem

Gasilov N. A., Fatullayev A. G., EMRAH Ş., Khastan A.

SOFT COMPUTING, vol.18, no.2, pp.217-225, 2014 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 18 Issue: 2
  • Publication Date: 2014
  • Doi Number: 10.1007/s00500-013-1081-z
  • Journal Name: SOFT COMPUTING
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.217-225
  • Keywords: Fuzzy initial value problem, Fuzzy differential equation, Fuzzy set, Linear transformation, DIFFERENTIAL-EQUATIONS, LINEAR-SYSTEMS
  • Ankara University Affiliated: Yes

Abstract

In this paper, we consider a high-order linear differential equation with fuzzy initial values. We present solution as a fuzzy set of real functions such that each real function satisfies the initial value problem by some membership degree. Also we propose a method based on properties of linear transformations to find the fuzzy solution. We find out the solution determined by our method coincides with one of the solutions obtained by the extension principle method. Some examples are presented to illustrate applicability of the proposed method.