Fuzzy Sumudu transform approach to solving fuzzy differential equations with Z-numbers

Raheleh Jafari, Sina Razvarz, Alexander Gegov, Satyam Paul, Sajjad Keshtkar

Research output: Chapter in Book/Report/Conference proceedingChapter (peer-reviewed)peer-review

Abstract

Uncertain nonlinear systems can be modeled with fuzzy differential equations (FDEs) and the solutions of these equations are applied to analyze many engineering problems. However, it is very difficult to obtain solutions of FDEs.
In this book chapter, the solutions of FDEs are approximated by utilizing the fuzzy Sumudu transform (FST) method. Here, the uncertainties are in the sense of fuzzy numbers and Z-numbers. Important theorems are laid down to illustrate the properties of FST. This new technique is compared with Average Euler method and Max-Min Euler method. The theoretical analysis and simulation results show that the FST method is effective in estimating the solutions of FDEs.
Original languageEnglish
Title of host publicationAdvanced Fuzzy Logic Approaches in Engineering Science
EditorsMangey Ram
PublisherIGI Global
Chapter2
Pages18-48
Number of pages31
ISBN (Electronic)9781522557104
ISBN (Print)9781522557098
DOIs
Publication statusPublished - 1 Sep 2018

Keywords

  • Fuzzy Sumudu transform
  • Fuzzy differential equations
  • Modeling
  • Approximate solution
  • Z-numbers
  • Fuzzy numbers
  • Euler method
  • Uncertain nonlinear systems
  • Max-Min Euler

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