Approximate Solution of Intuitionistic Fuzzy Differential Equations by Using Picard’s Method

  • R. Ettoussi
  • Said MellianiEmail author
  • L. S. Chadli
Part of the Studies in Fuzziness and Soft Computing book series (STUDFUZZ, volume 372)


Our main result in this paper is to find the power series solution of an intuitionistic fuzzy differential equation \(x'(t)=f(t,x(t))\), \(x(t_0)=x_0\) by using successive approximation method and we prove that the approximate solution converge uniformly in t to the exact solution. Finally, we illustrate this result with a numerical example.


  1. 1.
    K. Atanassov, Intuitionistic fuzzy sets. Fuzzy Sets Syst. 20, 87–96 (1986)CrossRefGoogle Scholar
  2. 2.
    Atanassov K., Intuitionistic Fuzzy Sets. Theory and Applications, Physica-Verlag (1999)Google Scholar
  3. 3.
    L.A. Zadeh, Fuzzy set. Inf. Control 8(3), 338–353 (1965)CrossRefGoogle Scholar
  4. 4.
    S. Melliani, L.S. Chadli, Introduction to intuitionistic fuzzy partial differential Equations. in Fifth International Conference on IFSs (Sofia, 2001), pp 22–23Google Scholar
  5. 5.
    M. Keyanpour, T. Akbarian, Solving intuitionistic fuzzy nonlinear equations. J. Fuzzy Set Valued Anal. 2014, 1–6 (2014)MathSciNetCrossRefGoogle Scholar
  6. 6.
    R. Ettoussi, S. Melliani, M. Elomari, L.S. Chadli, Solution of intuitionistic fuzzy differential equations by successive approximations method. Notes Intuitionistic Fuzzy Sets 21(2), 51–62 (2015)Google Scholar
  7. 7.
    S. Melliani, M. Elomari, L.S. Chadli, R. Ettoussi, Intuitionistic fuzzy metric spaces. Notes Intuitionistic Fuzzy Sets 21(1), 43–53 (2015)Google Scholar
  8. 8.
    R. Ettoussi, S. Melliani, L.S. Chadli, Differential equation with intuitionistic fuzzy parameters. Notes Intuitionistic Fuzzy Sets 23(4), 46–61 (2017)Google Scholar

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Sultan Moulay Slimane UniversityBeni MellalMorocco

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