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Issue:Solution of n-th order intuitionistic fuzzy differential equation by variational iteration method

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Title of paper: Solution of n-th order intuitionistic fuzzy differential equation by variational iteration method
Author(s):
Said Melliani
Department of Mathematics, Sultan Moulay Slimane University, LMACS, Laboratoire de Math´ematiques Appliqu´ees & Calcul Scientifique, PO Box 523, 23000 Beni Mellal, Morocco
saidmelliani@gmail.com
H. Atti
Department of Mathematics, Sultan Moulay Slimane University, LMACS, Laboratoire de Math´ematiques Appliqu´ees & Calcul Scientifique, PO Box 523, 23000 Beni Mellal, Morocco
B. Ben Amma
Department of Mathematics, Sultan Moulay Slimane University, LMACS, Laboratoire de Math´ematiques Appliqu´ees & Calcul Scientifique, PO Box 523, 23000 Beni Mellal, Morocco
Lalla Saadia Chadli
Department of Mathematics, Sultan Moulay Slimane University, LMACS, Laboratoire de Math´ematiques Appliqu´ees & Calcul Scientifique, PO Box 523, 23000 Beni Mellal, Morocco
Published in: "Notes on IFS", Volume 24, 2018, Number 3, pages 92—105
DOI: https://doi.org/10.7546/nifs.2018.24.3.92-105
Download:  PDF (206  Kb, Info)
Abstract: In this paper, the variational iteration method proposed by Ji-Huan He is applied to solve n-th order intuitionistic fuzzy differential equations with intuitionistic fuzzy initial conditions. Several numerical examples are given to illustrate the efficiency of the presented method.
Keywords: Intuitionistic fuzzy number, Intuitionistic fuzzy differential equation, Variational iteration method.
AMS Classification: 03E72, 34A07.
References:
  1. Abbasbandy, S., & Allahviranloo, T. (2002) Numerical solution of fuzzy differential equation by Runge-Kutta method and the intuitionistic treatment, Notes on Intuitionistic Fuzzy Sets, 8(3), 45–53.
  2. Atanassov, K. (1983) Intuitionistic fuzzy sets, VII ITKR Session, Sofia, 20-23 June 1983 (Deposed in Centr. Sci.-Techn. Library of the Bulg. Acad. of Sci., 1697/84) (in Bulgarian). Reprinted: Int. J. Bioautomation, 2016, 20(S1), S1–S6.
  3. Atanassov, K. T. (1986) Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20 (1), 87–96.
  4. Atanassov, K. T. (1994) Operators over interval valued intuitionistic fuzzy sets, Fuzzy Sets and Systems, 64(2), 159–174.
  5. Ben Amma, B., Melliani, S., & Chadli, L. S. (2016) Numerical solution of intuitionistic fuzzy differential equations by Euler and Taylor methods, Notes on Intuitionistic Fuzzy Sets, 22 (2), 71–86.
  6. Ben Amma, B., Melliani, S., & Chadli, L. S., (2016) Numerical solution of intuitionistic fuzzy differential equations by Adams' three order predictor-corrector method, Notes on Intuitionistic Fuzzy Sets, 22 (3), 47–69.
  7. Ben Amma, B. & Chadli, L. S. (2016) Numerical solution of intuitionistic fuzzy differential equations by Runge–Kutta Method of order four, Notes on Intuitionistic Fuzzy Sets, 22 (4), 42–52.
  8. Ben Amma, B., Melliani, S., & Chadli, L. S. (2018) The Cauchy problem for intuitionistic fuzzy differential equations, Notes on Intuitionistic Fuzzy Sets, 24 (1), 37–47.
  9. Ben Amma, B., Melliani, S., & Chadli, L. S. (2018) Intuitionistic Fuzzy Functional Differential Equations, Fuzzy Logic in Intelligent System Design: Theory and Applications, P. Melin, O. Castillo, J. Kacprzyk, M. Reformat, W. Melek, Ed. Cham: Springer International Publishing, 335–357.
  10. De, S. K., Biswas, R. & Roy, A. R. (2001) An application of intuitionistic fuzzy sets in medical diagnosis, Fuzzy Sets and Systems, 117, 209–213.
  11. He, J. H. (1998) Approximate solution of non linear differential equations with convolution product nonlinearities, Comput. Methods Appl. Mech. Engrg., 167, 69–73.
  12. He, J. H., & Wu, X.-H. (2007) Variational iteration method: New development and applications, Comput. Math. Appl., 54 (78), 881–894.
  13. He, J.H., Wu, G. C. ,& Austin, F. (2010) The variational iteration method which should be followed, Nonlinear Sci. Lett., A 1, 1–30.
  14. Li, D. F., & Cheng, C. T. (2002) New similarity measures of intuitionistic fuzzy sets and application to pattern recognitions, Pattern Recognit. Lett., 23, 221–225.
  15. Li, D. F. (2005) Multiattribute decision making models and methods using intuitionistic fuzzy sets, J.Comput. Syst. Sci., 70, 73–85
  16. Melliani, S., & Chadli, L. S. (2000) Intuitionistic fuzzy differential equation. Part 1, Notes on Intuitionistic Fuzzy Sets, 6 (2), 37–41.
  17. Melliani, S., Elomari, M., Chadli, L. S., & Ettoussi, R. (2015) Intuitionistic fuzzy metric space, Notes on Intuitionistic Fuzzy Sets, 21 (1), 43–53.
  18. Melliani, S., Elomari, M., Chadli, L. S., & Ettoussi, R. (2015) Intuitionistic fuzzy fractional equation, Notes on Intuitionistic Fuzzy sets, 21 (4), 76–89.
  19. Melliani, S., Elomari, M., Atraoui, M., & Chadli, L. S. (2015) Intuitionistic fuzzy differential equation with nonlocal condition, Notes on Intuitionistic Fuzzy sets, 21 (4), 58–68.
  20. Nirmala, V. (2015) Numerical Approach for Solving Intuitionistic Fuzzy Differential Equation under Generalised Differentiability Concept, Applied Mathematical Sciences, 9 (67), 3337–3346.
  21. Parimala, V., Rajarajeswari, P., & Nirmala, V. (2017) Numerical Solution of Intuitionistic Fuzzy Differential Equation by Milne’s Predictor-Corrector Method Under Generalised Differentiability, International Journal of Mathematics And its Applications, 5, 45–54.
  22. Shu, M. H., Cheng, C. H. & Chang, J. R. (2006) Using intuitionistic fuzzy sets for fault-tree analysis on printed circuit board assembly, Microelectron. Reliab., 46 (12), 2139–2148.
  23. Sankar, P. M. & Roy, T. K. (2014) First order homogeneous ordinary differential equation with initial value as triangular intuitionistic fuzzy number, Journal of Uncertainty in Mathematics Science, 2014, 1–17.
  24. Sankar, P. M., & Roy, T. K., (2015) System of Differential Equation with Initial Value as Triangular Intuitionistic Fuzzy Number and its Application, Int. J. Appl. Comput. Math, 1 (3), 449–474.
  25. Tatari, M. & Dehghan, M. (2008) On the convergence of He’s variational iteration method, J. Comput. Appl. Math., 207 (1), 121–128.
  26. Wang, Z., Li, K. W., & Wang, W. (2009) An approach to multiattribute decision making with interval-valued intuitionistic fuzzy assessments and incomplete weights., Information Sciences, 179 (17), 3026–3040.
  27. Ye, J. (2009) Multicriteria fuzzy decision-making method based on a novel accuracy function under interval valued intuitionistic fuzzy environment, Expert Syst. Applicat., 36, 6899– 6902.
  28. Zadeh, L.A. (1965) Fuzzy sets, Inf. Control, 8 (3), 338–353.
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