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Issue:Solving intuitionistic fuzzy differential equations with linear differential operator by Adomian decomposition method

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Title of paper: Solving intuitionistic fuzzy differential equations with linear differential operator by Adomian decomposition method
Author(s):
Suvankar Biswas
Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah-711103, West Bengal, India
suvo180591@gmail.com
Sanhita Banerjee
Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah-711103, West Bengal, India
Tapan Kumar Roy
Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah-711103, West Bengal, India
Presented at: 3rd International Intuitionistic Fuzzy Sets Conference, 9 Aug – 1 Sep 2016, Mersin, Turkey
Published in: "Notes on IFS", Volume 22, 2016, Number 4, pages 25—41
Download:  PDF (318  Kb, Info)
Abstract: In this paper we have taken the intuitionistic fuzzy differential equation with linear differential operator. Adomian decomposition method (ADM) has been used to find the approximate solution. We have given two numerical examples and by comparing the numerical results obtain from ADM with the exact solution, we have studied their accuracy.
Keywords: Fuzzy differential, Fuzzy differential equations, Intuitionistic fuzzy differential equations, Initial value problem, Adomian decomposition method.
AMS Classification: 03E72.
References:
  1. Adomian, G. (1980) Stochastic systems analysis, Applied Stochastic Processes, Academic Press, New York, 1–18.
  2. Adomian, G. (1994) Solving Frontier Problems of Physics: The Decomposition Method, Kluwer Academic Publishers, Dordrecht.
  3. Adomian, G. (1988) A review of the decomposition method in applied mathematics, Journal of Mathematical Analysis and Applications, 135, 501–544.
  4. Adomian, G. (1984) Convergent series solution of nonlinear equations, Journal of Computational and Applied Mathematics, 11, 225–230.
  5. Adomian, G. (1982) On Green’s function in higher order stochastic differential equations, Journal of Mathematical Analysis and Applications, 88, 604–606.
  6. Babolian, E., Sadeghi, H., & Javadi, Sh. (2004) Numerically solution of fuzzy differential equations by Adomian method, Applied Mathematics and Computation, 149, 547–557.
  7. Paripour, M., Hajilou, E., Hajilou, A. & Heidari, H. (2015) Application of Adomian decomposition method to solve hybrid fuzzy differential equations, Journal of Taibah University for Science, 9, 95–103.
  8. Wang, L., & Guo, S. (2011) Adomian method for second-order fuzzy differential equation, World Academy of Science, Engineering and Technology, 5, 4–23.
  9. Zadeh, L. (2005) Toward a generalized theory of uncertainty (GTU) – an outline, Information Sciences, 175, 1–40.
  10. Kaleva, O. (1987) Fuzzy differential equations, Fuzzy Sets and Systems, 24, 301–317.
  11. Bede, B., Rudas, I. J. & Bencsik, A. L. (2007) First order linear fuzzy differential equations under generalized differentiability, Information Sciences, 177, 1648–1662.
  12. Chalco-Cano, Y., & Roman-Flores, H. (2009) Comparation between some approaches to solve fuzzy differential equations, Fuzzy Sets and Systems, 160, 1517–1527.
  13. Ding, Z., Ma, M., & Kandel, A. (1997) Existence of the solutions of fuzzy differential equations with parameters, Information Sciences, 99, 205–217.
  14. Seikkala, S. (1987) On the fuzzy initial value problem, Fuzzy Sets and Systems, 24, 319–330.
  15. Mizukoshi, M. T., Barros, L. C., Chalco-Cano, Y., Roman-Flores, H., & Bassanezi, R. C. (2007) Fuzzy differential equations and extension principle, Information Sciences, 177, 3627–3635.
  16. Allahviranloo, T., Kiani, N. A. & Motamedi, N. (2009) Solving fuzzy differential equations by differential transformation method, Information Sciences, 179, 956–966.
  17. Rodriguez-Lopez, R. (2008) Monotone method for fuzzy differential equations, Fuzzy Sets and Systems, 159, 2047–2076.
  18. Ghazanfari, B., & Shakerami, A. (2011) Numerical Solutions of fuzzy differential equations by extended Runge-Kutta-like formulae of order 4, Fuzzy Sets and Systems, 189 74–91.
  19. Wu, C., Song, S., & Lee, E. S. (1996) Approximate solutions, existence and uniqueness of the Cauchy problem of fuzzy differential equations, Journal of Mathematical Analysis and Applications, 202, 629–644.
  20. Buckley, J. J., & Feuring, T. (2000) Fuzzy differential equations, Fuzzy Sets and Systems, 110, 43–54.
  21. Wu, C., & Song, S. (1998) Existence theorem to the Cauchy problem of fuzzy differential equations under compactness- type conditions, Information Sciences, 108, 123–134.
  22. Khastan, A., & Rodriguez-Lopez, R. (2015) On periodic solutions to first order linear fuzzy differential equations under differential inclusions’ approach, Information Sciences, 322, 31–50.
  23. Song, S., & Wu, C. (2000) Existence and uniqueness of solutions to the Cauchy problem of fuzzy differential equations, Fuzzy Sets and Systems, 110, 55–67.
  24. Friedman, M., Ma, M., & Kandel, A. (1999) Numerical solutions of fuzzy differential and integral equations, Fuzzy Sets and Systems, 106, 35–48.
  25. Mosleh, M., & Otadi, M. (2015) Approximate solution of fuzzy differential equations under generalized differentiability, Applied Mathematical Modelling, 39, 3003–3015.
  26. Cabral, V. M., & Barros, L. C. (2015) Fuzzy differential equation with completely correlated parameters. Fuzzy Sets and Systems, 265, 86–98.
  27. Atanassov, K. T. Intuitionistic fuzzy sets. VII ITKR’s session, Sofia (deposited in Central Science and Technical Library of the Bulgarian Academy of Sciences 1697/84) (1983). Reprinted: Int. J. Bioautomation, 2016, 20(S1), S1-S6
  28. Atanassov, K. T. (1986) Intuitionistic fuzzy sets. Fuzzy Sets and Systems, 20 (1), 87–96.
  29. Atanassov, K. T. (1994) Operators over interval valued intuitionistic fuzzy sets. Fuzzy Sets and Systems, 64(2), 159–174.
  30. Nikolova, M., Nikolov, N. Cornelis, C., & Deschrijver, G. (2002) Survey of the research on intuitionistic fuzzy sets. Adv. Stud. Contempor. Math, 4(2), 127–157.
  31. De, S. K., Biswas, R., & Roy, A. R. (2001) An application of intuitionistic fuzzy sets in medical diagnosis. Fuzzy Sets and Systems, 117(2), 209–213.
  32. 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.
  33. 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.
  34. 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.
  35. Li, D. F. (2005) Multiattribute decision making models and methods using intuitionistic fuzzy sets. J. Comput. Syst. Sci., 70, 73–85.
  36. Kharal, A. (2009) Homeopathic drug selection using intuitionistic fuzzy sets. Homeopathy, 98(1), 35–39.
  37. Oberguggenberger, M., & Pittschmann, S. (1999) Differential equations with fuzzy parameters. Math. Mod. Syst., 5, 181–202.
  38. Casasnovas, J., & Rossell, F. (2005) Averaging fuzzy biopolymers. Fuzzy Sets and Systems, 152, 139–158.
  39. Ahmad, M. Z., & De Baets, B. (2009) A predator–prey model with fuzzy initial populations. Proceedings of the 13th IFSA World Congress and 6th European Society of Fuzzy Logic and Technology Conference, IFSA-EUSFLAT (2009), 1311–1314.
  40. Barros, L. C., Bassanezi, R. C., & Tonelli, P. A. (2000) Fuzzy modelling in population dynamics. Ecol. Model., 128, 27–33.
  41. El Naschie, M. S. (2005) From experimental quantum optics to quantum gravity via a fuzzy Khler manifold. Chaos, Solitons & Fractals, 25, 969–977.
  42. Mondal, S. P., & Roy, T. K. (2013) First order linear non homogeneous ordinary differential equation in fuzzy environment. Math. Theory Model, 3(1), 85–95.
  43. Hassan, Z., Kamyad, A.V., & Heydari, A. A. (2012) Fuzzy modeling and control of HIV infection. Comput. Math. Methods Med., Volume 2012, Article ID 893474, 17 pages.
  44. Mondal, S. P., Banerjee, S., & Roy, T. K. (2013) First order linear homogeneous ordinary differential equation in fuzzy environment. Int. J. Pure Appl. Sci. Technol., 14(1), 16–26.
  45. Bencsik, A. L., Bede, B., Tar, J. K., & Fodor, J. (2006) Fuzzy differential equations in modeling hydraulic Differential servo cylinders. Third Romanian-Hungarian joint symposium on applied computational intelligence (SACI), Timisoara, Romania.
  46. Nirmala, V. & Pandian, S. C. (2015) Numerical Approach for Solving Intuitionistic Fuzzy Differential Equation under Generalised Differentiability Concept, Applied Mathematical Sciences, 9(67), 3337–3346.
  47. Ettoussi, R., Melliani, S., Elomari, M. & Chadli, L. S. (2015) Solution of intuitionistic fuzzy differential equations by successive approximations method, Notes on Intuitionistic Fuzzy Sets, 21(2), 51–62.
  48. Melliani, S., Elomari, M., Atraoui, M., & Chadli, L. S. (2015) Intuitionistic fuzzy differ-ential equation with nonlocal condition, Notes on Intuitionistic Fuzzy Sets, 21(4), 58–68.
  49. Mondal, S. P., & 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, 449– 474.
Citations:
  1. BISWAS, SUVANKAR, and TAPAN KUMAR ROY. "APPLICATION OF INTUITIONISTIC DIFFERENTIAL TRANSFORMATION METHOD TO SOLVE INTUITIONISTIC FUZZY VOLTERRA INTEGRO-DIFFERENTIAL EQUATION." International Journal of Mathematical Archive EISSN 2229-5046 9.1 (2018), pp. 141-149.

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