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Issue:System of intuitionistic fuzzy differential equations with intuitionistic fuzzy initial values

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Title of paper: System of intuitionistic fuzzy differential equations with intuitionistic fuzzy initial values
Author(s):
Ömer Akin
Department of Mathematics, TOBB Economics and Technology University, Sogutozu Mahallesi, Sogutozu Cd. No:43, 06510 Cankaya/Ankara, Turkey
omerakin@etu.edu.tr
Selami Bayeğ
Department of Mathematics, TOBB Economics and Technology University, Sogutozu Mahallesi, Sogutozu Cd. No:43, 06510 Cankaya/Ankara, Turkey
sbayeg@etu.edu.tr
Published in: Notes on Intuitionistic Fuzzy Sets, Volume 24 (2018), Number 4, pages 141–171
DOI: https://doi.org/10.7546/nifs.2018.24.4.141-171
Download:  PDF (3342 Kb  Kb, Info)
Abstract: In this paper, we have studied the system of differential equations with intuitionistic fuzzy initial values under the interpretation of (i,ii)-GH differentiability concepts and Zadeh's extension principle interpretation. And we have given some numerical examples.
Keywords: Intuitionistic fuzzy sets, Strongly generalized Hukuhara differentiability, Intuitionistic fuzzy initial value problems, Intuitionistic Zadeh's extension principle.
AMS Classification: 03E72.
References:
  1. Akın, Ö ., & Bayeg, S. (2017). Intuitionistic fuzzy initial value problems - an application, Hacettepe Journal of Mathematics and Statistics, Doi:10.15672/HJMS.2018.598.
  2. Akın, Ö., & Bayeg, S. (2017). Initial Value Problems in Intuitionistic Fuzzy Environment. Proceedings of the 5th International Fuzzy Systems Symposium, 14–15, Ankara, Turkey.
  3. Akın, Ö., Khaniyev, T., Öruc¸, Ö. & Turksen, I. B. (2013). An algorithm for the solution of second order fuzzy initial value problems, Expert Systems with Applications, 40 (3), 953– 957.
  4. Akın, Ö., Khaniyev, T., Bayeg˘, S. & Turksen (2016). Solving a Second Order Fuzzy Initial Value Problem Using The Heaviside mapping, Turk. J. Math. Comput. Sci., 4, 16–25.
  5. Akın, Ö., & Oruc¸, Ö. (2012). A prey predator model with fuzzy initial values, Hacettepe Journal of Mathematics and Statistics, 41, 387–395.
  6. Amrahov, S¸ . E., Khastan, A., Gasilov , N. & Fatullayev, A. G. (2016). Relationship between Bede–Gal differentiable set-valued mappings and their associated support mappings, Fuzzy Sets and Systems, 295, 57–71.
  7. Atanassov K. T. (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.
  8. Atanassov, K. T. (1986). Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20 (1), 87–96.
  9. Atanassov, K. T. (1994). Operators over interval valued intuitionistic fuzzy sets, Fuzzy Sets and Systems, 64 (2), 159–174.
  10. Atanassov, K. T. (1995). Remarks on the intuitionistic fuzzy sets - III, Fuzzy Sets and Systems, 75 (3), 401–402.
  11. Atanassov, K. T. (1989). More on intuitionistic fuzzy sets. Fuzzy Sets and Systems, 33 (1), 37–45.
  12. Atanassov, K. T. (1988). Remark on the intuitionistic fuzzy logics, Fuzzy Sets and Systems, 95 (1), 127–129.
  13. Atanassov, K. T. (2000). Two theorems for intuitionistic fuzzy sets, Fuzzy Sets and Systems, 110(2), 267–269.
  14. Atanassov, K. T., Kacprzyk, J. & Szmidt, E. (2003). Separability of intuitionistic fuzzy sets, Fuzzy Sets and Systems, 64, 285–292.
  15. Atanassov, K. T., & Georgiev, C. (1993). Intuitionistic fuzzy Prolog, Fuzzy Sets and Systems, 53(2), 121–128.
  16. Atanassova, L. (2007). On intuitionistic fuzzy versions of L. Zadeh’s extension principle. Notes on Intuitionistic Fuzzy Sets, 13(3), 33–36.
  17. Barros, L. C., Bassanezi, R. C. & Tonelli, P. A. (2000). Fuzzy modelling in population dynamics, Ecological Modelling, 128(1), 27–33.
  18. Bede, B. (2010). Solutions of fuzzy differential equations based on generalized differentiability, Communication in Mathematical Analysis, 9, 22–41.
  19. Bede, B., & Gal, S. G. (2005). Generalizations of the differentiability of fuzzy-numbervalued mappings with applications to fuzzy differential equations, Fuzzy Sets and Systems, 151(3), 581–599.
  20. Bede, B., Rudas, I. J., & Bencsik, B. (2007). First order linear differential equations under generalized differentiability, Information Sciences, 177, 1648–1662.
  21. Bede, B., Stefanini, L. (2010). Generalized differentiability of fuzzy-valued functions, Fuzzy Sets and Systems, 9, 22–41.
  22. Buckley, J. J. & Feuring, T. (2000). Fuzzy differential equations, Fuzzy Sets and Systems, 110, 43–54.
  23. Casasnovas, J. & Rossell, F. (2005). Averaging fuzzy bio polymers , Fuzzy Sets and Systems, 152 (1), 139–158.
  24. 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.
  25. Diamond, P. (2000). Stability and periodicity in fuzzy differential equations, IEEE Transactions on Fuzzy Systems, 8, 583–590.
  26. Diamond, P. & Kloeden, P. (1994). Metric Spaces of Fuzzy Sets, World Scientific Publishing, MA.
  27. Dost, S., & Brown, L. M. (2005). Intuitionistic textures revisited, Hacettepe Journal of Mathematics and Statistics, 34, 115–130.
  28. Duman, O. (2010). Statistical fuzzy approximation to fuzzy differentiable mappings by fuzzy linear operators, Hacettepe Journal of Mathematics and Statistics, 39, 497–514.
  29. Gasilov, N., Amrahov, S¸ . E. & Fatullayev, A. G. (2014). Solution of linear differential equations with fuzzy boundary values, Fuzzy Sets and Systems, 257, 169–183.
  30. Goguen, J. A. (1967). L-fuzzy sets, Journal of Mathematical Analysis and Applications, 18(1), 145–174.
  31. Gouyandeha, Z., Allahviranloo, T., Abbasbandy, S., & Atefeh, A. (2017). A fuzzy solution of heat equation under generalized Hukuhara differentiability by fuzzy Fourier transform, Fuzzy Sets and Systems, 309, 81–97.
  32. Hullermeier, E. (1997). An approach to modelling and simulation of uncertain dynamical systems, Int. J. Uncertainty, Fuzziness and Knowledge-Based Systems, 5, 117–137.
  33. Kharal, A. (2009). Homeopathic drug selection using intuitionistic fuzzy sets, Homeopathy, 98 (1), 35–39.
  34. Lei, Q., & Xu, Z. (2015). Fundamental properties of intuitionistic fuzzy calculus, Knowledge-Based Systems, 76, 1–16.
  35. Li, D. F. (2005). Multi-attribute decision making models and methods using intuitionistic fuzzy sets. Journal of Computer and System Sciences, 70(1), 73–85.
  36. Li, D. F., & Cheng, C. T. (2002). New similarity measures of intuitionistic fuzzy sets and application to pattern recognitions. Pattern Recognition Letters, 23(1–3), 221–225.
  37. Mendel, J. M. (2007). Advances in type-2 fuzzy sets and systems, Information Sciences, 177, 84–110.
  38. 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.
  39. Mondal, S. P., & Roy, T. K. (2014). First order homogeneous ordinary differential equation with initial value as triangular intuitionistic fuzzy number, Journal of Uncertainity in Mathematics Science, 1–17.
  40. Oberguggenberger, M. & Pittschmann, S. (1999). Differential equations with fuzzy parameters, Mathematical and Computer Modelling of Dynamical Systems, 5, 181–202.
  41. Puri, L. M., & Ralescu, D. (1983). Differentials of fuzzy functions, Journal of Mathematical Analysis and Applications, 91(2), 552–558.
  42. Shu, M.H., Cheng, C.H., & Chang, J. R. (2006). Using intuitionistic fuzzy sets for fault-tree analysis on printed circuit board assembly, Microelectronics Reliability, 46(12), 2139–2148.
  43. Simon, C. P. & Blume, L. E. (2004). Mathematics for Economics, W. W. Norton Company, New York.
  44. Tiel, J. V. (2004). Convex Analysis: An Introductory Text, John Wiley & Sons Ltd., New York.
  45. Ye, J. (2009). Multicriteria fuzzy decision-making method based on a novel accuracy mapping under interval valued intuitionistic fuzzy environment. Expert Systems with Applications, 36(3), 6899–6902.
  46. Zadeh, L. A. (1965). Fuzzy sets, Information and Control, 8(3), 338–353.
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