Title of paper:
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System of intuitionistic fuzzy differential equations with intuitionistic fuzzy initial values
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Author(s):
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Ömer Akin
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Department of Mathematics, TOBB Economics and Technology University, Sogutozu Mahallesi, Sogutozu Cd. No:43, 06510 Cankaya/Ankara, Turkey
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omerakin@etu.edu.tr
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Selami Bayeğ
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Department of Mathematics, TOBB Economics and Technology University, Sogutozu Mahallesi, Sogutozu Cd. No:43, 06510 Cankaya/Ankara, Turkey
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sbayeg@etu.edu.tr
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Published in:
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Notes on Intuitionistic Fuzzy Sets, Volume 24 (2018), Number 4, pages 141–171
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DOI:
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https://doi.org/10.7546/nifs.2018.24.4.141-171
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Download:
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PDF (3342 Kb Kb, File info)
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Abstract:
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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.
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Keywords:
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Intuitionistic fuzzy sets, Strongly generalized Hukuhara differentiability, Intuitionistic fuzzy initial value problems, Intuitionistic Zadeh's extension principle.
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AMS Classification:
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03E72.
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References:
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- Akın, Ö ., & Bayeg, S. (2017). Intuitionistic fuzzy initial value problems - an application, Hacettepe Journal of Mathematics and Statistics, Doi:10.15672/HJMS.2018.598.
- Akın, Ö., & Bayeg, S. (2017). Initial Value Problems in Intuitionistic Fuzzy Environment. Proceedings of the 5th International Fuzzy Systems Symposium, 14–15, Ankara, Turkey.
- 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.
- 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.
- Akın, Ö., & Oruc¸, Ö. (2012). A prey predator model with fuzzy initial values, Hacettepe Journal of Mathematics and Statistics, 41, 387–395.
- 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.
- 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.
- Atanassov, K. T. (1986). Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20 (1), 87–96.
- Atanassov, K. T. (1994). Operators over interval valued intuitionistic fuzzy sets, Fuzzy Sets and Systems, 64 (2), 159–174.
- Atanassov, K. T. (1995). Remarks on the intuitionistic fuzzy sets - III, Fuzzy Sets and Systems, 75 (3), 401–402.
- Atanassov, K. T. (1989). More on intuitionistic fuzzy sets. Fuzzy Sets and Systems, 33 (1), 37–45.
- Atanassov, K. T. (1988). Remark on the intuitionistic fuzzy logics, Fuzzy Sets and Systems, 95 (1), 127–129.
- Atanassov, K. T. (2000). Two theorems for intuitionistic fuzzy sets, Fuzzy Sets and Systems, 110(2), 267–269.
- Atanassov, K. T., Kacprzyk, J. & Szmidt, E. (2003). Separability of intuitionistic fuzzy sets, Fuzzy Sets and Systems, 64, 285–292.
- Atanassov, K. T., & Georgiev, C. (1993). Intuitionistic fuzzy Prolog, Fuzzy Sets and Systems, 53(2), 121–128.
- Atanassova, L. (2007). On intuitionistic fuzzy versions of L. Zadeh’s extension principle. Notes on Intuitionistic Fuzzy Sets, 13(3), 33–36.
- Barros, L. C., Bassanezi, R. C. & Tonelli, P. A. (2000). Fuzzy modelling in population dynamics, Ecological Modelling, 128(1), 27–33.
- Bede, B. (2010). Solutions of fuzzy differential equations based on generalized differentiability, Communication in Mathematical Analysis, 9, 22–41.
- 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.
- Bede, B., Rudas, I. J., & Bencsik, B. (2007). First order linear differential equations under generalized differentiability, Information Sciences, 177, 1648–1662.
- Bede, B., Stefanini, L. (2010). Generalized differentiability of fuzzy-valued functions, Fuzzy Sets and Systems, 9, 22–41.
- Buckley, J. J. & Feuring, T. (2000). Fuzzy differential equations, Fuzzy Sets and Systems, 110, 43–54.
- Casasnovas, J. & Rossell, F. (2005). Averaging fuzzy bio polymers , Fuzzy Sets and Systems, 152 (1), 139–158.
- 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.
- Diamond, P. (2000). Stability and periodicity in fuzzy differential equations, IEEE Transactions on Fuzzy Systems, 8, 583–590.
- Diamond, P. & Kloeden, P. (1994). Metric Spaces of Fuzzy Sets, World Scientific Publishing, MA.
- Dost, S., & Brown, L. M. (2005). Intuitionistic textures revisited, Hacettepe Journal of Mathematics and Statistics, 34, 115–130.
- Duman, O. (2010). Statistical fuzzy approximation to fuzzy differentiable mappings by fuzzy linear operators, Hacettepe Journal of Mathematics and Statistics, 39, 497–514.
- 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.
- Goguen, J. A. (1967). L-fuzzy sets, Journal of Mathematical Analysis and Applications, 18(1), 145–174.
- 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.
- Hullermeier, E. (1997). An approach to modelling and simulation of uncertain dynamical systems, Int. J. Uncertainty, Fuzziness and Knowledge-Based Systems, 5, 117–137.
- Kharal, A. (2009). Homeopathic drug selection using intuitionistic fuzzy sets, Homeopathy, 98 (1), 35–39.
- Lei, Q., & Xu, Z. (2015). Fundamental properties of intuitionistic fuzzy calculus, Knowledge-Based Systems, 76, 1–16.
- 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.
- 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.
- Mendel, J. M. (2007). Advances in type-2 fuzzy sets and systems, Information Sciences, 177, 84–110.
- 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.
- 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.
- Oberguggenberger, M. & Pittschmann, S. (1999). Differential equations with fuzzy parameters, Mathematical and Computer Modelling of Dynamical Systems, 5, 181–202.
- Puri, L. M., & Ralescu, D. (1983). Differentials of fuzzy functions, Journal of Mathematical Analysis and Applications, 91(2), 552–558.
- 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.
- Simon, C. P. & Blume, L. E. (2004). Mathematics for Economics, W. W. Norton Company, New York.
- Tiel, J. V. (2004). Convex Analysis: An Introductory Text, John Wiley & Sons Ltd., New York.
- 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.
- Zadeh, L. A. (1965). Fuzzy sets, Information and Control, 8(3), 338–353.
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