IJPAM: Volume 113, No. 5 (2017)
PREDICTOR CORRECTOR METHOD FOR SOLVING
FUZZY DIFFERENTIAL EQUATIONS DRIVEN
BY LIU'S PROCESS , M. Gachpazan, O. Fard
Department Of Applied Mathematics
School of Mathematical Sciences
Ferdowsi University Of Mashhad
-path to FDE is presented, which is a type of certain function that solves an associate ordinary differential equation. Then, an improved predictor corrector (IPC) method is introduced to solve FDEs, which essentially solves each -path and produces an inverse credibility distribution of the solution. Moreover, the convergence and stability of the IPC method is presented in details. We explain that our estimation has a good degree of accuracy.
Received: December 11, 2016
Revised: February 2, 2017
Published: April 1, 2017
AMS Subject Classification: Key Words and Phrases: Fuzzy Liu's process, Improved predictor corrector (IPC) method, Convergence, Stability
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- X. Chen, X. Qin, A new existence and uniqueness theorem for fuzzy differential equations. International Journal of Fuzzy Systems, 13, 2 13 148-151.
- Z. Ding, M. Ma, A. Kandel, Existence of the solutions of fuzzy differential equations with parameters. J. Information Sciences, 99, 1 (1999) 1205-1217.
- W. Dai, Lipschitz continuity of Liu process. Proceedings of the Eighth International Conference on Information and Management Science, China (2009) 756-760.
- W. Fei, Uniqueness of solutions to fuzzy differential equations driven by Lius process with non-Lipschitz coefficients, Internatinal Confrance On Fuzzy and Knowledge Discovery (2009) 565-569.
- M. Friedman, M. Ming, A. Kandel, Numerical procedures for solving fuzzy differential and integral equations, Internat Confrance Fuzzy Logic and Applications, Israel (1997) 18-21.
- J. Gao, Credibilistic Option Pricing, Journal of Uncertain Systems, 2, 4 (2008) 243-247.
- J. Hale, Theory of functional differential equations, New-York: Springer, 2, 4 (1997) 243-247.
- O. Kaleva, Fuzzy differential equation, J. Fuzzy Sets and Systems, 24, 2 (1987) 301-317.
- X. Li, B. Liu, A suffcient and necessary condition for credibility measures. International Journal of Uncertainty, Fuzziness and Knowledge BasedSystems, 14, 5 (2004) 527-535.
- B. Liu, Uncertainty Theory, Springer-Verlag, Berlin (2004).
- B. Liu, A survey of credibility theory, J. Fuzzy Optimization and Decision Making, 5, 4 2006 387-408.
- B. Liu, Uncertainty Theory, 2nd ed. Springer-Verlag, Berlin (2007).
- B. Liu, Fuzzy process, hybrid process and uncertain process, Journal of Uncertain Systems, 2, 1 (2008) 3-16.
- B. Liu, Y. Liu, Expected value of fuzzy variable and fuzzy expected value models, IEEE Transactions on Fuzzy Systems, 10, 4 (2002) 445-450.
- J. Peng, A General Stock Model for Fuzzy Markets, Journal of Uncertain Systems, 2, 4 (2008) 248-254.
- Z. Qin, X. Li, Option pricing formula for fuzzy financial market. Journal of Uncertain Systems, 2, 1 (2008) 17-21.
- Z. Qin, X. Gao, Fractional Liu process with application to finance, J. Mathematical and Computer Modeling, 50, 9 (2009) 1538-1543.
- Y. Shen, K. Yao, Runge-Kutta method for solving uncertain differential equations, Journal of Uncertainty Analysis and Applications, 2, 1 (2015) 3-17.
- X. Wanga,Y. Tauqir, A. Moughal, X. Chena, Adams-Simpson method for solving uncertain differential equation, Applied Mathematics and Computation, 271 (2015) 209-219.
- X. Yang, Dan A. Ralescu, Adams method for solving uncertain differential equations, Applied Mathematics and Computation, 270 (2015) 993-1003.
- K. Yao, X. Chen, A numerical method for solving uncertain differential equations, J. Intell. Fuzzy Syst., 25, 3 (2013) 825-832.
- C. You, Multi-dimensional Liu process, differential and integral, Proceedings of the First Intelligent Computing Conference, China (2007) 153-158.
- C. You, W. Wang, H. Huo, Existence and Uniqueness Theorems for Fuzzy Differential Equations, Journal of Uncertain Systems, 7, 4 (2013) 303-315.
- L. A. Zadeh, Fuzzy sets, J. Information and Control, 8, 1 (1965) 338-353.
- Y. Zhu, A Fuzzy option control with application to portfolio selection, Journalof Uncertain Systems, 3, 4 (2009) 270-279.
Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Pages: 627 - 641