As of August 2024, International Journal "Notes on Intuitionistic Fuzzy Sets" is being indexed in Scopus.
Please check our Instructions to Authors and send your manuscripts to nifs.journal@gmail.com. Next issue: September/October 2024.
Open Call for Papers: International Workshop on Intuitionistic Fuzzy Sets • 13 December 2024 • Banska Bystrica, Slovakia/ online (hybrid mode).
Deadline for submissions: 16 November 2024.

Issue:Numerical solution of fuzzy differential equation by Runge-Kutta method and the intuitionistic treatment

From Ifigenia, the wiki for intuitionistic fuzzy sets and generalized nets
Revision as of 18:39, 28 August 2024 by Vassia Atanassova (talk | contribs) (Text replacement - "Conference proceedings," to "")
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to navigation Jump to search
shortcut
http://ifigenia.org/wiki/issue:nifs/8/3/43-53
Title of paper: Numerical solution of fuzzy differential equation by Runge-Kutta method and the intuitionistic treatment
Author(s):
S. Abbasbandy
Department of Mathematics, Imam Khomeini International University, Qazvin, Iran
abbasbandy@yahoo.com
T. Allah Viranloo
Department of Mathematics, Science and Research Branch,

Islamic Azad University, Tehran, Iran

alahviranlo@yahoo.com
Presented at: 6th ICIFS, Varna, 13—14 Sept 2002
Published in: "Notes on Intuitionistic Fuzzy Sets", Volume 8 (2002) Number 3, pages 43—53
Download:  PDF (4451  Kb, File info)
Abstract: In this paper numerical algorithms for solving ’fuzzy ordinary differential equations’ are considered. A scheme based on the 4th Runge-Kutta method in detail is discussed and this is followed by a complete error analysis. The algorithm is illustrated by solving some linear and nonlinear fuzzy Cauchy problems. Comments on intuitionistic fuzzy differential equations are included.
Keywords: Fuzzy differential equation, 4th Runge-Kutta method, Fuzzy Cauchy problem
AMS Classification: 34A12, 65L05
References:
  1. S.L. Chang, L.A. Zadeh, On fuzzy mapping and control, IEEE Trans, Systems Man Cybernet. 2 (1972) 30-34.
  2. D.Dubois, H. Prade, Towards fuzzy differential calculus: Part 3, differentiation, Fuzzy Sets and Systems 8 (1982) 225-233.
  3. M.L Puri, D.A. Ralescu, Differentials of fuzzy functions, J. Math. Anal. Appl. 91 (1983) 321-325.
  4. R. Goetschel, W. Voxman, Elementary fuzzy calculus, Fuzzy Sets and Systems 18 (1986) 31-43.
  5. O. Kaleva, Fuzzy differential equations, Fuzzy Sets and Systems 24 (1987) 301-317.
  6. O. Kaleva, The Cauchy problem for Fuzzy differential equations, Fuzzy Sets and Systems 35 (1990) 389-396.
  7. S. Seikkala, On the fuzzy initial value problem, Fuzzy Sets and Systems 24 (1987) 319-330.
  8. R. L. Burden, J. D. Faires, Numerical Analysis, (1997)
  9. A. Ralston, P. Rabinowitz, First Course In Numerical Analysis, (1978)
  10. M. Ma, M. Friedman, A. Kandel, Numerical Solutions of fuzzy differential equations, Fuzzy Sets and Systems 105 (1999) 133-138.
  11. James J. Buckley, Thomas Feuring, Fuzzy differential equations, Fuzzy Sets and Systems 110 (2000) 43-54.
  12. K. Atanassov, Intuitionistic Fuzzy Sets, Physica-Verlag, Heidelberg, New York, (1999).
  13. K. Peeva, Intuitionistic fuzzy languages in syntactic pattern recognition, Notes on Intuitionistic Fuzzy Sets, Proceedings of the Fifth International Conference on Intuitionistic Fuzzy Sets, Sofia, 22-23 Sept. 2001, Vol. 7 (4) (2001) 77-83.
  14. K. Peeva, Resolution of composite intuitionistic fuzzy relational equations, Notes on Intuitionistic Fuzzy sets, 6(1) (2000), 15-24.
  15. K. Peeva, Min-max-fuzzy linear systems of equations, in 26th Summer School Applications of Mathematics in Engineering and Economics, B. Cheshankov, M. Todorov (Eds.), Sozopol 2000, Heron Press, 2001, 254-259.
Citations:

The list of publications, citing this article may be empty or incomplete. If you can provide relevant data, please, write on the talk page.

Retrieved from "https://ifigenia.org/index.php?title=Issue:Numerical_solution_of_fuzzy_differential_equation_by_Runge-Kutta_method_and_the_intuitionistic_treatment&oldid=13141"