| Title of paper:
|
Differential equation with intuitionistic fuzzy parameters
|
| Author(s):
|
| R. Ettoussi
|
| Laboratoire de Mathématiques Appliquées & Calcul Scientifique, Sultan Moulay Slimane University, BP 523, 23000 Beni Mellal, Morocco
|
|
|
| Said Melliani
|
| Laboratoire de Mathématiques Appliquées & Calcul Scientifique, Sultan Moulay Slimane University, BP 523, 23000 Beni Mellal, Morocco
|
| said.melliani@gmail.com
|
| L. S. Chadli
|
| Laboratoire de Mathématiques Appliquées & Calcul Scientifique, Sultan Moulay Slimane University, BP 523, 23000 Beni Mellal, Morocco
|
|
|
|
| Published in:
|
"Notes on IFS", Volume 23, 2017, Number 4, pages 46—61
|
| Download:
|
 PDF (157 Kb Kb, File info)
|
| Abstract:
|
In this paper, we study differentiability and integrability properties of intuitionistic fuzzy-set-valued mappings and we discuss the existence and uniqueness of solution for differential equations with intuitionistic fuzzy data using the theorem of fixed point in the complete metric space. Then by method of α-cuts we explicit the solution in an example.
|
| Keywords:
|
Differentiability, Integrability, Intuitionistic fuzzy differential equations, Intuitionistic fuzzy solution.
|
| AMS Classification:
|
03E72.
|
| References:
|
- Atanassov, K. (1986) Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20, 87–96.
- Atanassov, K. (1999) Intuitionistic fuzzy sets, Springer Physica-Verlag, Berlin.
- Atanassov, K. (2003) Intuitionistic fuzzy sets: past, present and future, 3rd Conference of the European Society for Fuzzy Logic and Technology, Zittau, Germany, 10–12 September 2003, 12–19.
- Aumann, R. J. (1965) Integrals of set-valued functions, J. Math. Anal. Appl., 12, 1–12.
- Debreu, G. (1967) Integration of correspondences, Proc. Fifth Berkeley Syrup. Math. Statist. Probab., Part 1, Univ. California Press, Berkeley, CA, 2, 351–372.
- Castaing, C., & Valadier, M. (1977) Convex Analysis and Measurable Multifunctions, Springer, Berlin.
- 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.
- Kaleva, O. (1987) Fuzzy differential equations, Fuzzy Sets and Systems, 24, 301–317.
- Kaleva, O. (1990) The Cauchy problem for fuzzy differential equations, Fuzzy Sets and Systems, 35, 389–396.
- Lakshmikantham, V., & Mohapatra. R. N. (2003) Theory of fuzzy differential equations and enclusions, Taylor and Francis, New York.
- Melliani, S., Elomari, M., Chadli, L. S., & Ettoussi R. (2015) Intuitionistic fuzzy metric space, Notes on Intuitionistic Fuzzy Sets, 21(1), 43–53.
- Melliani, S., Elomari, M., Chadli, L. S., & Ettoussi, R. (2015) Extension of Hukuhara difference in intuitionistic fuzzy theory, Notes on Intuitionistic Fuzzy Sets, 21(4), 34–47.
- Seikkala, S. (1987) On the fuzzy initial value problem, Fuzzy Sets and Systems, 24, 319–330.
- Zadeh L. A. (1965) Fuzzy sets, Information and Control, 8, 338–353.
|
| 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.
|
|
