Perspectives of fuzzy initial value problems

Communications in Applied Analysis

Volumn 11, Issue 3-4, 2007, Pages 339-358

  Bede, Barnabás ^a   Bhaskar, T Gnana ^b   Lakshmikantham, V ^b  

^a UNIVERSITY OF TEXAS PAN AMERICAN   (United States)

^b Florida Institute of Technology ^*  (United States)

Author keywords

Fuzzy differential equations; Modeling under uncertainty

Indexed keywords

EID: 37349131979     PISSN: 10832564     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (20)

1. J.P. Aubin, A. Cellina, Differential Inclusions, Springer-Verlag, Berlin, Heidelberg, New York, Tokyo, 1984.
2. B. Bede, S.G. Gal, Generalizations of the differentiability of fuzzy-number-valued functions with applications to fuzzy differential equations, Fuzzy Sets and Systems 151(2005), 581-599.
3. B. Bede, I.J. Rudas, A. Bencsik, First order linear differential equations under generalized differentiability, Information Sciences, to appear.
4. J.J. Buckley T. Feuring, Fuzzy differential equations, Fuzzy Sets and Systems 110(2000), 43-54.
5. J.J. Buckley, L. Jowers, Simulating Continuous Fuzzy Systems, Springer, Berlin-Heidelberg, 2006.
6. Y. Chalco-Cano, H. Román-Flores, On new solutions of fuzzy differential equations, Chaos Solitons and Fractals, to appear.
7. C. Carlsson, R. Fullér, P. Majlender, On possibilistic correlation, Fuzzy Sets and Systems 155(2005), 425-445.
8. P. Diamond, Stability and periodicity in fuzzy differential equations, IEEE Transactions on Fuzzy Systems 8(2000), 583-590.
9. T. Gnana Bhaskar, V. Lakshmikantham, V. Devi, Revisiting fuzzy differential equations, Nonlinear Analysis 58(2004), 351-358.
10. E. Hüllermeier, An approach to modelling and simulation of uncertain dynamical systems, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 5(1997), 117-137.
11. Kaleva, Fuzzy Differential Equations, Fuzzy Sets and Systems, 24, 1987, 301-317.
12. Kaleva, A note on fuzzy differential equations, Nonlinear Analysis 64(2006), 895-900.
13. G. J. Klir, The role of constrained fuzzy arithmetic in engineering, In Ayyub BM (Ed) Uncertainty Analysis in Engineering and the Sciences, Boston: Kluwer, 1997.
14. G.J. Klir, Y. Pan, Constrained fuzzy arithmetic: Basic questions and some answers, Soft Computing 2(1998), 100-108.
15. K. K. Majumdar, D. D. Majumdar, Fuzzy differential inclusions in Atmospheric and medical cybernatics, IEEE tran. Sys. Man and Cyber. Part B: Cybernetics, 34 (2), 2004, 877-887.
16. M.T. Mizukoshi, L.C. Barros, Y. Chalco-Cano, H. Román-Flores, R.C. Bassanezi, Fuzzy differential equations and the extension principle, Information Sciences 177, (2007), 3627-3635.
17. M. Navara and Z. Žabokrtský, How to make constrained fuzzy arithmetic efficient, Soft Computing 5(2001), 412-417.
18. J.J. Nieto, R. Rodríguez-López, D. Franco, Linear first-order fuzzy differential equations, International Journal of Uncertainty, Fuzziness and Knowlege-Based Systems, 14 (2006), 687-709.
19. M. Puri, D. Ralescu, Differentials of fuzzy functions, Journal of Mathematical Analysis Applications, 91(1983), 552-558.
20. L. Stefanini, L. Sorini, M. L. Guerra, Parametric representation of fuzzy numbers and application to fuzzy calculus, Fuzzy Sets and Systems, 157(2006), 2423-2455.