Journal of Applied Mathematics

About Projections of Solutions for Fuzzy Differential Equations

Moiseis S. Cecconello, Jefferson Leite, Rodney C. Bassanezi, and Joao de Deus M. Silva

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In this paper we propose the concept of fuzzy projections on subspaces of n, obtained from Zadeh's extension of canonical projections in n, and we study some of the main properties of such projections. Furthermore, we will review some properties of fuzzy projection solution of fuzzy differential equations. As we will see, the concept of fuzzy projection can be interesting for the graphical representation of fuzzy solutions.

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J. Appl. Math., Volume 2013 (2013), Article ID 184950, 9 pages.

First available in Project Euclid: 14 March 2014

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Cecconello, Moiseis S.; Leite, Jefferson; Bassanezi, Rodney C.; Silva, Joao de Deus M. About Projections of Solutions for Fuzzy Differential Equations. J. Appl. Math. 2013 (2013), Article ID 184950, 9 pages. doi:10.1155/2013/184950.

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  • P. Diamond and P. Kloeden, Metric Spaces of Fuzzy Sets: Theory and Applications, World Scientific, Singapore, 1994.
  • M. T. Mizukoshi, L. C. Barros, Y. Chalco-Cano, H. Román-Flores, and R. C. Bassanezi, “Fuzzy differential equations and the extension principle,” Information Sciences, vol. 177, no. 17, pp. 3627–3635, 2007.
  • M. S. Cecconello, Sistemas dinamicos em espaços metricos fuzzy–-aplicacoes em biomatematica [Ph.D. thesis], IMECC; UNICAMP, 2010.
  • C. D. Aliprantis and K. C. Border, Infinite Dimensional Analysis, Springer, New York, NY, USA, 3rd edition, 2005.
  • L. C. Barros, R. C. Bassanezi, and P. A. Tonelli, “On the continuity of the Zadeh's extension,” in Proceedings of the 7th IFSA World Congress, vol. 2, Praga, 1997.
  • M. Oberguggenberger and S. Pittschmann, “Differential equations with fuzzy parameters,” Mathematical and Computer Modelling of Dynamical Systems, vol. 5, no. 3, pp. 181–202, 1999.
  • M. T. Mizukoshi, Estabilidade de sistemas dinamicos fuzzy [Ph.D. thesis], IMECC; UNICAMP, 2004.
  • J. J. Buckley and T. Feuring, “Fuzzy differential equations,” Fuzzy Sets and Systems, vol. 110, no. 1, pp. 43–54, 2000.