A note on asymptotic smoothness of the extensions of Zadeh


  • Laécio C. Barros Universidade Estadual de Campinas.
  • Suzana A. Oliveira Souza Universidade de Sao Paulo.
  • Pedro A. Tonelli Universidade de Sao Paulo.




Fuzzy dynamical systems, global attractors, sistemas dinámicos difusos, atractores globales.


The concept of asymptotic smooth transformation was introduced by J. Hale [10]. It is a very important property for a transformation between complete metric spaces to have a global attractor. This property has also consequences on asymptotic stability of attractors. In our work we study the conditions under which the Zadeh’s extension of a continuous map f : R??R? is asymptotically smooth in the complete metric space F(R?) of normal fuzzy sets with the induced Hausdorff metric d?(see Kloeden and Diamond [8]).

Author Biographies

Laécio C. Barros, Universidade Estadual de Campinas.

Departamento de Matemática Aplicada.

Suzana A. Oliveira Souza, Universidade de Sao Paulo.

Departamento de Matemática Aplicada.

Pedro A. Tonelli, Universidade de Sao Paulo.

Departamento de Matemática Aplicada.


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How to Cite

L. C. Barros, S. A. Oliveira Souza, and P. A. Tonelli, “A note on asymptotic smoothness of the extensions of Zadeh”, Proyecciones (Antofagasta, On line), vol. 21, no. 2, pp. 141-153, May 2017.




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