A note on asymptotic smoothness of the extensions of Zadeh

Laécio C. Barros, Suzana A. Oliveira Souza, Pedro A. Tonelli


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 : Rⁿ→Rⁿ is asymptotically smooth in the complete metric space F(Rⁿ) of normal fuzzy sets with the induced Hausdorff metric d(see Kloeden and Diamond [8]).

Palabras clave

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


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DOI: http://dx.doi.org/10.4067/S0716-09172002000200003

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