A note on asymptotic smoothness of the extensions of Zadeh

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

Resumen


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.

Referencias


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

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