A note on asymptotic smoothness of the extensions of Zadeh
Barros, Laécio C.
Oliveira Souza, Suzana A.
Tonelli, Pedro A.
The concept of asymptotic smooth transformation was introduced by J. Hale . 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 ).