A note on asymptotic smoothness of the extensions of Zadeh
Author
Barros, Laécio C.
Oliveira Souza, Suzana A.
Tonelli, Pedro A.
Full text
https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/158110.4067/S0716-09172002000200003
Abstract
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]).