A note on asymptotic smoothness of the extensions of Zadeh

• Barros, Laécio C. ^[1] ; Oliveira Souza, Suzana A. ^[2] ; Tonelli, Pedro A. ^[2]
  1. [1] Universidade Estadual de Campinas

     Universidade Estadual de Campinas

     Brasil

     
  2. [2] Universidade de São Paulo

     Universidade de São Paulo

     Brasil

     
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 21, Nº. 2, 2002, págs. 141-153
• Idioma: inglés
• DOI: 10.4067/S0716-09172002000200003
• Enlaces
  • Texto completo
• 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]).

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