On turbulent, erratic and other dynamical properties of Zadeh’s extensions |
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| Authors: | H Román-Flores Y Chalco-Cano GN Silva Ji?í Kupka |
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| Institution: | aInstituto de Alta Investigación, Universidad de Tarapacá, Casilla 7-D, Arica, Chile;bDepartamento de Ciência da Computação e Estatística, Universidade Estadual Paulista, São José do Rio Preto-SP, Brazil;cInstitute for Research and Applications of Fuzzy Modeling, University of Ostrava, 30, dubna 22, 701 33 Ostrava, Czech Republic |
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| Abstract: | Let (X, d) be a compact metric space and f : X → X a continuous function. Consider the hyperspace (K(X),H) of all nonempty compact subsets of X endowed with the Hausdorff metric induced by d, and let (F(X),d∞) be the metric space of all nonempty compact fuzzy set on X equipped with the supremum metric d∞ which is calculated as the supremum of the Hausdorff distances of the corresponding level sets. If  is the natural extension of f to (K(X),H) and  is the Zadeh’s extension of f to (F(X),d∞), then the aim of this paper is to study the dynamics of  and  when f is turbulent (erratic, respectively). |
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