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 f ¯ is the natural extension of f to ( K ( X ) , H ) and f ˆ is the Zadeh’s extension of f to ( F ( X ) , d ∞ ) , then the aim of this paper is to study the dynamics of f ¯ and f ˆ when f is turbulent (erratic, respectively).
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