On turbulent, erratic and other dynamical properties of Zadeh’s extensions

H. Román-Flores, Y. Chalco-Cano, G.N. Silva and Jiří Kupka

Chaos, Solitons & Fractals, 2011, vol. 44, issue 11, 990-994

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 fˆ 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 fˆ when f is turbulent (erratic, respectively).

Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:44:y:2011:i:11:p:990-994

DOI: 10.1016/j.chaos.2011.08.004

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