The Notion of Topological Entropy in Fuzzy Metric Spaces

The aim of this paper is to extend the notion of topological entropy for fuzzy semidynamical systems created by a self-map on a fuzzy metric space. We show that if a metric space has two uniformly equivalent metrics, then fuzzy entropy is a constant up to these two metrics. We present a method to construct chaotic fuzzy semidynamical systems with arbitrary large fuzzy entropy. We also prove that fuzzy entropy is a persistent object under a fuzzy uniformly topological equivalent relation.

Keywords:

Fuzzy entropy, fuzzy metric space semicompact, fuzzy semicompact,

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