The Notion of Topological Entropy in Fuzzy Metric Spaces

Year 2012, Volume: 9 Issue: 2, - , 01.04.2012

Mehdi Karami Mohammad Reza Molaei

Abstract

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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