On the notion of fuzzy shadowing property

TL;DR

This paper explores fuzzy shadowing and transitivity in fuzzy dynamical systems within fuzzy metric spaces, establishing relationships between these properties to deepen understanding of their dynamics.

Contribution

It introduces fuzzy shadowing and topological transitivity concepts for fuzzy systems and proves their interrelations, advancing the theoretical framework of fuzzy dynamical systems.

Findings

Fuzzy shadowing and transitivity are defined for fuzzy discrete systems.

Relationships between fuzzy shadowing and transitivity are established.

Theoretical properties of fuzzy dynamical systems are analyzed.

Abstract

This paper is concerned with the study of fuzzy dynamical systems. Let (X;M; *) be a fuzzy metric space in the sense of George and Veeramani. A fuzzy discrete dynamical system is given by any fuzzy continuous self-map defined on X. We introduce the various fuzzy shadowing and fuzzy topological transitivity on a fuzzy discrete dynamical systems. Some relations between this notions have been proved.