A characterization of the fuzzy fractals generated by an orbital fuzzy iterated function system

TL;DR

This paper studies fuzzy fractals generated by orbital fuzzy iterated function systems, showing they are uniquely determined by initial conditions and the action of the Picard iteration sequence.

Contribution

It introduces a structure theorem for fuzzy fractals in orbital fuzzy iterated function systems, linking them to the initial Picard iteration and orbit closures.

Findings

Fuzzy operator is weakly Picard.

Fuzzy fractals are determined by initial Picard iteration.

Fixed points are characterized as fuzzy fractals.

Abstract

Orbital fuzzy iterated function systems are obtained as a combination of the concepts of iterated fuzzy set system and orbital iterated function system. It turns out that, for such a system, the corresponding fuzzy operator is weakly Picard, its fixed points being called fuzzy fractals. In this paper we present a structure result concerning fuzzy fractals associated to an orbital fuzzy iterated function system by proving that such an object is perfectly determined by the action of the initial term of the Picard iteration sequence on the closure of the orbits of certain elements.