On Product Neutrosophic Fractal Spaces and α-Density Theory with Arbitrarily Small and Controlled Error

Abstract

In this manuscript, we present the classical Hutchinson–Barnsley theory on the product neutrosophic fractal spaces by utilizing an iterated function system, which is enclosed by neutrosophic Edelstein contractions and a finite number of neutrosophic b-contractions. Further, we provide a sequence of sets that, under appropriate conditions and in terms of the Hausdorff neutrosophic metric, converge to the attractor set of specific neutrosophic iterated function systems. Furthermore, we present a fuzzy variant of α-dense curves that can accurately approximate the attractor set of certain iterated function systems with barely noticeable and controlled errors. In the end, we make a connection between the above-discussed concepts of neutrosophic theory and α-density theory.

Keywords

• product neutrosophic metric space
• neutrosophic iterated function systems
• neutrosophic fractals
• fuzzy Edelstein contraction
• fuzzy α-dense curves