Construction and properties of fuzzy-valued fractal interpolation function by using iterated function system

TL;DR

This paper develops fuzzy-valued fractal interpolation functions using iterated function systems to model phenomena with irregularity and uncertainty, and analyzes their continuity properties.

Contribution

It introduces a method to construct fuzzy-valued fractal interpolation functions via IFS and studies their Holder continuity, advancing fuzzy and fractal interpolation techniques.

Findings

Constructed fuzzy-valued fractal interpolation functions from data sets.

Established the relationship between fuzzy fractal functions and level set fractal functions.

Proved the Holder continuity of the constructed fuzzy fractal interpolation functions.

Abstract

In nature, there are many phenomena with both irregularity and uncertainty. Therefore, a fuzzy-valued fractal interpolation is more useful for modeling them than fuzzy interpolation or fractal interpolation. We construct fractal interpolation functions that interpolate a given data set of fuzzy numbers using an iterated function system and study the Holder continuity of the constructed function. Firstly, we construct an iterated function system (IFS) using the given data set and construct a fuzzy-valued fractal interpolation function whose graph is the attractor of the constructed IFS. Next, we find the relationship between the fuzzy-valued fractal interpolation function and the fractal interpolation function of the level set of the data set. Finally, we prove the Holder continuity of the fuzzy-valued fractal interpolation function.