Construction of fuzzy valued recurrent fractal interpolation functions and their properties

TL;DR

This paper introduces fuzzy valued recurrent fractal interpolation functions for data with local self-similarity and uncertainty, demonstrating their properties like Holder continuity and stability under data perturbations.

Contribution

It presents a novel construction of fuzzy valued RFIFs using recurrent iterated function systems for interpolating uncertain, self-similar data.

Findings

The constructed fuzzy RFIFs are Holder continuous.

The interpolation functions are stable under data perturbations.

The method effectively handles data with local self-similarity and uncertainty.

Abstract

In the process of measuring objects with local self-similarity, such as satellite images or coastlines, we obtain a data set with both local self-similarity and uncertainty. To better interpolate such data sets, an interpolation function with both local self-similarity and uncertainty is necessary. In this paper, we propose a construction of fuzzy valued recurrent fractal interpolation function using recurrent iterated function system that interpolates the given data set of fuzzy numbers. And we show some properties of the constructed fuzzy valued RFIFs: Holder continuity and stability of the interpolation function due to perturbations in the data set or the vertical scaling factors.