Construction of fuzzy valued recurrent fractal interpolation functions and their properties

H. Choe, R. Mi-Gyong, Ch. Yun

Kim Il Sung University, Pyongyang, Democratic People’s Republic of Korea

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 (FZRFIF) using recurrent iterated function system (RIFS) that interpolates the given data set of fuzzy numbers. And we show some properties of the constructed FZRFIFs: Hölder continuity and stability of FZRFIFs due to perturbations in the data set or the vertical scaling factors.

Keywords: fuzzy interpolation, recurrent fractal interpolation function, recurrent iterated function system, fuzzy fractal interpolation, Hölder continuity, stability.

MSC: 03E72, 28A80, 41A05

Received: 18.02.2025
Revised: 29.10.2025
Accepted: 18.11.2025

Language: English

DOI: 10.26456/fssc129

Bibliographic databases:

•