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Article | Open Access

A Study on Hutchinson-Barnsley Theory in Product Intuitionistic Fuzzy Fractal Space

Mathavan Priya1( ), Ramasamy Uthayakumar1
Department of Mathematics, the Gandhigram Rural Institute, Dindigul 624302, India
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Abstract

This work constitutes classical Hutchinson-Barnsley theory on the product intuitionistic fuzzy fractal space with the aid of iterated function system, in which a finite number of intuitionistic fuzzy B-contractions and intuitionistic fuzzy Edelstein contractions are enclosed. A fixed point theorem is exhibited by proving that the Hutchinson-Barnsley operator is an intuitionistic fuzzy B-contraction and intuitionistic fuzzy Edelstein contraction. To show the primary goal of the article, the Hausdorff product intuitionistic fuzzy metric space is constructed, then the notion of product intuitionistic fuzzy metric space on complete and compact spaces in the sense of intuitionistic fuzzy B-contraction and the intuitionistic fuzzy Edelstein contraction are defined.

Keywords

product intuitionistic fuzzy metric spacefuzzy B-contractionfuzzy Edelstein contractionHutchinson-Barnsley operatorproduct intuitionistic fuzzy fractal

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Fuzzy Information and Engineering
Volume 15 Issue 3,
September 2023
Pages 233-247
DOI: 10.26599/FIE.2023.9270018
Cite this article:
Priya M, Uthayakumar R. A Study on Hutchinson-Barnsley Theory in Product Intuitionistic Fuzzy Fractal Space. Fuzzy Information and Engineering, 2023, 15(3): 233-247. https://doi.org/10.26599/FIE.2023.9270018

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Received: 19 January 2023
Revised: 13 July 2023
Accepted: 06 August 2023
Published: 01 September 2023
© The Author(s) 2023. Published by Tsinghua University Press.

This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
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