8-9 October 2020 • Burgas, Bulgaria

Submission: 15 May 2020 • Notification: 31 May 2020 • Final Version: 15 June 2020

Issue:A new fractal dimension definition based on intuitionistic fuzzy logic

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Title of paper: A new fractal dimension definition based on intuitionistic fuzzy logic
Oscar Castillo
Division of Graduate Studies and Research, Tijuana Institute of Technology, Tijuana, Mexico
ocastilloAt sign.pngtectijuana.mx
Patricia Melin
Division of Graduate Studies and Research, Tijuana Institute of Technology, Tijuana, Mexico
pmelinAt sign.pngtectijuana.mx
Published in: Notes on Intuitionistic Fuzzy Sets, Volume 25 (2019), Number 2, pages 53–59
DOI: https://doi.org/10.7546/nifs.2019.25.2.53-59
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Abstract: In this paper we describe a method for the estimation of the fractal dimension of a geometrical object using Intuitionistic fuzzy logic techniques. The mathematical concept of

fractal dimension serves to measure the geometrical complexity of an object. The algorithms for estimating the fractal dimension compute a numerical value using as input the time series data for a particular problem. The result is a crisp value (number) that defines the complexity of the geometrical object or the time series. The estimation of the fractal dimension exhibits some inherent uncertainty due to the fact that we only use a sample of points of the object, as well as due to the incomplete accuracy of the numerical algorithms for fractal dimension. For this reason, a new definition of the fractal dimension is being proposed, incorporating the concept of intuitionistic fuzzy sets, which we consider to better capture the uncertainty of the concept.

Keywords: Fractal dimension, Geometrical complexity, Fuzzy sets, Intuitionistic fuzzy sets.
AMS Classification: 03E72, 28A80, 91Gxx.
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