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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
Author(s):
Oscar Castillo
Division of Graduate Studies and Research, Tijuana Institute of Technology, Tijuana, Mexico
ocastillo@tectijuana.mx
Patricia Melin
Division of Graduate Studies and Research, Tijuana Institute of Technology, Tijuana, Mexico
pmelin@tectijuana.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
Download:  PDF (111  Kb, File info)
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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