Abstract
Multifractal analysis is the well developed theory in the non-linear analysis of chaotic signals. Quantification of chaotic nature and complexity of the waveforms requires estimation of the Generalized Fractal Dimensions (GFD) spectrum where the complexity means higher variability in general fractal dimension spectrum. The focal theme of this paper is to develop a fuzzy multifractal theory to define the Fuzzy Generalized Fractal Dimensions (F-GFD) by introducing fuzzy membership function in classical Generalized Fractal Dimensions method. It was shown that, the designed Fuzzy GFD method accurately classifies the complexity of the chaotic waveforms such as Weierstrass functions by comparing graphically with the classical GFD method. Hence the fuzzy multifractal analysis performs significantly than the classical multifractal analysis and also the proposed Fuzzy GFD is a generalized method of the classical GFD.
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Acknowledgements
The research work has been supported by University Grants Commission (UGC – MRP and SAP), Government of India, New Delhi, India.
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Uthayakumar, R., Easwaramoorthy, D. (2014). Fuzzy Generalized Fractal Dimensions for Chaotic Waveforms. In: Banerjee, S., Erçetin, Ş. (eds) Chaos, Complexity and Leadership 2012. Springer Proceedings in Complexity. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-7362-2_48
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DOI: https://doi.org/10.1007/978-94-007-7362-2_48
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