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Open AccessArticle

Centered and Averaged Fuzzy Entropy to Improve Fuzzy Entropy Precision

Groupe ESEO, 49000 Angers, France
Laboratoire Angevin de Recherche en Ingénierie des Systèmes (LARIS), Univ Angers, 49000 Angers, France
Author to whom correspondence should be addressed.
Entropy 2018, 20(4), 287;
Received: 16 March 2018 / Revised: 13 April 2018 / Accepted: 13 April 2018 / Published: 15 April 2018
PDF [460 KB, uploaded 3 May 2018]


Several entropy measures are now widely used to analyze real-world time series. Among them, we can cite approximate entropy, sample entropy and fuzzy entropy (FuzzyEn), the latter one being probably the most efficient among the three. However, FuzzyEn precision depends on the number of samples in the data under study. The longer the signal, the better it is. Nevertheless, long signals are often difficult to obtain in real applications. This is why we herein propose a new FuzzyEn that presents better precision than the standard FuzzyEn. This is performed by increasing the number of samples used in the computation of the entropy measure, without changing the length of the time series. Thus, for the comparisons of the patterns, the mean value is no longer a constraint. Moreover, translated patterns are not the only ones considered: reflected, inversed, and glide-reflected patterns are also taken into account. The new measure (so-called centered and averaged FuzzyEn) is applied to synthetic and biomedical signals. The results show that the centered and averaged FuzzyEn leads to more precise results than the standard FuzzyEn: the relative percentile range is reduced compared to the standard sample entropy and fuzzy entropy measures. The centered and averaged FuzzyEn could now be used in other applications to compare its performances to those of other already-existing entropy measures. View Full-Text
Keywords: entropy; fuzzy entropy; sample entropy; irregularity; fetal heart rate; time series; symmetrical m-patterns entropy; fuzzy entropy; sample entropy; irregularity; fetal heart rate; time series; symmetrical m-patterns

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Girault, J.-M.; Humeau-Heurtier, A. Centered and Averaged Fuzzy Entropy to Improve Fuzzy Entropy Precision. Entropy 2018, 20, 287.

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