Fuzzy Entropy Metrics for the Analysis of Biomedical Signals: Assessment and Comparison

Hamed Azami, Peng Li, Steven E. Arnold, Javier Escudero, Anne Humeau-Heurtier

Research output: Contribution to journalArticlepeer-review


Fuzzy entropy (FuzEn) was introduced to alleviate limitations associated with sample entropy (SampEn) in the analysis of physiological signals. Over the past decade, FuzEn-based methods have been widely used in various real-world biomedical applications. Several fuzzy membership functions (MFs) have been employed in FuzEn. However, these FuzEn-based metrics have not been systematically compared yet. There is another issue in using different MFs but has been overlooked in existing works - the importance of their parameters - specifically as the threshold value r is not directly comparable across different MFs including triangular, trapezoidal, Z-shaped, bell-shaped, Gaussian, constant-Gaussian, and exponential functions. To evaluate these MFs, we analyze several synthetic and three clinical datasets.We here proposed to apply a defuzzification approach using a surrogate parameter called ‘center of gravity’ to re-enable such a fair and direct comparison. FuzEn using the triangular, trapezoidal, and Z-shaped MFs may lead to undefined entropy values for short signals, thus providing very limited advantage over SampEn. When dealing with an equal value of centre of gravity, the Gaussian MF, as the fastest algorithm, results in the highest Hedges’ g effect size for long signals. Our results also indicate that the FuzEn based on exponential MF of order 4 better distinguishes short white, pink, and brown noises, and yields more significant differences for the short real signals based on Hedges’ g effect size. The triangular, trapezoidal, and Z-shaped MFs are not recommended for short signals. We propose to use FuzEn with Gaussian and exponential MF of order 4 for characterization of short (around 50-400 sample points) and long data (longer than 500 sample points), respectively. We expect FuzEn with Gaussian and exponential MF as well as the concept of defuzzification to play prominent roles in the irregularity analysis of biomedical signals.
Original languageEnglish
Pages (from-to)104833-104847
JournalIEEE Access
Issue number1
Early online date23 Jul 2019
Publication statusPublished - Dec 2019


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