Abstract
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), including triangular, trapezoidal, Z-shaped, bell-shaped, Gaussian, constant-Gaussian, and exponential functions have been employed in FuzEn. However, these FuzEn-based metrics have not been systematically compared yet. Since the threshold value r used in FuzEn is not directly comparable across different MFs, we here propose to apply a defuzzification approach using a surrogate parameter called 'center of gravity' to re-enable a fair and direct comparison. To evaluate these MFs, we analyze several synthetic and three clinical datasets. FuzEn using the triangular, trapezoidal, and Z-shaped MFs may lead to undefined entropy values for short signals, thus providing a very limited advantage over SampEn. When dealing with an equal value of the center 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 four 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 four 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. The MATLAB codes for the FuzEn with different MFs are available at https://github.com/HamedAzami/FuzzyEntropy_Matlab.
Highlights
Entropy is a powerful and popular nonlinear metric used to assess the dynamical characteristics of time series [1]
The results showed that Fuzzy entropy (FuzEn) and support vector machine give the best results for gender classification – an accuracy of 0.995 and an area under the curve (AUC) of 0.995
The results showed that the new measure applied to clinical diastolic period variability (DPV) outperforms sample entropy (SampEn) and FuzEn in distinguishing the patient group and the healthy group [52]
Summary
Entropy is a powerful and popular nonlinear metric used to assess the dynamical characteristics of time series [1]. Mu et al used four types of entropy measures to obtain EEG signal features for person recognition They revealed that FuzEn achieves the best performance for this task and outperforms the other state-of-the-art methods [35]. Hu and Wang evaluated sample, fuzzy, approximate, and spectral entropy, to process EEG signals on which noise was added Ability to compute FuzEn with m = 1, consideration of the local and global characteristics of embedded vectors, and computational time for FuzEn(Glb), FuzEn(Loc), and FuzMEn in comparison with the popular SampEn. The fuzzy measure entropy (a variant of the FuzEn that uses the fuzzy local and fuzzy global measure entropy) was used to analyze heart rate variability (HRV) signals recorded from healthy subjects and patients suffering from heart failure [30]. How to choose the parameters of these approaches is described
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
