Using Fuzzy Measure Entropy to improve the stability of traditional entropy measures

Traditional entropy measures, such as Approximate Entropy (ApEn) and Sample Entropy (SampEn), are widely used for analyzing heart rate variability (HRV) signals in clinical cardiovascular disease studies. Nevertheless, traditional entropy measures have a poor statistical stability due to the 0-1 judgment of Heaviside function. The objective of this study is to introduce a new entropy measure - Fuzzy Measure Entropy (FuzzyMEn) in order to improve the stability of traditional entropy measures through introducing the concept of fuzzy sets theory. By drawing on Chen et al's research in fuzzy entropy (FuzzyEn), FuzzyMEn uses the membership degree of fuzzy function instead of the 0-1 judgment of Heaviside function as used in the ApEn and SampEn. Simultaneity, FuzzyMEn utilizes the fuzzy local and fuzzy global measure entropy to reflect the whole complexity implied in physiological signals and improves the limitation of FuzzyEn, which only focus on the local complexity. Detailed contrastive analysis and discussion of ApEn, SampEn, FuzzyEn and FuzzyMEn were also given in this study.