Abstract: Previous study indicates that refined fuzzy entropy（rFuzzyEn） based on physical fuzzy membership function, improves significantly in terms of both stability and robustness against additive noise. Its performance in analysing cardiac electro-mechanical time series is further examined by the analysis of RR Interval（RRI） and Systolic Time Interval（STI） series in 5 minutes. Meanwhile, a refined cross fuzzy entropy（rC-FuzzyEn） is developed by substituting the physical fuzzy membership function for the ideal fuzzy membership function in cross fuzzy entropy（C-FuzzyEn） measure. It is used to analyse the coupling of RRI and STI between patients with coronary artery disease（CAD） and healthy volunteers, compared with cross sample entropy（C-SampEn） and cross fuzzy entropy（C-FuzzyEn） simutaneously. The results indicate that rC-FuzzyEn can be used to discriminate between CAD patients and healthy volunteers, it performs better than C-SampEn and C-FuzzyEn in discriminating the two groups.

Key words: physical fuzzy membership function, refined fuzzy entropy, refined cross fuzzy entropy, coupling analysis, RR interval, systolic time interval

摘要： 基于物理模糊隶属度函数的改进模糊熵（refined fuzzy entropy，rFuzzyEn）在算法的稳定性和抗噪声性能上有显著提升。通过分析5分钟心动周期（RR interval，RRI）和收缩间期（systolic time interval，STI）序列，进一步检验了rFuzzyEn用于分析心脏电-机械活动时间序列的性能。同时，将物理模糊隶属度函数引入互模糊熵（cross fuzzy entropy，C-FuzzyEn），提出改进的互模糊熵（refined C-FuzzyEn，rC-FuzzyEn）算法。使用所提出的rC-FuzzyEn算法，分析了冠心病患者和健康志愿者的RRI-STI序列耦合性，并与传统的互样本熵（cross sample entropy，C-SampEn）和互模糊熵（C-FuzzyEn）进行对比。结果表明，相较于C-SampEn和C-FuzzyEn，所提出rC-FuzzyEn算法的区分能力显著提高，可用于区分冠心病患者和健康志愿者。

关键词: 物理模糊隶属度函数, 改进模糊熵, 改进互模糊熵, 耦合性分析, 心动周期, 收缩间期