Chen Weiting, Wang Zhizhong, Xie Hongbo, Yu Wangxin
Department of Biomedical Engineering, Shanghai Jiaotong University, Shanghai 200240, China.
IEEE Trans Neural Syst Rehabil Eng. 2007 Jun;15(2):266-72. doi: 10.1109/TNSRE.2007.897025.
Fuzzy entropy (FuzzyEn), a new measure of time series regularity, was proposed and applied to the characterization of surface electromyography (EMG) signals. Similar to the two existing related measures ApEn and SampEn, FuzzyEn is the negative natural logarithm of the conditional probability that two vectors similar for m points remain similar for the next m + 1 points. Importing the concept of fuzzy sets, vectors' similarity is fuzzily defined in FuzzyEn on the basis of exponential function and their shapes. Besides possessing the good properties of SampEn superior to ApEn, FuzzyEn also succeeds in giving the entropy definition in the case of small parameters. Its performance on characterizing surface EMG signals, as well as independent, identically distributed (i.i.d.) random numbers and periodical sinusoidal signals, shows that FuzzyEn can more efficiently measure the regularity of time series. The method introduced here can also be applied to other noisy physiological signals with relatively short datasets.
模糊熵（FuzzyEn）是一种新的时间序列规律性度量方法，已被提出并应用于表面肌电图（EMG）信号的特征描述。与现有的两种相关度量方法近似熵（ApEn）和样本熵（SampEn）类似，模糊熵是指两个在m个点上相似的向量在下一个m + 1个点上仍保持相似的条件概率的负自然对数。引入模糊集的概念后，基于指数函数及其形状在模糊熵中对向量的相似性进行了模糊定义。除了具有优于近似熵的样本熵的良好特性外，模糊熵还成功地在小参数情况下给出了熵的定义。其在表征表面肌电图信号以及独立同分布（i.i.d.）随机数和周期性正弦信号方面的性能表明，模糊熵能够更有效地测量时间序列的规律性。这里介绍的方法也可应用于数据集相对较短的其他有噪声的生理信号。
