Quantifying randomness and complexity of a signal via maximum fuzzy membership difference entropy

Traditional entropies are powerful tools for dynamic analysis. However, they can merely measure one aspect of the nonlinear characteristics of a signal, such as irregularity, complexity and etc. To characterize randomness and complexity of a signal, a dual-index algorithm named maximum fuzzy membership difference entropy (MFMDE) was proposed. The proposal was evaluated using synthetic and real-world signals. Experimental results indicate that MFMDE can quantify both randomness and complexity of simulation signals. Randomness and complexity can be revealed via MFMDE with low and high embedded dimensions. Meanwhile, MFMDE shows comparable performance in differentiating focal and non-focal electroencephalography (EEG) signals, and it also outperforms Fuzzy entropy (FE) in characterizing normal, interictal and ictal EEGs as well as rolling bearing fault and normal signals, with almost half computation time of FE. Besides, comparison of MFMDE against other nonlinear analysis methods manifests the proposal possesses higher distinguish degree than other approaches for different datasets.