Fuzzy dispersion entropy-based Lempel-Ziv complexity and its multiscale version for measuring the complexity of time series

Lempel-Ziv complexity (LZC) has important significance in nonlinear science as a measure of time series complexity. The previously proposed dispersion entropy-based Lempel-Ziv complexity (DELZC) effectively improves the performance of traditional LZC, but it still has problems such as information loss and inaccurate complexity characterization. To overcome these limitations, fuzzy dispersion entropy-based Lempel-Ziv complexity (FDELZC) is proposed, which utilizes fuzzy function to obtain accurate pattern partitioning and the accurate pattern information makes the symbol information more accurate, the result is a more accurate complexity characterization for signals. Furthermore, FDELZC is extended to multiscale fuzzy dispersion entropybased Lempel-Ziv complexity (MFDELZC), which characterizes the sequence complexity information from different scales. Three sets of simulation signal experiments show that FDELZC can effectively captures dynamic time series changes, and has good anti-interference and differentiation ability. Two sets of real-world signal experiments demonstrate the significant advantage of FDELZC over LZC, PLZC, DLZC, and DELZC in distinguishing real-world hydroacoustic signals.