Fuzzy DES for Accurate Quantitative Amplitude Fluctuations in Biomedical Signals

Distribution of equal states (DES) has recently been proposed to quantify amplitude fluctuations. While DES features simplicity and effectiveness, it fails to accurately distinguish variations. To address this limitation, a novel fuzzy DES (fDES) is proposed, which quantifies differential states using gradient fuzzy boundaries. Triangular and exponential membership functions develop fDES, whose performance was evaluated using sleep electroencephalogram (EEG) and heartbeat signals. Results indicate that fDES of sleep EEG increases significantly with sleep depth from awake to stages I-III and rapid eye movement (REM), with awake and REM stages exhibiting greater differences. Heartbeats of aging and particularly congestive heart failure subjects have larger fDES, resolving misclassifications observed with threshold DES. Notably, fDES demonstrates a remarkable capacity in very short data segments, i.e., as few as 20 EEG points (0.08 s) and 5 heartbeats. Overall, fDES enables precise quantitative amplitude fluctuations, and this study contribute to the sleep stage classification and cardiac condition diagnosis.