Calculation of Approximate Entropy, Improved Sample Entropy, and Optimized Fuzzy Entropy

In this article, we introduce three distinct entropy computation methods: approximate entropy, improved sample entropy, and optimized fuzzy entropy. These techniques are implemented using MATLAB-coded programs designed to serve as effective complexity indicators for evaluating algorithmic complexity and performance. Specifically, approximate entropy calculation leverages the self-similarity of input data through pattern recurrence analysis, where the algorithm compares sequences of data points to measure regularity. The improved sample entropy method extends traditional sample entropy with enhanced tolerance to noise and non-stationary data, utilizing vector matching techniques to reduce bias in short datasets. Lastly, the optimized fuzzy entropy approach incorporates fuzzy set theory to handle uncertain or imprecise data, employing membership functions and similarity measures to compute entropy for fuzzy data systems. By integrating these entropy computation methods, researchers can accurately quantify algorithmic complexity and performance, providing critical insights for algorithm optimization and refinement. The MATLAB implementations include key functions for template matching, distance thresholding, and fuzzy membership calculations, ensuring reproducibility and adaptability across diverse data types.