# Entropy and Statistical Complexity in Bioelectrical Signals: A Literature Review
## 3 Results
### Diffuse Entropy  
To describe the uncertainty caused by randomness, probability theory is the most appropriate option. In contrast, the fuzzy sets introduced by [PERSON] in 1965 describe more precisely the aspects of uncertainty related to imprecision. [PERSON] and [PERSON] (1972) built on the principle of fuzzy sets and proposed the concept of fuzzy entropy [34]. This entropy is usually known as FuzzyEn [27; 35], FuEn [32], or FEn [14]. It originates as a variant of Shannon entropy [17; 34] or Sample entropy (SampEn) [14], sharing its properties with some of these entropies [17]. Furthermore, it is useful for overcoming the limitations of SampEn [35]. FuzzyEn is a measure [34; 35] or method [17; 27] useful in time series analysis [27]. Unlike SampEn, which employs the step function [17], Heaviside [35] or Chebyshev distance [14], to perform comparisons between vectors [17] or, instead of resorting to a binary approach [17; 27] in order to evaluate the relevance of the patterns [27], FuzzyEn uses smooth, continuous, and convex functions [27], or fuzzy sets [17], or fuzzy membership functions [27; 32; 35], or exponential functions of fuzzy definition [14]. These are used to compare, estimate, or evaluate the similarity [14; 27; 32] among segments [32], patterns [27; 32], or continuous [32] data vectors of N points [14; 32] with initial and final observation sizes of m and m + 1 [14], facilitating not only the generalization of the vectors but also reducing the variations in measurements [32]. The use of fuzzy functions as an approach is effective even with small values of the tolerance parameter r [14]; additionally, they allow for more accurate probability calculations, making FuzzyEn more robust [14; 27] and precise [27], especially in the analysis of shorter and/or reduced datasets or time series [14; 27], compared to entropies like SampEn [27; 35]. [PERSON] introduced approximate entropy around 1991 [10; 14; 34]. As a mathematical tool, it was mainly introduced to quantify probability in biological data [13]. It is derived from the Kolmogorov entropy [34] and is commonly referred to as ApEn [10; 14; 29; 32; 34; 36]. It is a statistic [36], measure [10; 14; 36; 37], technique [34], or method [13] used to capture disorder [10], the randomness, and unpredictability of variations in a data set [34; 36]; to assess regularity [10; 14; 18; 34; 37] in signals, through a rapid calculation [18] in time series [34; 37]; and to evaluate the pattern correspondence of the latter [14], as well as the complexity of a system [10; 37]. Likewise, ApEn is used to quantify the conditional probability [29; 32] of the occurrence of a new state [32], or that two similar sequences in the data points, which are within a specific tolerance level [14; 29], continue to be similar when adding a consecutive point [29]. In other words, ApEn detects more identical patterns accompanying existing ones [36]. If ApEn is low, it indicates that there is more repetition of identical patterns, which suggests greater regularity. Conversely, a high ApEn indicates greater complexity and less repetition, implying higher randomness [10]. Due to the characteristics that facilitate its use, ApEn can be applied with good reproducibility in contrast to other entropy metrics [9]. In time series [9; 32], it is used to evaluate their complexity [32]. It is less affected by noise and remains finite in processes considered deterministic, noisy, composite, and stochastic. Thanks to this measure, it is possible to detect changes in underlying episodic variations that are not observed through the occurrence of peaks or amplitudes [9]. Its calculation is based on (i) a data series and (ii) the requirement of two parameters m and r. The size of the sequences to compare is defined by m, and r sets the level of tolerance that allows for similar patterns between two segments [32]. A high ApEn value indicates greater disorder, complexity, and randomness, whereas a low value denotes greater regularity in the system [10].