Study about fuzzy entropy and similarity measure on intuitionistic fuzzy sets (IFSs) were proposed, and analyzed. Unlike fuzzy set, IFSs contains uncertainty named hesistancy, which is contained in fuzzy membership function itself. Hence, designing fuzzy entropy is not easy because of ununified entropy definition. By considering different fuzzy entropy definitions, fuzzy entropy is designed and...

Heart rate variability (HRV) analysis is a non-invasive tool for assessing cardiac health. Entropy measures quantify the chaotic properties of HRV, but they are sensitive to the choice of their required parameters. Previous studies therefore have performed parameter optimization, targeting solely their particular patient cohort. In contrast, this work aimed to challenge entropy measures with re...

Entropy is a measure of the uncertainty associated with a variable whose value cannot be exactly predicated. In uncertainty theory, it has been quantified so far by logarithmic entropy. However, logarithmic entropy sometimes fails to measure the uncertainty. This paper will propose another type of entropy named sine entropy as a supplement, and explore its properties. After that, the maximum en...

We consider the concept of generalized Kolmogorov–Sinai entropy, where instead of the Shannon entropy function, we consider an arbitrary concave function defined on the unit interval, vanishing in the origin. Under mild assumptions on this function, we show that this isomorphism invariant is linearly dependent on the Kolmogorov–Sinai entropy.

Heart rate variability (HRV) is the variation of the time interval between consecutive heartbeats and depends on the extrinsic regulation of the heart rate. It can be quantified using nonlinear methods such as entropy measures, which determine the irregularity of the time intervals. In this work, approximate entropy (ApEn), sample entropy (SampEn), fuzzy entropy (FuzzyEn) and fuzzy measure entr...

In this study a modified entropy-based measure is presented for evaluating the serviceability level of water distribution networks in which the hydraulic uncertainties (flow rates in pipes) as well as the uncertainties due to mechanical parameters (failure probabilities of links) are considered simultaneously. In the proposed entropy calculation method, the connectivity order of the network dem...

We introduce a novel way of measuring the entropy of a set of values undergoing changes. Such a measure becomes useful when analyzing the temporal development of an algorithm designed to numerically update a collection of values such as artificial neural network weights undergoing adjustments during learning. We measure the entropy as a function of the phase-space of the values, i.e. their magn...

We recall here the entropy-like measure {S F } proposed in [1] and we compare it to our network entropy measure S. The results presented in [1] are substantially different from our achievements and the reason lies in the conceptual foundation of the two measures. We clarify their relation thank to a simple toy model. The “entropy of information flux distribution" {S F } is a single-node entropy...

In the context of multicriteria decision making whose aggregation process is based on the Choquet integral, bi-capacities can be regarded as a natural extension of capacities when the underlying evaluation scale is bipolar. The notion of entropy, recently generalized to capacities to measure their uniformity, is now extended to bi-capacities. We show that the resulting entropy measure has a ver...

Here H(X) measures the average uncertainty associated with the random variable X. If X is the lifetime of a system and if the system has survived up to time t, then to measure the uncertainty about the remaining lifetime of such a system the measure (1) is not appropriate. Ebrahimi (1996) proposed a measure which measures the uncertainty about the remaining lifetime of a system if it is working...