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In this paper, we study the connections between generalized mean operators and entropies, where the mean value operators are related to the strictly monotone logical operators of fuzzy theory. Here, we propose a new entropy measure based on the family of generalized Dombi operators. Namely, this measure is obtained by using the Dombi operator as a generator function in the general solution of the bisymmetric functional equation. We show how the proposed entropy can be used in a fuzzy system where the performance is consistent in choosing the best alternative in the Multiple Attribute Decision-Making Problem. This newly defined entropy was also applied to the problem of extracting useful information from time-frequency representations of noisy, nonstationary, and multicomponent signals. The denoising results were compared to Shannon and Rényi entropies. The proposed entropy measure is shown to significantly outperform the competing ones in terms of denoising classification accuracy and the F1-score due to its sensitivity to small changes in the probability distribution. [ABSTRACT FROM AUTHOR]

This paper proposes an automatic method for extraction of useful information content from time-frequency distributions of nonstationary signals heavily corrupted by additive noise. The proposed method, which does not require prior knowledge of the signal, initially performs a one-dimensional clustering of the time-frequency distribution aimed at segmenting it into a fixed number of classes. This procedure points out basic structural differences of noise and signal components (i.e., useful information) in the time-frequency plane. In fact, noise presents a flat spectrum with large time-frequency supports, while signal components are narrow energy ridges. The time-frequency supports are estimated for each of the obtained classes and used as input for an algorithm aimed at discriminating “noise” affine classes, containing mainly non-zero coefficients located outside the components time-frequency supports, from “useful information” affine classes, containing mainly coefficients inside time-frequency supports of the signal components. Simulations show the superiority of the proposed algorithm, mainly in terms of error rate reduction of classified time-frequency coefficients, compared to hard amplitude thresholding methods, as well as to a recently proposed method for information content extraction based on adaptive thresholding, which is also outperformed in terms of computational complexity and execution time (by up to 43 and 28 times, respectively). [ABSTRACT FROM AUTHOR]

This study proposes an adaptive method for components instantaneous frequency (IF) estimation of noisy non‐stationary multicomponent signals, combined with the components time‐support estimation method based on the short‐time Rényi entropy (STRE). Components localisation and separation are done using a double‐direction component tracking and extraction method presented here, while the IF estimation is done using the adaptive algorithms based on the intersection of confidence intervals (ICI) rule and the relative intersection of confidence intervals (RICI) rule. The results obtained using the ICI and RICI rules are compared for various window types, signal‐to‐noise ratios and time–frequency distributions, both with and without using the information on components time support. Most of the errors in IF estimation using the ICI and RICI‐based methods are caused by imprecise components time‐support estimation. The proposed methods combined with the STRE have achieved a significant accuracy improvement in terms of the mean absolute error and the mean squared error, reducing them by up to 73 and 93%, respectively. The method has been applied to real‐life signals and proven to be an efficient tool for IF estimation of noisy non‐stationary multicomponent signals. [ABSTRACT FROM AUTHOR]