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A New Class of Fractional Cumulative Residual Entropy - Some Theoretical Results

Benmahmoud Slimane

Journal of Telecommunications and Information Technology

2023

nr 1

25--29

In this paper, by differentiating the entropy’s generating function (i.e., h(t) = R SX̄F tX (x)dx) using a Caputo fractional-order derivative, we derive a generalized non-logarithmic fractional cumulative residual entropy (FCRE). When the order of differentiation α → 1, the ordinary Rao CRE is recovered, which corresponds to the results from first-order ordinary differentiation. Some properties and examples of the proposed FCRE are also presented.

Wavelet-based Entropy Measure for Rate-Distortion Optimization in Image Coding

Garcia-Alvarez J., Führ H., Castellanos-Dominguez G.

International Journal of Electronics and Telecommunications

2010

Vol. 56, No. 1

25-31

A novel method for calculation of the entropy measure in wavelet space is proposed. This perceived-based entropy measure uses a Second Order Model entropy estimator, in which the occurrence of neighbors is considered in formulation. It has the intention to allow the implementation of a more suitable measure in coding processes and a relationship between the metric and the description of perceptual features. This method is used for the Rate-Distortion optimization in order to improve the bit-allocation coding algorithm, demonstrating that the wavelet-based entropy estimates a truncation step close to the target rate. The hypothesis is founded in the effect of distortion on the coefficient allocation. Because entropy measure is a close approximation of the conditional probability of image in multiresolution space, it provides an adequate representation for the information of a Detail feature. A definition of Detail-based homogeneity variance criteria is used for the information quantity - wavelet representation space, in order to find the image that fits a given Quality Level criteria. Experimental results are obtained for artificial and natural databases.

Fuzzy certainty on fuzzy values

Gonzales A., Marin N., Pons O., Vila M. A.

Control and Cybernetics

2009

Vol. 38, no 2

311-339

Imprecision and uncertainty appear together in many applications of soft computing. Imprecise and uncertain values are usually expressed by means of linguistic terms, specially when they have been provided by or for a human being. However, in many applications it is desirable that both aspects are combined into a single value that appropriately describes the intended information. In this work, we extend our previous research on this topic and we study how to combine imprecision and uncertainty when both of them are expressed by fuzzy numbers and the final goal is to obtain a normalized fuzzy value that provides the same amount of information about the described fact.