The definition of weighted entropy allows for easy calculation of the entropy of the mixture of measures. In this paper we investigate the problem of equivalent definition of the general entropy function in weighted form. We show that under reasonable condition, which is satisfied by the well-known Shannon, Rényi and Tsallis entropies, every entropy function can be defined equivalently in the w...

If optimality is measured by average codeword length, Huffman's algorithm gives optimal codes, and the redundancy can be measured as the difference between the average codeword length and Shannon's entropy. If the objective function is replaced by an exponentially weighted average, then a simple modification of Huffman's algorithm gives optimal codes. The redundancy can now be measured as the d...

The present theory leads to a set of subjective weights such that the utility of an uncertain alternative (gamble) is partitioned into three terms involving those weights — a conventional subjectively weighted utility function over pure consequences, a subjectively weighted value function over events, and a subjectively weighted function of the subjective weights. Under several assumptions, thi...

in this paper, the ambiguity of nite state irreducible markov chain trajectories is reminded and is obtained for two state markov chain. i give an applicable example of this concept in president election

A number of inequalities for the weighted entropies is proposed, mirroring properties of a standard (Shannon) entropy and related quantities. 2000 MSC. 60A10, 60B05, 60C05

Ultrasound backscattering signals depend on the microstructures of tissues. Some studies have applied Shannon entropy to analyze the uncertainty of raw radiofrequency (RF) data. However, we found that the sensitivity of entropy in detecting various scatterer concentrations is limited; thus, we propose a weighted entropy as a new information entropy-based approach to enhance the performance of s...

A measure is derived to quantify directed information transfer between pairs of vertices in a weighted network, over paths of a specified maximal length. Our approach employs a general, probabilistic model of network traffic, from which the informational distance between dynamics on two weighted networks can be naturally expressed as a Jensen Shannon divergence. Our network transfer entropy mea...

In this paper the author analyzes the weighted Renyi entropy in order to derive several inequalities in weighted case. Furthermore, using the proposed notions α-th generalized deviation and (α, p)-th weighted Fisher information, extended versions of the moment-entropy, Fisher information and Cramér-Rao inequalities in terms of generalized Gaussian densities are given. 1 The weighted p-Renyi ent...

In this research paper, weighted / unweighted, directed / undirected graphs are associated with interesting Discrete Time Markov Chains (DTMCs) as well as Continuous Time Markov Chains ( CTMCs ). The equilibrium / transient behavior of such Markov chains is studied. Also entropy dynamics ( Shannon entropy ) of certain structured Markov chains is investigated. Finally certain structured graphs a...