On measures of “useful” information

The quantitative-qualitative measure of information as given by Belis and Guiaşu is additive, the additivity being a modification of the additivity of Shannon's measure with due place for utilities of the scheme in this property. A characterization of Belis and Guiaşu's measure depending upon the additivity postulate has been provided. The additivity can be relaxed, and there can be several ways of choosing a nonadditive law in place of additivity. Starting from a particular type of nonadditivity relation we characterize a measure of nonadditive “useful” information, which may be considered as a quantitative-qualitative measure corresponding to the Havrda-Charvat-Vajda-Daróczy entropy of degree β

On the Gini–Simpson index and its generalisation—A historic note

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The Statistical Foundations of Entropy

In the last two decades, the understanding of complex dynamical systems underwent important conceptual shifts. The catalyst was the infusion of new ideas from the theory of critical phenomena (scaling laws, renormalization group, etc.), (multi)fractals and trees, random matrix theory, network theory, and non-Shannonian information theory. The usual Boltzmann–Gibbs statistics were proven to be grossly inadequate in this context. While successful in describing stationary systems characterized by ergodicity or metric transitivity, Boltzmann–Gibbs statistics fail to reproduce the complex statistical behavior of many real-world systems in biology, astrophysics, geology, and the economic and social sciences.The aim of this Special Issue was to extend the state of the art by original contributions that could contribute to an ongoing discussion on the statistical foundations of entropy, with a particular emphasis on non-conventional entropies that go significantly beyond Boltzmann, Gibbs, and Shannon paradigms. The accepted contributions addressed various aspects including information theoretic, thermodynamic and quantum aspects of complex systems and found several important applications of generalized entropies in various systems

Useful information or weighted entropy: review and developments

This paper reviews the concept of weighted entropy - also called useful information - proposing a semiotic interpretation of the theme in terms of the relevance or informative value of events in a sample space and a context of usefulness. Still, we discuss other related developments, namely: contribution and mean contributive value. It is also presented an extensive literature review on the subject and numerical examples---------------------------------------------Neste artigo revê-se o conceito de entropia ponderada - também designada por informação útil -, propondo-se uma interpretação semiótica do tema em termos da relevância ou valor informativo de eventos num espaço amostral e contexto de utilidade. Ainda se discutem outros desenvolvimentos relacionados, nomeadamente: contribuição e valor contributivo médio. Apresenta-se também uma vasta revisão bibliográfica sobre o assunto e exemplificações numérica