Connections between information theory and decision under uncertainty have been attracting attention in econophysics, neuroeconomics and quantum decision theory. This paper proposes a psychophysical theory of Shannon entropy based on a mathematical equivalence of delay and uncertainty in decision-making, and psychophysics of the perception of waiting time in probabilistic choices. Furthermore, ...

The Tsallis entropy was proposed as a possible generalization of the standard Boltzmann-Gibbs-Shannon (BGS) entropy as a concept aimed at efficient characterisation of non-extensive complex systems. Ever since its introduction [1], it has been successfully applied in various fields [2]. In parallel, there have been numerous attempts to provide its formal derivation from an axiomatic foundation,...

Shannon Entropy has been extensively used for characterizing complexity of time series arising from chaotic dynamical systems and stochastic processes such as Markov chains. However, for short and noisy time series, Shannon entropy performs poorly. Complexity measures which are based on lossless compression algorithms are a good substitute in such scenarios. We evaluate the performance of two s...

In diagnostic decision-support systems, test selection amounts to selecting, in a sequential manner, a test that is expected to yield the largest decrease in the uncertainty about a patient’s diagnosis. For capturing this uncertainty, often an information measure is used. In this paper, we study the Shannon entropy, the Gini index, and the misclassification error for this purpose. We argue that...

We propose entropy functions based on fractional calculus. We show that this new entropy has the same properties than the Shannon entropy except that of additivity, therefore making this entropy non-extensive. We show that this entropy function satisfies the Lesche and thermodynamic stability criteria.

The Tsallis entropy is shown to be an additive entropy of degree-q that information scientists have been using for almost forty years. Neither is it a unique solution to the nonadditive functional equation from which random entropies are derived. Notions of additivity, extensivity and homogeneity are clarified. The relation between mean code lengths in coding theory and various expressions for ...

After generalization of Shannon‘s entropy measure by Renyi in 1961, many generalized versions of Shannon measure were proposed by different authors. Shannon measure can be obtained from these generalized measures asymptotically. A natural question arises in the parametric generalization of Shannon‘s entropy measure. What is the role of the parameter(s) from application point of view? In the pre...

We analyze the performance of the top-down multiclass classification algorithm for decision tree learning called LOMtree, recently proposed in the literature Choromanska and Langford (2014) for solving efficiently classification problems with very large number of classes. The algorithm online optimizes the objective function which simultaneously controls the depth of the tree and its statistica...