By replacing linear averaging in Shannon entropy with Kolmogorov-Nagumo average (KN-averages) or quasilinear mean and further imposing the additivity constraint, Rényi proposed the first formal generalization of Shannon entropy. Using this recipe of Rényi, one can prepare only two information measures: Shannon and Rényi entropy. Indeed, using this formalism Rényi characterized these additive en...

We design, implement and test a simple algorithm which computes the approximate entropy of a finite binary string of arbitrary length. The algorithm uses a weighted average of the Shannon Entropies of the string and all but the last binary derivative of the string. We successfully test the algorithm in the fields of Prime Number Theory (where we prove explicitly that the sequence of prime numbe...

Past work shows that one can associate a notion of Shannon entropy to Dirichlet polynomial, regarded as an empirical distribution. Indeed, be extracted from any d:Dir by two-step process, where the first step is rig homomorphism out Dir, *set* polynomials, with structure given standard addition and multiplication. In this short note, we show upgraded *functor*, when replace set polynomials *cat...

respectively We note that these operators are quite di erent in the sense that the rst one fo cuses the total weight on only one argument pro jection on the rst argument whereas the second one distributes the total weight among all the ar guments evenly arithmetic mean In order to capture this idea one can de ne a measure of dispersion associated to the weight vector of the weighted arithmetic ...

We present a somewhat different way of looking on Shannon entropy. This leads to an axiomatisation of Shannon entropy that is essentially equivalent to that of Fadeev.

The purpose of this study is to define the concepts of Tsallis entropy and conditional Tsallis entropy of fuzzy partitions and to obtain some results concerning this kind entropy. We show that the Tsallis entropy of fuzzy partitions has the subadditivity and concavity properties. We study this information measure under the refinement and zero mode subset relations. We check the chain rules for ...