Tsallis Entropy of Product MV-Algebra Dynamical Systems.

This paper is concerned with the mathematical modelling of Tsallis entropy in product MV-algebra dynamical systems. We define the Tsallis entropy of order α , where α ∈ ( 0 , 1 ) ∪ ( 1 , ∞ ) , of a partition in a product MV-algebra and its conditional version and we examine their properties. Among other, it is shown that the Tsallis entropy of order α , where α > 1 , has the property of sub-additivity.

Rényi Entropy and Rényi Divergence in Product MV-Algebras.

This article deals with new concepts in a product MV-algebra, namely, with the concepts of Rényi entropy and Rényi divergence. We define the Rényi entropy of order of a partition in a product MV-algebra and its conditional version and we study their properties. It is shown that the proposed concepts are consistent, in the case of the limit of going to 1, with the Shannon entropy of partitions in a product MV-algebra defined and studied by Petrovičová ( , , 41-44).

-Norm Entropy and -Norm Divergence in Fuzzy Probability Spaces.

In the presented article, we define the -norm entropy and the conditional -norm entropy of partitions of a given fuzzy probability space and study the properties of the suggested entropy measures. In addition, we introduce the concept of -norm divergence of fuzzy P-measures and we derive fundamental properties of this quantity. Specifically, it is shown that the Shannon entropy and the conditional Shannon entropy of fuzzy partitions can be derived from the -norm entropy and conditional -norm entropy of fuzzy partitions, respectively, as the limiting cases for going to 1; the Kullback-Leibler divergence of fuzzy P-measures may be inferred from the -norm divergence of fuzzy P-measures as the limiting case for going to 1.

Logical Divergence, Logical Entropy, and Logical Mutual Information in Product MV-Algebras.

In the paper we propose, using the logical entropy function, a new kind of entropy in product MV-algebras, namely the logical entropy and its conditional version. Fundamental characteristics of these quantities have been shown and subsequently, the results regarding the logical entropy have been used to define the logical mutual information of experiments in the studied case. In addition, we define the logical cross entropy and logical divergence for the examined situation and prove basic properties of the suggested quantities.

Logical Entropy and Logical Mutual Information of Experiments in the Intuitionistic Fuzzy Case.

In this contribution, we introduce the concepts of logical entropy and logical mutual information of experiments in the intuitionistic fuzzy case, and study the basic properties of the suggested measures. Subsequently, by means of the suggested notion of logical entropy of an IF-partition, we define the logical entropy of an IF-dynamical system. It is shown that the logical entropy of IF-dynamical systems is invariant under isomorphism.

The analysis of professional competencies of a lecturer in adult education.

In this article, we present the andragogical research project and evaluation of its results using nonparametric statistical methods and the semantic differential method. The presented research was realized in the years 2012-2013 in the dissertation of I. Žeravíková: Analysis of professional competencies of lecturer and creating his competence profile (Žeravíková 2013), and its purpose was based on the analysis of work activities of a lecturer to identify his most important professional competencies and to create a suggestion of competence profile of a lecturer in adult education.