Kullback-Leibler divergence and mutual information of partitions in product MV algebras

Markechová, Dagmar

Kullback-Leibler divergence and mutual information of partitions in product MV algebras / Dagmar Markechová, Beloslav Riečan. -- The purpose of the paper is to introduce, using the known results concerning the entropy in product MV algebras, the concepts of mutual information and Kullback-Leibler divergence for the case of product MV algebras and examine algebraic properties of the proposed measures. In particular, a convexity of Kullback-Leibler divergence with respect to states in product MV algebras is proved, and chain rules for mutual information and Kullback-Leibler divergence are established. In addition, the data processing inequality for conditionally independent partitions in product MV algebras is proved.

In Entropy. -- Basel : MDPI, 2017. -- ISSN 1099-4300. -- 267