Entropy on effect algebras with Riesz decomposition property II: MV-algebras

Abstract

We continue the study of entropy. In Part I, we have introduced basic properties of entropy. Here we concentrate mainly on the state space which allows us to understand the entropy better, Section 8, and we introduce also quotient effect algebras. Section 9 studies shortly the problem of a so-called entropy generator theorem for effect algebras or MV-algebras. The main results of the present part are in Section 10 and Section 11. There we study the entropy on tribes of fuzzy sets and using the Loomis-Sikorski theorem also on cr-complete MV-algebras. That generalizes results from [14] and [15] which were proved only for full tribes. In addition, we give also a solution to Problem 7 from [14].

Cite this paper

@article{Nola2005EntropyOE, title={Entropy on effect algebras with Riesz decomposition property II: MV-algebras}, author={Antonio di Nola and Anatolij Dvurecenskij and Marek Hycko and Corrado Manara}, journal={Kybernetika}, year={2005}, volume={41}, pages={161-176} }