Entropy on effect algebras with the Riesz decomposition property I: Basic properties

Antonio Di Nola; Anatolij Dvurečenskij; Marek Hyčko; Corrado Manara

Kybernetika (2005)

  • Volume: 41, Issue: 2, page [143]-160
  • ISSN: 0023-5954

Abstract

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We define the entropy, lower and upper entropy, and the conditional entropy of a dynamical system consisting of an effect algebra with the Riesz decomposition property, a state, and a transformation. Such effect algebras allow many refinements of two partitions. We present the basic properties of these entropies and these notions are illustrated by many examples. Entropy on MV-algebras is postponed to Part II.

How to cite

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Di Nola, Antonio, et al. "Entropy on effect algebras with the Riesz decomposition property I: Basic properties." Kybernetika 41.2 (2005): [143]-160. <http://eudml.org/doc/33746>.

@article{DiNola2005,
abstract = {We define the entropy, lower and upper entropy, and the conditional entropy of a dynamical system consisting of an effect algebra with the Riesz decomposition property, a state, and a transformation. Such effect algebras allow many refinements of two partitions. We present the basic properties of these entropies and these notions are illustrated by many examples. Entropy on MV-algebras is postponed to Part II.},
author = {Di Nola, Antonio, Dvurečenskij, Anatolij, Hyčko, Marek, Manara, Corrado},
journal = {Kybernetika},
keywords = {effect algebra; Riesz decomposition property; MV-algebra; state; entropy; effect algebra; Riesz decomposition property; MV-algebra; state; entropy},
language = {eng},
number = {2},
pages = {[143]-160},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Entropy on effect algebras with the Riesz decomposition property I: Basic properties},
url = {http://eudml.org/doc/33746},
volume = {41},
year = {2005},
}

TY - JOUR
AU - Di Nola, Antonio
AU - Dvurečenskij, Anatolij
AU - Hyčko, Marek
AU - Manara, Corrado
TI - Entropy on effect algebras with the Riesz decomposition property I: Basic properties
JO - Kybernetika
PY - 2005
PB - Institute of Information Theory and Automation AS CR
VL - 41
IS - 2
SP - [143]
EP - 160
AB - We define the entropy, lower and upper entropy, and the conditional entropy of a dynamical system consisting of an effect algebra with the Riesz decomposition property, a state, and a transformation. Such effect algebras allow many refinements of two partitions. We present the basic properties of these entropies and these notions are illustrated by many examples. Entropy on MV-algebras is postponed to Part II.
LA - eng
KW - effect algebra; Riesz decomposition property; MV-algebra; state; entropy; effect algebra; Riesz decomposition property; MV-algebra; state; entropy
UR - http://eudml.org/doc/33746
ER -

References

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