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

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

Kybernetika (2005)

  • Volume: 41, Issue: 2, page [161]-176
  • ISSN: 0023-5954

Abstract

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We study the entropy mainly on special effect algebras with (RDP), namely on tribes of fuzzy sets and sigma-complete MV-algebras. We generalize results from [RiMu] and [RiNe] which were known only for special tribes.

How to cite

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Di Nola, Antonio, et al. "Entropy on effect algebras with Riesz decomposition property II: MV-algebras." Kybernetika 41.2 (2005): [161]-176. <http://eudml.org/doc/33747>.

@article{DiNola2005,
abstract = {We study the entropy mainly on special effect algebras with (RDP), namely on tribes of fuzzy sets and sigma-complete MV-algebras. We generalize results from [RiMu] and [RiNe] which were known only for special tribes.},
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; tribe; Loomis-Sikorski theorem; entropy generator theorem},
language = {eng},
number = {2},
pages = {[161]-176},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Entropy on effect algebras with Riesz decomposition property II: MV-algebras},
url = {http://eudml.org/doc/33747},
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 Riesz decomposition property II: MV-algebras
JO - Kybernetika
PY - 2005
PB - Institute of Information Theory and Automation AS CR
VL - 41
IS - 2
SP - [161]
EP - 176
AB - We study the entropy mainly on special effect algebras with (RDP), namely on tribes of fuzzy sets and sigma-complete MV-algebras. We generalize results from [RiMu] and [RiNe] which were known only for special tribes.
LA - eng
KW - effect algebra; Riesz decomposition property; MV-algebra; state; entropy; effect algebra; Riesz decomposition property; MV-algebra; tribe; Loomis-Sikorski theorem; entropy generator theorem
UR - http://eudml.org/doc/33747
ER -

References

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  3. Nola A. Di, Dvurečenskij, A., Jakubík J., Good and bad infinitesimals, and states on pseudo MV-algebras, submitte 
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  10. Fuchs L., Partially Ordered Algebraic Systems, Pergamon Press, Oxford – London – New York – Paris 1963 Zbl0137.02001MR0171864
  11. Goodearl K. R., Partially Ordered Abelian Groups with Interpolation, (Math. Surveys and Monographs No. 20.) Amer. Math. Society, Providence, RI 1986 Zbl0589.06008MR0845783
  12. Mundici D., 10.1006/aama.1998.0631, Advan. Appl. Math. 22 (1999), 227–248 (1999) Zbl0926.06004MR1659410DOI10.1006/aama.1998.0631
  13. Riečan B., Kolmogorov–Sinaj entropy on MV-algebras, submitte 
  14. Riečan B., Mundici D., Probability on MV-algebras, In: Handbook of Measure Theory (E. Pap, ed.), Elsevier Science, Amsterdam 2002, Vol. II, pp. 869–909 Zbl1017.28002MR1954631
  15. Riečan B., Neubrunn T., Integral, Measure and Ordering, Kluwer Academic Publishers, Dordrecht and Ister Science, Bratislava 199 MR1489521

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