On some contributions to quantum structures by fuzzy sets

Beloslav Riečan

Kybernetika (2007)

  • Volume: 43, Issue: 4, page 481-490
  • ISSN: 0023-5954

Abstract

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It is well known that the fuzzy sets theory can be successfully used in quantum models ([5, 26]). In this paper we give first a review of recent development in the probability theory on tribes and their generalizations – multivalued (MV)-algebras. Secondly we show some applications of the described method to develop probability theory on IF-events.

How to cite

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Riečan, Beloslav. "On some contributions to quantum structures by fuzzy sets." Kybernetika 43.4 (2007): 481-490. <http://eudml.org/doc/33873>.

@article{Riečan2007,
abstract = {It is well known that the fuzzy sets theory can be successfully used in quantum models ([5, 26]). In this paper we give first a review of recent development in the probability theory on tribes and their generalizations – multivalued (MV)-algebras. Secondly we show some applications of the described method to develop probability theory on IF-events.},
author = {Riečan, Beloslav},
journal = {Kybernetika},
keywords = {probability; fuzzy sets; MV-algebra; IF events; probability; fuzzy sets, MV-algebras; IF events.},
language = {eng},
number = {4},
pages = {481-490},
publisher = {Institute of Information Theory and Automation AS CR},
title = {On some contributions to quantum structures by fuzzy sets},
url = {http://eudml.org/doc/33873},
volume = {43},
year = {2007},
}

TY - JOUR
AU - Riečan, Beloslav
TI - On some contributions to quantum structures by fuzzy sets
JO - Kybernetika
PY - 2007
PB - Institute of Information Theory and Automation AS CR
VL - 43
IS - 4
SP - 481
EP - 490
AB - It is well known that the fuzzy sets theory can be successfully used in quantum models ([5, 26]). In this paper we give first a review of recent development in the probability theory on tribes and their generalizations – multivalued (MV)-algebras. Secondly we show some applications of the described method to develop probability theory on IF-events.
LA - eng
KW - probability; fuzzy sets; MV-algebra; IF events; probability; fuzzy sets, MV-algebras; IF events.
UR - http://eudml.org/doc/33873
ER -

References

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  19. Riečan B., Free products of probability MV-algebras, Atti Sem. Mat. Fis. Univ. Modena 50 (2002), 173–186 Zbl1072.06007MR1910785
  20. Riečan B., The conjugacy of probability MV- σ -algebras with the unit interval, Atti Sem. Mat. Fis. Univ. Modena 52 (2004), 241–248 Zbl1115.28018MR2152490
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  22. Riečan B., On the probability on IF-sets and MV-algebras, Notes on IFS 11 (2005), 6, 21–25 
  23. Riečan B., On the probability and random variables on IF events, In: Applied Artificial Intelligence (Proc. 7th FLINS Conf. Genova, Da Ruan et al., eds.), World Scientific 2006, pp. 138–145 
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  27. Schmidt E., Kacprzyk J., Probability of intuitionistic fuzzy events and their applications in decision making, In: Proc. EUSFLAT’99, Palma de Mallorca 1999, pp. 457–460 (1999) 

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