16-17 May 2019 • Sofia, Bulgaria

Submission: 21 February 2019Notification: 11 March 2019Final Version: 1 April 2019

Issue:On some methods of probability

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Title of paper: On some methods of probability
Author(s):
Alžbeta Michalíková
Faculty of Natural Sciences, Matej Bel University, Tajovskeho 40, Banska Bystrica, Slovakia
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Beloslav Riečan
Faculty of Natural Sciences, Matej Bel University, Tajovskeho 40, Banska Bystrica, Slovakia
Mathematical Institute, Slovak Academy of Sciences, Ďumbierska 1, Banská Bystrica, Slovakia
beloslav.riecanAt sign.pngumb.sk
Published in: Notes on Intuitionistic Fuzzy Sets, Volume 24 (2018), Number 2, pages 76–83
DOI: https://doi.org/10.7546/nifs.2018.24.2.76-83
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Abstract: The paper contains a review of some methods for building probability theory on intuitionistic fuzzy sets. They are based on some representation of states by Kolmogorov probability spaces as well as the embedding of IF-spaces into the MV -algebras.
Keywords: IF-sets, IF-states, IV-sets, MV-algebras
AMS Classification: 03E72
References:
  1. Atanassov K. T. (1999) Intuitionistic Fuzzy Sets: Theory and Applications. Springer Physica-Verlag, Heidelberg.
  2. Atanassov, K. T. (2012) On Intuitionistic Fuzzy Set Theory. Springer, Berlin.
  3. Butnariu, D. & Klement, E. P. (1993) Triangular norm-based measures. In Triangular Norm–Based Measures and Games with Fuzzy Coalitions, 37–68.
  4. Ciungu, L. & Riecan, B. (2009) General form of probabilities on IF-sets. Fuzzy Logic and Applications, 101–107.
  5. Ciungu, L. C. & Riecan, B. (2010) Representation theorem for probabilities on IFS-events. Information Sciences, 180(5), 793–798.
  6. Cunderlıkova, K. & Riecan, B. (2016, October) On Two Formulations of the Representation Theorem for an IF–state. In International Workshop on Intuitionistic Fuzzy Sets and Generalized Nets, 65–70.
  7. Di Nola, A., Dvurecenskij, A., Hycko, M. & Manara, C. (2005) Entropy on effect algebras with the Riesz decomposition property I: Basic properties, Kybernetika, 41(2), 143–160.
  8. Di Nola, A., Dvurecenskij, A., Hycko, M. & Manara, C. (2005) Entropy on effect algebras with Riesz decomposition property II: MV-algebras., Kybernetika, 41(2), 161–176.
  9. Durica, M. (2007) Entropy on IF–events. entropy. In Third International Workshop on IFSs, Banska Bystrica, Slovakia, 3 Oct. 2007, Notes on Intuitionistic Fuzzy Sets, 13(4), 30–40.
  10. Grzegorzewski, P. & Mrowka, E. (2002) Probability of intuitionistic fuzzy events. In Soft Methods in Probability, Statistics and Data Analysis, 105–115.
  11. Halmos, P. R. (1950) Measure Theory, Springer, New York.
  12. Jureckova, M. (2001) On the conditional expectation on probability MV-algebras with product. Soft Computing – A Fusion of Foundations, Methodologies and Applications, 5(5), 381–385.
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