| Title of paper:
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On some methods of probability
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| Author(s):
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| Alžbeta Michalíková
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| Faculty of Natural Sciences, Matej Bel University, Tajovskeho 40, Banska Bystrica, Slovakia
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| alzbeta.michalikova@umb.sk
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| Beloslav Riečan
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| Mathematical Institute, Slovak Academy of Sciences, Ďumbierska 1, Banská Bystrica, Slovakia
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| beloslav.riecan@umb.sk
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| Published in:
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Notes on Intuitionistic Fuzzy Sets, Volume 24 (2018), Number 2, pages 76–83
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| DOI:
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https://doi.org/10.7546/nifs.2018.24.2.76-83
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| Download:
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 PDF (174 Kb Kb, File info)
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| Abstract:
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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.
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| Keywords:
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IF-sets, IF-states, IV-sets, MV-algebras
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| AMS Classification:
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03E72
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| References:
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- Atanassov K. T. (1999) Intuitionistic Fuzzy Sets: Theory and Applications. Springer Physica-Verlag, Heidelberg.
- Atanassov, K. T. (2012) On Intuitionistic Fuzzy Set Theory. Springer, Berlin.
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- Ciungu, L. & Rieˇcan, B. (2009) General form of probabilities on IF-sets. Fuzzy Logic and Applications, 101–107.
- Ciungu, L. C. & Rieˇcan, B. (2010) Representation theorem for probabilities on IFS-events. Information Sciences, 180(5), 793–798.
- Cˇ underl´ıkova´, K. & Riecˇan, 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.
- Di Nola, A., Dvureˇcenskij, A., Hyˇcko, M. & Manara, C. (2005) Entropy on effect algebras with the Riesz decomposition property I: Basic properties, Kybernetika, 41(2), 143–160.
- Di Nola, A., Dvureˇcenskij, A., Hyˇcko, M. & Manara, C. (2005) Entropy on effect algebras with Riesz decomposition property II: MV-algebras., Kybernetika, 41(2), 161–176.
- Dˇ urica, 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.
- Grzegorzewski, P. & Mr´owka, E. (2002) Probability of intuitionistic fuzzy events. In Soft Methods in Probability, Statistics and Data Analysis, 105–115.
- Halmos, P. R. (1950) Measure Theory, Springer, New York.
- Jureˇckov´a, 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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| Citations:
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