| Title of paper:
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D-posets and effect algebras
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| Author(s):
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| Martina Paulínyová
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| Faculty of Natural Sciences, Matej Bel University, Tajovského 40, 974 01 Banská Bystrica, Slovakia
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| Published in:
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"Notes on IFS", Volume 20, 2014, Number 4, pages 32–40
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| Download:
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 PDF (171 Kb, File info)
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| Abstract:
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In the paper two algebraizations of IF-sets families are considered: D-posets [11] and effect algebras [5]. An elementary proof is presented of the fact that D-posets and effect algebras are isomorphic structures [12, 13]. Moreover a product is defined on effect algebras and it is proved that the corresponding algebraic structure is equivalent with the Kôpka D-poset [15, 16].
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| Keywords:
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D-poset, Effect algebra, Multiplicative operation.
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| AMS Classification:
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03G12, 03B5D
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| References:
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- Atanassov, K., Intuitionistic Fuzzy Sets, Springer, Heidelberg, 1999.
- Atanassov, K., On Intuitionistic Fuzzy Sets Theory, Springer, Berlin, 2012.
- Atanassov, K., On a new algebraic object. Third scientific session of the mathematical foundations artificial intelligence seminar, Part 1, Sofia 1990, 1–5.
- Foulis, J. D., Algebraic measure theory. Atti Sem. Mat. Fis. Univ. Modena, Vol. 48, 2000, 435–461.
- Foulis, D. J., M. K. Bennett, Effect algebras and unsharp quantum logics. Found. Phys., Vol. 24, 1994, 1331–1352.
- Frič, R., M. Papčo, On probability domains. Internat. J. Theoret. Phys., Vol. 49, 2010, 3092–3100.
- Frič, R., M. Papčo, On probability domains II. Internat. J. Theoret. Phys., Vol. 50, 2011, 3778–3786.
- Frič, R., M. Papčo, On probability domains III. Internat. J. Theoret. Phys. (submitted)
- Chovanec, F., Difference Posets and their Graphical Representation (in Slovak). Liptovský Mikuláš, 2014.
- Chovanec, F., E. Drobná, On a construction of linearly ordered totaly nonatomic D-posets. Proc. Third Seminar Fuzzy sets and Quantum Structures, 2003, 12–27.
- Chovanec, F., F. Kôpka, D-posets. Math. Slovaca, Vol. 44, 1994, 21–34.
- Chovanec, F., F. Kôpka, D-posets. In: Integral, Measure, and Ordering (B. Riečan and T. Neubrunn), Kluwer, 1997, 278–311.
- Kôpka, F., F. Chovanec, D-posets. In: Handbook of Quantum Logic and Quantum Structures, Elsevier, Amsterdam, 2007, 367–428.
- Dvurečenskij A., M. Kuková, Observables on quantum structures. Information Sciences, 2013.
- Dvurečenskij A., S. Pulmannová, New Trends in Quantum Structures, Kluwer, Dordrecht, 2000.
- Kôpka, F., D-posets with meet function. Tatra Mt. Math. Publ., Vol. 1, 1992, 83–87.
- Kôpka, F., Quasi product on Boolean D-posets. Inter. J. Theor. Phys., Vol. 47, 2008, 26–35.
- Kôpka, F., F. Chovanec, D-posets. Math. Slovaca, Vol. 44, 1994, 21–34.
- Kuková, M., Strong law of large numbers on the Kôpka D- posets. In: FSTA 2012, 79.
- Kuková, M., M. Navara, Central limit theorem and laws of large numbers in quantum structures. In: 11th Bienal IQSA Meeting, Cagliari 2012, 44–45.
- Montagna, F., An algebraic approach to propositional fuzzy logic. J. Logic. Lang. Inf., Special Issue on Logics of Uncertainty (Mundici, D. ed.), Vol. 9, 2000, 91–124.
- Papčo, M., On effect algebras. Soft Computing, Vol. 12, 2007, 26–35.
- Riečan, B., On the product MV-algebras. Tatra Mt. Math. Publ., Vol. 16, 1999, 299–306.
- Riečan, B., On a new approach to probablity theory on MV algebras, Proc. of Workshop on Generalized Nets, Intutionistic Fuzzy Sets and Knowledge Engeneerng, London, 2010, 57–65.
- Riečan, B., Analysis of Fuzzy Logic Models. In: Intelligent Systems (V. M. Koleshko ed.),INTECH 2012, 219–240.
- Riečan, B., Embedding of IF-states to MV-algebras. Proc. of IWIFSGN, Warsawa, 2014.(in press)
- Riečan, B., L. Lašová, On the probability on the Kôpka D-posets. In: Developments in Fuzzy Sets, Intuitionistic Fuzzy sets, Generalized Nets and Related Topics. Vol. I (K. Atanassov et al. eds.), Warsaw, 2010, 167–176.
- Riečan, B., D. Mundici, Probability on MV-algebras. In: Handbook of Measure Theory, Elsevier, Amsterdam, 2002, 869–910.
- Samuelčík, K., I. Hollá, Conditional probability on the Kôpka D-posets. Acta Mathematica Sinica, Vol. 28, 2012, 2197–2204.
- Samuelčík, K., I. Hollá, Disjointness relations on D-posets. Proc. of 2nd InternationalWorkshop on Generalized Nets, Intuitionistic Fuzzy Sets and Knowledge Engineering, July 2010,London, 71–74.
- Skřivánek, V., R. Frič, R.: Generalized random events (submitted).
- Vrábelová, M., On the conditional probability in product MV-algebras. Soft Computing, Vol. 4, 2000, 58–61.
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