| Title of paper:
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The limit theorems on the interval valued events
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| Author(s):
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| Karol Samuelčík
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| Department of Mathematics, Faculty of Humanities, Žilinská univerzita v Žiline, Univerzitná 8215/1, 010 26 Žilina, Slovakia
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| karol.samuelcik@fhv.uniza.sk
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| Ivana Hollá
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| Department of Mathematics, Faculty of Humanities, Žilinská univerzita v Žiline, Univerzitná 8215/1, 010 26 Žilina, Slovakia
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| Published in:
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"Notes on IFS", Volume 19, 2013, Number 2, pages 31—41
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| Download:
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 PDF (124 Kb, File info)
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| Abstract:
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Interval valued event (IV event) is a pair A=(μA, νA) of fuzzy events such that μ A ≤ ν A. The IV theory is isomorphic to the intuitionistic fuzzy theory. The paper contains a construction of mathematical apparatus and the proofs of some limit theorems in a space of IV events.
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| Keywords:
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Intuitionistic fuzzy events, Interval valued events; The limit theorems.
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| AMS Classification:
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03E72
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| References:
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- Atanassov, K. Intuitionistic Fuzzy Sets: Theory and Applications. Springer-Physica Verlag, Heidelberg, 1999.
- Ciungu, L., B. Riečan. General form of probability on IF-sets. Fuzzy Logic and Applications, Proc. of 8th Int. Workshop WILF, Lecture Notes in Artificial Intelligence, 2009, 101–107.
- Riečan, B., P. Král. Probability on interval valued events. Proc. of the 11th International Workshop on Generalized Nets and the Second International Workshop on Generalized Nets, Intuitionistic Fuzzy Sets and Knowledge Engineering, London 9 July 2010, 66–70.
- Samuelčík, K.,I. Hollá. Conditional probability on the Kôpka’s D-posets.Acta Mathematica SINICA, English series, Vol. 28, Nov. 2012, No. 11, 2197–2204.
- Samuelčík, K. The weak law of large numbers in P-probability theory. Afrika Matematika,2011, DOI:10.1007/s13370-011-0032-z.
- Samuelčík, K., I. Hollá. Central limit theorem on IV sets. Recent Advances in Fuzzy Sets, Intuitionistic Fuzzy Sets, Generalized Nets and Related Topics, Volume I: Foundations (K. Atanassov, et al. eds.), 2010, 187–196.
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