| Title of paper:
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On two formulations of the IF state representation theorem
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| Author(s):
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| Jaroslav Považan
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| Faculty of Natural Sciences, Matej Bel University, Tajovského 40, 974 01 Banská Bystrica, Slovakia
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| jaroslav.povazan@umb.sk
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| Published in:
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"Notes on IFS", Volume 21, 2015, Number 5, pages 16–19
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| Download:
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 PDF (140 Kb, File info)
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| Abstract:
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The Recurrence theorem by Poincaré is one of basic results of the standard ergodic theory. In classical sense the main structure is a σ-algebra of sets and the measure-preserving maps are represented by preimages of classical maps. In this article we change the σ-algebra by a family ℱ of Intuitionistic Fuzzy Sets (IF-sets), which were introduced by Krassimir T. Atanassov, and the probability by an IF-state.
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| Keywords:
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recurrence theorem, IF-sets, s-preserving mappings, IF-state.
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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, Heidelberg.
- Bennett, M. K. & D. J. Foulis (1994) Effect algebras and unsharp quantum logics. Foundations of Physics, 24, 1331–1352.
- Dvurečenskij, A. (1976) On some properties of transformation of a logic. Math. Slovaca, 26, 131–137.
- Chovanec, F. & F. Kôpka (1994) D-posets. Math. Slovaca, 44, 21–34.
- Kôpka, F. (2008) Quasiproduct on Boolean D-posets. Int. J. Theor. Physics, 47, 26–35.
- Maličký, P. (2007) Category version of the Poincaré recurrence theorem. Topology Appl., 154, 2709–2713.
- Mundici, D. (2011) Advanced Lukasiewicz calculus and MV-algebras. Springer, New York.
- Poincaré, H. (1889) Les methodes nouvelles de la mechanique classique celeste, Vol. 3, Gauthiers-Villars, Paris.
- Riečan, B. (2013) Variation on a Poincaré theorem. Fuzzy Sets and Systems, 232, 39–45.
- Riečan, B. & D. Mundici (2002) Probability on MV-algebras. In: Handbook of Measure Theory (E. Pap. ed.), Elsevier Science, Amsterdam, 869– 909.
- Riečan, B. & T. Nebrunn (1997) Integral, Measure, and Ordering. Kluwer, Dordrecht.
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