Issue:Conditional probability on IF-events

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Title of paper: Conditional probability on IF-events Author(s): Veronika Valenčáková Faculty of Natural Sciences, Matej Bel University, Tajovského 40, SK-974 01 Banská Bystrica valencak@fpv.umb.sk Presented at: 3rd International Workshop on Intuitionistic Fuzzy Sets, 3 October 2007, Banská Bystrica, Slovakia. Published in: Notes on Intuitionistic Fuzzy Sets, Volume 13, Number 4, pages 22—26 Download:  PDF (253  Kb, File info) Abstract: Probability on collections of IF-sets can be considered as a generalization of the classical probability theory on σ-algebras of sets. The aim of this contribution is to formulate the version of the conditional probability on IF-events and show its properties. The paper is based on the idea for Łukasiewicz implication, but now there are a lot of different implications in the theory of IF-sets. Keywords: Intuitionistic fuzzy event, Conditional probability References: Atanassov, K. (1999). Intuitionistic Fuzzy Sets: Theory and Applications. In Physica Verlag, New York. Atanassov, K. (2001). Remarks on the conjunctions, disjunctions and implications of the intuitionistic fuzzy logic. Int. J. of Uncertainty, Fuzziness and Knowledge-Based Systems Vol. 9, No. 1, 55-65. Atanassov, K. (2006). On eight new intuitionistic fuzzy implications. Proc. of 3rd Int. IEEE Conf. "Intelligent Systems" IS06, London, 4-6 Sept. 2006, 741-746. Cignoli, R. L. O., D’Ottaviano, I. M. L., Mundici, D. (2000). Algebraic Foundations of Many-valued Reasoning. In Kluwer Academic Publishers, Dordrecht. Dvurecenskij, A., Pulmannová, S. (2000). New Trends in Quantum Structures. In Kluwer Academic Publishers, Dordrecht. Lendelová, K. (2006). Conditional IF-probability. In Soft Methods for Integrated Uncertainty Modelling, Advances in Soft Computing, Springer. Riecan, B., Mundici, D. (2002). Probability on MV-algebras. In Handbook of Measure Theory (E. Pap. ed.), Elsevier, Amsterdam, 869-909. Riecan, B., Neubrunn, T. (1997). Integral, Measure and Ordering. In Kluwer Academic Publishers, Dordrecht and Ister Science, Bratislava. Valencáková, V. Conditional probability on the product MV algebras induced by IF-events. Submitted in Mathematica Slovaca. Citations: The list of publications, citing this article may be empty or incomplete. If you can provide relevant data, please, write on the talk page. See also Conditional probability and independence of intuitionistic fuzzy events by Przemysław Grzegorzewski