Issue:M-almost everywhere convergence of intuitionistic fuzzy observables induced by Borel measurable function

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Title of paper: m-almost everywhere convergence of intuitionistic fuzzy observables induced by Borel measurable function Author(s): Katarína Čunderlíková Mathematical Institute, Slovak Academy of Sciences, Štefánikova 898/49, 814 73 Bratislava, Slovakia cunderlikova.lendelova@gmail.com Published in: Notes on Intuitionistic Fuzzy Sets, Volume 25 (2019), Number 2, pages 29–40 DOI: https://doi.org/10.7546/nifs.2019.25.2.29-40 Download:  PDF (195  Kb, File info) Abstract: In paper [4] we studied the upper and the lower limits of sequence of intuitionistic fuzzy observables. We used an intuitionistic fuzzy state m for a definition the notion of almost everywhere convergence. We compared two concepts of m-almost everywhere convergence. The aim of this paper is to show the connection between almost everywhere convergence in classical probability space induced by Kolmogorov construction and m-almost everywhere convergence in intuitionistic fuzzy space. We studied the sequence of intuitionistic fuzzy observables induced by Borel measurable function. Keywords: Intuitionistic fuzzy event, Intuitionistic fuzzy observable, Intuitionistic fuzzy state, Joint intuitionistic fuzzy observable, Product, Upper limit, Lower limit, m-almost everywhere convergence, Function of several intuitionistic fuzzy observables, Borel measurable function, Kolmogorov construction. AMS Classification: 03B52, 60A86, 60B10. References: Atanassov, K. T. (1983). Intuitionistic Fuzzy Sets, VII ITKR Session, Sofia, 20-23 June 1983 (Deposed in Centr. Sci.-Techn. Library of the Bulg. Acad. of Sci., 1697/84) (in Bulgarian). Reprinted: Int. J. Bioautomation, 2016, 20(S1), S1–S6. Atannasov, K. T. (1999). Intuitionistic Fuzzy Sets: Theory and Applications , Physica Verlag, New York. Atanassov, K. T. (2012). On Intuitionistic Fuzzy Sets, Springer, Berlin. Čunderlíková, K. (2018). Upper and lower limits and m-almost everywhere convergence of intuitionistic fuzzy observables, Notes on Intuitionistic Fuzzy Sets, 24(4), 40–49. Lendelová, K. (2006). Conditional IF-probability, Advances in Soft Computing: Soft Methods for Integrated Uncertainty Modelling, 275–283. Riečan, B. & Neubrunn, T. (1997). Integral, Measure and Ordering, Kluwer Academic Publishers, Dordrecht and Ister Science, Bratislava. Riečan, B. (2006). On a problem of Radko Mesiar: general form of IF-probabilities, Fuzzy Sets and Systems, 152, 1485–1490. Riečan, B. (2006). On the probability and random variables on IF events, Applied Artifical Intelligence, Proc. 7th FLINS Conf., Genova, D. Ruan et al. eds., 138–145. Riečan, B. (2012). Analysis of fuzzy logic models, Intelligent systems (V. Koleshko ed.), INTECH, 219–244. Citations: Issue:Convergence in measure of intuitionistic fuzzy observables ‎ (← links) Issue:Intuitionistic fuzzy probability and convergence of intuitionistic fuzzy observables ‎ (← links) Issue:About the Lp space of intuitionistic fuzzy observables ‎ (← links) Issue:Intuitionistic fuzzy probability and two theorems from extreme value theory ‎ (← links) The list of publications, citing this article may be empty or incomplete. If you can provide relevant data, please, write on the talk page.