Issue:Coincidence of intuitionistic fuzzy observables

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http://ifigenia.org/wiki/issue:nifs/31/4/458-464

Title of paper: Coincidence of intuitionistic fuzzy observables Author(s): Katarína Čunderlíková     0000-0002-9772-2717 Mathematical Institute, Slovak Academy of Sciences, Stefánikova 49, 814 73 Bratislava, Slovakia cunderlikova.lendelova@gmail.com Published in: Notes on Intuitionistic Fuzzy Sets, Volume 31 (2025), Number 4, pages 458–464 DOI: https://doi.org/10.7546/nifs.2025.31.4.458-464 Download:  PDF (195  Kb, File info) Abstract: The aim of this paper is to define the notion of coincidence for intuitionistic fuzzy observables. We study the almost everywhere coincidence using intuitionistic fuzzy state [math]\displaystyle{ \bf m }[/math] or intuitionistic fuzzy probability [math]\displaystyle{ \mathcal P }[/math]. We further show the connection between [math]\displaystyle{ \bf m }[/math]-almost everywhere coincidence and [math]\displaystyle{ \mathcal P }[/math]-almost everywhere coincidence of intuicionistic fuzzy observables. Keywords: Intuitionistic fuzzy observable, Intuitionistic fuzzy state, Intuitionistic fuzzy probability, Almost everywhere coincidence, Joint intuitionistic fuzzy observable, Product. AMS Classification: 60A86, 60A10. 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 in: International Journal Bioautomation, 20(S1), S1–S6. Atanassov, K. T. (1999). Intuitionistic Fuzzy Sets: Theory and Applications. Physica Verlag, Heidelberg. Atanassov, K. T. (2012). On Intuitionistic Fuzzy Sets. Springer, Berlin. Jureckova, M. (2001). The coincidence of observables on MV-algebras with product. In: Komornikova, M., & Mesiar, R. (Eds.). Proceeding Uncertainty Modeling, STU, Bratislava, Slovakia, pp. 160–165. Jurecková, M. (2003). The addition to the ergodic theorem on probability MV-algebras with product. Soft Computing, 7, 472–475. Jurecková, M., & Riečan, B. (2005). Invariant observables and the individual ergodic theorem. International Journal of Theoretical Physics, 44, 1587–1597. Lendelová, K. (2006). Conditional IF-probability. Advances in Soft Computing: Soft Methods for Integrated Uncertainty Modelling, Proceedings of the 3rd International Conference on Soft Methods in Probability and Statistics, 5–7 September 2006, Bristol, UK, 37, 275–283. Riečan, B. (2003). A descriptive definition of the probability on intuitionistic fuzzy sets. Proceedings of the 3rd Conference of the European Society for Fuzzy Logic and Technology, EUSFLAT ’2003, 10–12 September 2003, Zittau, Germany, 210–213. Riečan, B. (2004). Representation of probabilities on IFS events. Soft Methodology and Random Information Systems, Proceedings of the 2nd International Conference on Soft Methods in Probability and Statistics, SMPS’2004, 2–4 September 2004, Oviedo, Spain, 243–248. Riečan, B. (2005). On the probability on IF-sets and MV-algebras. Notes on Intuitionistic Fuzzy Sets, 11(6), 21–25. Riečan, B. (2006). On the probability and random variables on IF events. Applied Artifical Intelligence, Proceedings of 7th FLINS Conference, 29–31 August 2006, Genova, Italy, 138–145. Riečan, B. (2012). Analysis of fuzzy logic models. Intelligent Systems, INTECH, 219–244. Riečan, B., & Neubrunn, T. (1997). Integral, Measure, and Ordering. Kluwer Academic Publishers, Dordrecht and Ister Science, Bratislava. 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.