Issue:About the Lp space of intuitionistic fuzzy observables

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Title of paper: About the Lp space of intuitionistic fuzzy observables Author(s): Katarína Čunderlíková Mathematical Institute, Slovak Academy of Sciences, Štefánikova 49, 814 73 Bratislava, Slovakia cunderlikova.lendelova@gmail.com Presented at: 26th International Conference on Intuitionistic Fuzzy Sets, Sofia, 26—27 June 2023 Published in: Notes on Intuitionistic Fuzzy Sets, Volume 29 (2023), Number 2, pages 90–98 DOI: https://doi.org/10.7546/nifs.2023.29.2.90-98 Download:  PDF (220  Kb, File info) Abstract: The aim of this paper is to define an [math]\displaystyle{ L^p }[/math] space of intuitionistic fuzzy observables. We work in an intuitionistic fuzzy space [math]\displaystyle{ ({\mathcal F}, {\bf m}) }[/math] with product, where [math]\displaystyle{ \mathcal F }[/math] is a family of intuitionistic fuzzy events and [math]\displaystyle{ {\bf m} }[/math] is an intuitionistic fuzzy state. We prove that the space [math]\displaystyle{ L^p }[/math] with corresponding intuitionistic fuzzy pseudometric [math]\displaystyle{ \rho_{IF} }[/math] is a pseudometric space. Keywords: Intuitionistic fuzzy observable, Intuitionistic fuzzy state, Joint intuitionistic fuzzy observable, Function of several intuitionistic fuzzy observables, Product, Lp space, Pseudometric space, Intuitionistic fuzzy pseudometric. AMS Classification: 03B52, 60A86. 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. Atanassov, K. T. (1999). Intuitionistic Fuzzy Sets: Theory and Applications, Physica Verlag, New York. Atanassov, K. T. (2012). On Intuitionistic Fuzzy Sets, Springer, Berlin. Bartková, R., & Čunderlíková, K. (2018). About Fisher–Tippett–Gnedenko Theorem for Intuitionistic Fuzzy Events. In: Kacprzyk, J., et al. (eds) Advances in Fuzzy Logic and Technology 2017. IWIFSGN 2017, EUSFLAT 2017. Advances in Intelligent Systems and Computing, Vol. 641, Springer, Cham, 125–135. Čunderlíková, K. (2019). m-almost everywhere convergence of intuitionistic fuzzy observables induced by Borel measurable function. Notes on Intuitionistic Fuzzy Sets, 25(2), 29–40. Lendelová, K. (2006). Conditional IF-probability. Lawry, J. et al. (Eds.). Soft Methods for Integrated Uncertainty Modelling. Advances in Soft Computing, Vol. 37, Springer-Verlag Berlag Heidelberg, 275–283. Riečan, B. (1999). On the $L^p$ space of observables. Fuzzy Sets and Systems, 105(2), 299–306. Riečan, B. (2000). On the $L^p$ space of observables on product MV algebras. International Journal of Theoretical Physics, 39(3), 851–858. Riečan, B. (2006). On a problem of Radko Mesiar: General form of IF-probabilities. Fuzzy Sets and Systems, 157(11), 1485–1490. Riečan, B. (2006). On the probability and random variables on IF events. In: Ruan, D. et al. (Eds.). Applied Artificial Intelligence, Proceedings of the 7th FLINS Conference, Genova, 138–145. Riečan, B. (2007). Probability theory on intuitionistic fuzzy events. In: Aguzzoli, D. et al. (eds) A volume in honour of Daniele Mundici’s 60th birthday. Lecture Notes in Computer Science, Springer, 290–308. Riečan, B. (2012). Analysis of fuzzy logic models. In: Koleshko, V. (Ed.). Intelligent Systems, INTECH, 219–244. 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.