| Title of paper:
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Almost uniformly convergence on MV-algebra of intuitionistic fuzzy sets
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| Author(s):
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| Katarína Čunderlíková
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| Mathematical Institute, Slovak Academy of Sciences, Štefánikova 49, 814 73 Bratislava, Slovakia
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| cunderlikova.lendelova@gmail.com
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| Presented at:
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Proceedings of the International Workshop on Intuitionistic Fuzzy Sets, 15 December 2023, Banská Bystrica, Slovakia
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| Published in:
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Notes on Intuitionistic Fuzzy Sets, Volume 29 (2023), Number 4, pages 335–342
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| DOI:
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https://doi.org/10.7546/nifs.2023.29.4.335-342
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| Download:
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 PDF (179 Kb, File info)
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| Abstract:
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The aim of this contribution is to formulate some definitions of almost uniformly convergence for a sequence of observables in the MV-algebra of the intuitionistic fuzzy sets. We define a partial binary operation ⊖ called difference on MV-algebra of intuitionistic fuzzy sets. As an illustration of the use the almost uniformly convergence we prove a variation of Egorov’s theorem for the observables in MV-algebra of intuitionistic fuzzy sets.
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| Keywords:
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MV-algebra, ℓ-groups, Intuitionistic fuzzy sets, States, Observables, Difference, Almost uniformly convergence, Egorov’s theorem.
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| AMS Classification:
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03B52, 60A86, 60B10.
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| References:
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- 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: International Journal Bioautomation, 20, 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.
- Bartkova, R. & Riečan, B. & Tirp ˇ akov ´ a, A. (2017). ´ Probability Theory for Fuzzy Quantum Spaces with Statistical Applications. Bentham eBooks, Sharjah.
- Cunderlikova, K. (2023). On another type of convergence for intuitionistic fuzzy observables. Submitted to Mathematics.
- Riečan, B. (1997). On the convergece of observables in D-posets. Tatra Mountains Mathematical Publications, 12, 7–12.
- Riečan, B. (2007). Probability Theory on IF Events. Algebraic and Proof-theoretic Aspects of Non-classical Logics. Lecture Notes in Computer Science, vol 4460, Aguzzoli, S., Ciabattoni, A., Gerla, B., Manara, C., Marra, V. Eds., Springer, Berlin, Heidelberg, 290–308.
- Riečan, B. (2009). On the probability and random variables on IF events. Applied Artificial Intelligence, Proceedings of the 7th International FLINS Conference, 29–31 August 2006, Genova, Italy, 138–145.
- Riečan, B. (2015). On finitely additive IF-states. Mathematical Foundations, Theory, Analyses: Proceedings of the 7th IEEE International Conference Intelligent Systems, 24-26 September 2014, Warsaw, Poland, Volume 1, 149–156.
- Riečan, B. (2015). Embedding of IF-states to MV-algebras. ˇ Mathematical Foundations, Theory, Analyses: Proceedings of the 7th IEEE International Conference Intelligent Systems, 24-26 September 2014, Warsaw, Poland, Volume 1, pp. 157–162.
- Riečan, B. & Mundici, D. (2002). Probability in MV-algebras. ˇ Handbook of Measure Theory, Pap, E. Eds., Elsevier, Amsterdam, 869–909.
- Riecan, B., & Neubrunn, T. (1997). ˇ Integral, Measure, and Ordering. Kluwer Academic Publishers, Dordrecht and Ister Science, Bratislava.
- Zadeh, L.A. (1965). Fuzzy sets. Information and Control, 8, 338–358.
- Zadeh, L. A. (1968). Probability measures on fuzzy sets. Journal of Mathematical Analysis and Applications, 23, 421–427.
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