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Issue:On a family of billiards-inspired operators over intuitionistic fuzzy sets

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Title of paper: On a family of billiards-inspired operators over intuitionistic fuzzy sets
Author(s):
Peter Vassilev
Department of Bioinformatics and Mathematical Modelling, Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences, 105 Acad. G. Bonchev Str., Sofia 1113, Bulgaria
peter.vassilev@gmail.com
Vassia Atanassova
Department of Bioinformatics and Mathematical Modelling, Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences, 105 Acad. G. Bonchev Str., Sofia 1113, Bulgaria
vassia.atanassova@gmail.com
Presented at: Proceedings of the 27th International Conference on Intuitionistic Fuzzy Sets, 5–6 July 2024, Burgas, Bulgaria
Published in: Notes on Intuitionistic Fuzzy Sets, Volume 30 (2024), Number 1, pages 92–100
DOI: https://doi.org/10.7546/nifs.2024.30.1.92-100
Download:  PDF (322  Kb, File info)
Abstract: In the present work we introduce a family of geometrically inspired operators over intuitionistic fuzzy sets. In essence, if we consider the interpretational triangle as a billiards table with certain properties and each point of an intuitionistic fuzzy set as a ball propelled with a predetermined initial force, then its image after bouncing off from the boundaries of the triangle will, in general, be a new and different intuitionistic fuzzy point. The value of this image depends on the magnitude and direction of the force, which we will describe by using a parameter λ > 0 and another intuitionistic fuzzy set over the same universe.
Keywords: Intuitionistic fuzzy sets, Operator, Reflection.
AMS Classification: 03E72.
References:
  1. Atanassov, K. (1983), Intuitionistic Fuzzy Sets. VII ITKR Session, Sofia (Deposed in Central Sci. Techn. Library of Bulg. Acad. of Sci., 1697/84) (in Bulgarian).
  2. Atanassov, K. (1989). Geometrical interpretation of the elements of the intuitionistic fuzzy objects. Preprint IM-MFAIS-1-89, Sofia, 1989.
  3. Atanassov, K. (2002). Remark on a property of the intuitionistic fuzzy interpretation triangle. Notes on Intuitionistic Fuzzy Sets, 8(1), 34–36.
  4. Atanassov, K. (2012). On Intuitionistic Fuzzy Sets Theory. Springer, Berlin.
  5. Atanassov, K. (2016). A new geometrical interpretation of the intuitionistic fuzzy pairs. Notes on Intuitionistic Fuzzy Sets, 22(5), 12–18.
  6. Atanassov, K., & Vassilev, P. (2018). On the intuitionistic fuzzy sets of n-th type. In: Gaweda, A., Kacprzyk, J., Rutkowski, L., Yen, G. (eds) Advances in Data Analysis with Computational Intelligence Methods. Studies in Computational Intelligence, Vol. 738, Springer, 265–274.
  7. Atanassova, L., & Dworniczak, P. (2021). Operation Δ as the tool for the de-i-fuzzification procedure and for the correction of the unconscientious experts' evaluations. Notes on Intuitionistic Fuzzy Sets, 27(4), 9–19.
  8. Atanassova, V. (2010). Representation of fuzzy and intuitionistic fuzzy data by radar charts. Notes on Intuitionistic Fuzzy Sets, 16(1), 21–26.
  9. Atanassova, V. (2017). New modified level operator Nγ over intuitionistic fuzzy sets. In: (Christiansen, H., et al (Eds.), LNAI 10333, Springer, 209–214.
  10. Atanassova, V., & Doukovska, L. (2017). Compass-and-straightedge constructions in the intuitionistic fuzzy interpretational triangle: two new intuitionistic fuzzy modal operators. Notes on Intuitionistic Fuzzy Sets, 23(2), 1–7.
  11. Dantchev, S. (1996). A new geometrical interpretation of some concepts in the intuitionistic fuzzy logics. Notes on Intuitionistic Fuzzy Sets, 2(2), 1–10.
  12. Georgiev, P. R., & Atanassov, K. (1996). Geometrical interpretations of the interval-valued intuitionistic fuzzy sets. Notes on Intuitionistic Fuzzy Sets, 2(2), 1–10.
  13. Georgiev, P. R., & Atanassov, K. (1996). On the geometrical interpretations of the operations over intuitionistic fuzzy sets. Notes on Intuitionistic Fuzzy Sets, 4(1), 28–34.
  14. Hatzimichailidis, A., & Papadopoulos, B. (2005). A new geometrical interpretation of some concepts in the intuitionistic fuzzy logic. Notes on Intuitionistic Fuzzy Sets, 11(2), 38–46.
  15. Marinov, E. (2022). Software implementation of intuitionistic fuzzy sets and some operators. Notes on Intuitionistic Fuzzy Sets, 28(1), 51–85.
  16. Tasseva, V., Szmidt, E., & Kacprzyk, J. (2005). On one of the geometrical interpretations of the intuitionistic fuzzy sets. Notes on Intuitionistic Fuzzy Sets, 11(2), 21–27.
  17. Todorova, L., & Vassilev, P. (2009). A note on a geometric interpretation of the intuitionistic fuzzy set operators Pα,β and Qα,β. Notes on Intuitionistic Fuzzy Sets, 15(4), 25–29.
  18. Todorova, L., & Vassilev, P. (2010). Geometric interpretation and the properties of two new operators over the intuitionistic fuzzy sets. Notes on Intuitionistic Fuzzy Sets, 16(4), 12–16.
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