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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, 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.
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