| Title of paper:
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On the 3D-figure areas based on Pick's formula
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| Author(s):
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| Krassimir Atanassov
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| Department of Bioinformatics and Mathematical Modelling, Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Block 105, 1113 Sofia, Bulgaria
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| krat@bas.bg
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| Published in:
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Notes on Intuitionistic Fuzzy Sets, Volume 28 (2022), Number 1, pages 86–92
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| DOI:
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https://doi.org/10.7546/nifs.2022.28.1.86-92
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| Download:
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 PDF (216 Kb, File info)
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| Abstract:
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This work is based on previous research focused on iterative procedures for estimation of the area surrounded by a simple closed curve in the 2D space. Pick's formula is employed for calculating the area surrounded by a special type of polygons. Here, we propose 3D-figure areas based on Pick's formula and give intuitionistic fuzzy and interval-valued intuitionistic fuzzy estimations of these areas.
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| Keywords:
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Intuitionistic fuzzy set, Intuitionistic fuzzy interpretational triangle, Python, Software implementation.
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| AMS Classification:
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03E72
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| References:
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- Atanassov, K., Vassilev, P., Kacprzyk, J., & Szmidt, E. (2018). On interval valued intuitionistic fuzzy pairs. Journal of Universal Mathematics, 1(3), 261–268.
- Atanassov, K., Szmidt, E., & Kacprzyk, J. (2013). On intuitionistic fuzzy pairs. Notes on Intuitionistic Fuzzy Sets, 19(3), 1–13.
- Atanassov, K., Marinov, E., Vassilev, P., & Alexandrov, A. (2019). An Improved Intuitionistic Fuzzy Estimation of the Aread of 2D-Figures Based on the Pick’s Formula. Proceedings of the 4th International conference on Numerical and symbolic Computation – Developments and Applications, Porto, 11–12 April 2019, ECCOMAS, Portugal, 363–374.
- Marinov, E., Velizarova, E., & Atanassov, K. (2014). An Intuitionistic Fuzzy Estimation of the Area of 2D-figures based on the Pick’s Formula. In: Modern Approaches in Fuzzy Sets, Intuitionistic Fuzzy Sets, Generalized Nets and Related Topics, Volume 1: Foundations. (Atanassov, K., M. Baczynski, J. Drewniak, J. Kacprzyk, M. Krawczak, E. Szmidt, M. Wygralak, S. Zadrozny, eds.), SRI-PAS, Warsaw, 145–157.
- Marinov, E., Velizarova, E., & Atanassov, K. (2013). An intuitionistic fuzzy estimation of the area of 2D-figures. Notes on Intuitionistic Fuzzy Sets, 19(2), 57–70.
- Munkres, J. (2000). Topology, 2nd Ed., Prentice Hall.
- Pick, G. (1899). Geometrisches zür Zahlenlehre. Sitzungsberichte des deutschen naturwissenschaftlich-medicinischen Vereines für Böhmen “Lotos” in Prag. (Neue Folge), 19, 311–319.
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| Citations:
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