| Title of paper:
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Living on the perimeter: A new directional operation on intuitionistic fuzzy sets
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| Author(s):
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Krassimir Atanassov  0000-0001-5625-071X
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| Department of Bioinformatics and Mathematical Modelling, Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences, Acad. G. Bonchev Str. bl. 105, Sofia-1113, Bulgaria
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| krat@bas.bg , k.t.atanassov@gmail.com
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| Vassia Atanassova 0000-0002-3626-9461
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| Department of Bioinformatics and Mathematical Modelling, Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences, Acad. G. Bonchev Str. bl. 105, Sofia-1113, Bulgaria
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| vassia.atanassova@gmail.com
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| Published in:
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Notes on Intuitionistic Fuzzy Sets, Volume 32 (2026), Number 3, pages 315–324
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| DOI:
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https://doi.org/10.7546/nifs.2026.32.3.315-324
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| Download:
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 PDF (387 Kb, File info)
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| Abstract:
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In the present paper, we introduce a new directional operation on intuitionistic fuzzy pairs and study some of its properties. For distinct inputs, the operation extrapolates from the first through the second to the triangle’s perimeter. We provide an explicit formula and illustrate the possible geometric configurations. An accompanying interactive software application supports visualization and numerical exploration of the construction.
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| Keywords:
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Intuitionistic fuzzy pair, Intuitionistic fuzzy interpretational triangle.
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| AMS Classification:
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03E72.
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| References:
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- Atanassov, K. (2012). On Intuitionistic Fuzzy Sets. Springer, Berlin.
- Atanassov, K., Szmidt, E., & Kacprzyk, J. (2013). On intuitionistic fuzzy pairs. Notes on Intuitionistic Fuzzy Sets, 19(3), 1–13.
- Atanassov, K., Vassilev, P., & Atanassova, V. (2025). Geometrical interpretations of interval-valued intuitionistic fuzzy sets: Reconsiderations and new results. Mathematics, 13(12), Article ID 1967.
- Atanassova, V., & Vassilev, P. (2026). Parallels and meridians in the intuitionistic fuzzy triangle: A confidence-aware framework for decision making. Symmetry, 18(3), Article ID 468.
- Vassilev, P., & Atanassova, V. (2024). On a family of billiards-inspired operators over intuitionistic fuzzy sets. Notes on Intuitionistic Fuzzy Sets, 30(1), 92–100.
- Vassilev, P., Zhivkova, K., Atanassova, V., Todorova, L., & Petkova, D. (2025). On some new geometrically motivated operators over intuitionistic fuzzy sets. Notes on Intuitionistic Fuzzy Sets, 31(4), 448–457.
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