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Issue:On some new geometrically motivated operators over intuitionistic fuzzy sets

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Title of paper: On some new geometrically motivated operators over intuitionistic fuzzy sets
Author(s):
Peter Vassilev     0000-0002-7361-9272
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
peter.vassilev@gmail.com
Kristina Zhivkova
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
kristinadimitrova.zh@gmail.com
Vassia Atanassova     0000-0002-3626-9461
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
vassia.atanassova@gmail.com
Lyudmila Todorova     0000-0003-1496-9982
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
lpt@biomed.bas.bg
Diana Petkova
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
diana@biomed.bas.bg
Published in: Notes on Intuitionistic Fuzzy Sets, Volume 31 (2025), Number 4, pages 448–457
DOI: https://doi.org/10.7546/nifs.2025.31.4.448-457
Download:  PDF (204  Kb, File info)
Abstract: We consider four new geometrically motivated operators acting in the interior of the interpretation triangle used to depict intuitionistic fuzzy sets. The first operators uses the points resulting from the classical "necessity" and "possibility" operators, in combination with the point ⟨0, 0⟩. The definition of the second operator employs the projections of the considered point onto the sides of the triangle, as viewed from the vertices ⟨0, 0⟩, ⟨0, 1⟩, and ⟨1, 0⟩. The remaining two operators combine two of these projections with the result of the modal operators of the internal point. We also consider operators obtained as linear combinations of some of these four operators.
Keywords: Operator, Geometric interpretation, Interior point, Intuitionistic fuzzy set
AMS Classification: 03E72, 51Mxx.
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