| Title of paper:
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Multi-dimensional modal topological structures, extended intuitionistic fuzzy index matrices and multi-person multi-criteria decision making procedures
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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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| Published in:
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Notes on Intuitionistic Fuzzy Sets, Volume 32 (2026), Number 1, pages 15–29
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| DOI:
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https://doi.org/10.7546/nifs.32.1.15-29
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| Download:
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 PDF (220 Kb, File info)
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| Abstract:
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The concept of multi-dimensional modal topological structures was introduced in the middle of 2025. One of the special forms of these structures are the intuitionistic fuzzy multi-dimensional modal topological structures. Here, we give examples of intuitionistic fuzzy multi-dimensional modal topological structures, related to extended intuitionistic fuzzy index matrices and to multi-person multi-criteria decision making procedures with intuitionistic fuzzy evaluations of the experts, who have intuitionistic fuzzy scores and use criteria having intuitionistic fuzzy evaluations.
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| Keywords:
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Intuitionistic fuzzy extended index matrix, Intuitionistic fuzzy set, Intuitionistic fuzzy multi-dimensional modal topological structure, Multi-person multi-criteria decision making procedure.
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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 Theory. Springer, Berlin.
- Atanassov, K. (2013). On extended intuitionistic fuzzy index matrices. Notes on Intuitionistic Fuzzy Sets, 19(4), 27–41.
- Atanassov, K. (2014). Index Matrices: Towards an Augmented Matrix Calculus. Springer, Cham.
- Atanassov, K. (2020). Generalized Nets and Intuitionistic Fuzziness in Data Mining. “Prof. Marin Drinov” Academic Publishing House, Sofia.
- Atanassov, K. (2022). Intuitionistic fuzzy modal topological structure. Mathematics, 10, Article ID 3313.
- Atanassov, K. (2025). Intuitionistic fuzzy level topological structures. Notes on Intuitionistic Fuzzy Sets, 31(2), 242–252.
- Atanassov, K. (2025). Intuitionistic fuzzy multi-dimensional modal topological structures. In: Kahraman, C., et al. (Eds.) Intelligent and Fuzzy Systems. INFUS 2025. Lecture Notes in Networks and Systems, 1528, 11–21. Springer, Cham.
- Atanassov, K. (2025). Modal topological structures, index matrices and graphs through the prism of intuitionistic fuzziness. Proceedings of the 23rd International Workshop on Intuitionistic Fuzzy Sets and Generalized Nets, 17 October 2025, Warsaw, Poland, (in press).
- Atanassov, K., Pasi, G., & Yager, R. (2005). Intuitionistic fuzzy interpretations of multi-criteria multi-person and multi-measurement tool decision making. International Journal of Systems Science, 36(14), 859–868.
- Bourbaki, N. (1960). Chapitre 1: Structures Topologiques; Chapitre 2: Structures Uniformes. Éléments de mathématique, Livre III: Topologie générale (Third Edition, in French). Herman, Paris.
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| Citations:
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