| Title of paper:
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Intuitionistic fuzzy level topological structures
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| Author(s):
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Krassimir Atanassov  0000-0001-5625-071X
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| Bioinformatics and Mathematical Modelling Department, 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
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| Published in:
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Notes on Intuitionistic Fuzzy Sets, Volume 31 (2025), Number 2, pages 242–252
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| DOI:
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https://doi.org/10.7546/nifs.2025.31.2.242-252
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| Download:
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 PDF (179 Kb, File info)
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| Abstract:
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The paper is a continuation of the series of papers devoted to the concept of a Modal Topological Structure (MTS) and its modification and extension. Here we introduce two new modifications of MTSs – the Level Topological Structures (LTSs, when the level operators play the role of the modal ones) and Modal Level (Topological) Structures (ML(T)Ss, when the level operators play the role of the topological ones). In addition, three extended MTSs are discussed, too – the Modal LTSs (MLTSs, when they contain simultaneously modal, level and topological operators), Modal Level Temporal Topological Structures (MLTTSs, when they contain simultaneously modal, level, temporal and topological operators) and multi-LTSs (mLTSs, when the number of their level operators is higher than 1). All these structures are illustrated with examples from intuitionistic fuzzy sets theory.
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| Keywords:
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Intuitionistic fuzzy set, Intuitionistic fuzzy modal topological structure, Modal topological structure.
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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. (2022). Intuitionistic fuzzy modal topological structure. Mathematics, 10(18), Article ID 3313.
- Atanassov, K. (2022). On the intuitionistic fuzzy modal feeble topological structures. Notes on Intuitionistic Fuzzy Sets, 28(3), 211–222.
- Atanassov, K. (2023). Four new intuitionistic fuzzy bimodal topological structures. Notes on Intuitionistic Fuzzy Sets, 29(3), 239–246.
- Atanassov, K. (2023). Intuitionistic fuzzy bimodal topological structures. Notes on Intuitionistic Fuzzy Sets, 29(2), 133–143.
- Atanassov, K. (2023). On intuitionistic fuzzy temporal topological structures. Axioms, 12(2), Article ID 182.
- Atanassov, K. (2024). Intuitionistic fuzzy modal multi-topological structures and intuitionistic fuzzy multi-modal multi-topological structures. Mathematics, 12(3), Article ID 361.
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