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Issue:Intuitionistic fuzzy level topological structures: Difference between revisions

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Created page with "{{PAGENAME}} {{PAGENAME}} {{PAGENAME}} {{issue/title | title = Intuitionistic fuzzy level topological structures | shortcut = nifs/31/2/242-252 }} {{issue/author | author = Krassimir Atanassov | institution = Bioinformatics and Mathematical Modelling Dept., Institute of Biophisics and Biomedical Enginee..."
 
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  | abstract        = 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.
  | abstract        = 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.
  | keywords        = Intuitionistic fuzzy set, Intuitionistic fuzzy modal topological structure, Modal \linebreak  topological structure.
  | keywords        = Intuitionistic fuzzy set, Intuitionistic fuzzy modal topological structure, Modal topological structure.
  | ams            = 03E72.
  | ams            = 03E72.
  | references      =  
  | references      =  

Revision as of 05:29, 17 July 2025

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http://ifigenia.org/wiki/issue:nifs/31/2/242-252
Title of paper: Intuitionistic fuzzy level topological structures
Author(s):
Krassimir Atanassov     0000-0001-5625-071X
Bioinformatics and Mathematical Modelling Dept., Institute of Biophisics and Biomedical Engineering, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Bl. 105, Sofia-1113, Bulgaria
krat@bas.bg
Published in: Notes on Intuitionistic Fuzzy Sets, Volume 31 (2025), Number 2, pages 242–252
DOI: https://doi.org/10.7546/nifs.2025.31.2.242-252
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Abstract: 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.
Keywords: Intuitionistic fuzzy set, Intuitionistic fuzzy modal topological structure, Modal topological structure.
AMS Classification: 03E72.
References:
  1. Atanassov, K. (2012). On Intuitionistic Fuzzy Sets Theory. Springer, Berlin.
  2. Atanassov, K. (2022). Intuitionistic fuzzy modal topological structure. Mathematics, 10(18), Article ID 3313.
  3. Atanassov, K. (2022). On the intuitionistic fuzzy modal feeble topological structures. Notes on Intuitionistic Fuzzy Sets, 28(3), 211–222.
  4. Atanassov, K. (2023). Four new intuitionistic fuzzy bimodal topological structures. Notes on Intuitionistic Fuzzy Sets, 29(3), 239–246.
  5. Atanassov, K. (2023). Intuitionistic fuzzy bimodal topological structures. Notes on Intuitionistic Fuzzy Sets, 29(2), 133–143.
  6. Atanassov, K. (2023). On intuitionistic fuzzy temporal topological structures. Axioms, 12(2), Article ID 182.
  7. Atanassov, K. (2024). Intuitionistic fuzzy modal multi-topological structures and intuitionistic fuzzy multi-modal multi-topological structures. Mathematics, 12(3), Article ID 361.
  8. Atanassov, K. (2024). Intuitionistic fuzzy temporal operators and temporal topological structures. Notes on Intuitionistic Fuzzy Sets, 30(4), 285–296.
  9. Atanassov, K. (2024). Remark on intuitionistic fuzzy temporal modal topological structures. Axioms, 13(4), Article ID 256.
  10. Bourbaki, N. (1960). Elements De Mathematique, Livre III: Topologie Generale. (3rm Edition, in French) Chapitre 1: Structures Topologiques, Chapitre 2: Structures Uniformes. Herman, Paris.
  11. Feys, R. (1965). Modal Logics. Gauthier, Paris.
  12. Fitting, M., & Mendelsohn, R. (1998). First Order Modal Logic. Kluwer, Dordrecht.
  13. Kuratowski, K. (1966). Topology, Volume 1. Academic Press, New York.
  14. Mints, G. (1992). A Short Introduction to Modal Logic. University of Chicago Press, Chicago.
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