Weaker forms of increasingness of binary operations and their role in the characterization of meet and join operations
- Author
- Lemnaouar Zedam (UGent) and Bernard De Baets (UGent)
- Organization
- Abstract
- Due to the lack of transitivity of the pseudo-order relation of a proper trellis, its meet and join operations are not increasing. In this paper, we identify weaker forms of increasingness of binary operations that are satisfied by the meet and/or join operation of a trellis or lattice. Some of these forms coincide with the classical notion of increasingness when the trellis is a lattice. Furthermore, we demonstrate the role of these weaker forms in the characterization of the meet and join operations of a trellis, lattice or chain as specific idempotent operations.
- Keywords
- Binary operation, Increasingness, Join, Lattice, Meet, Trellis, FUZZY MATHEMATICAL MORPHOLOGY, MONOTONICITY, AGGREGATION, FUNDAMENTALS
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Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-01J6VQ5K6115DETSFJH4MXMVSC
- MLA
- Zedam, Lemnaouar, and Bernard De Baets. “Weaker Forms of Increasingness of Binary Operations and Their Role in the Characterization of Meet and Join Operations.” FUZZY SETS AND SYSTEMS, vol. 497, 2024, doi:10.1016/j.fss.2024.109116.
- APA
- Zedam, L., & De Baets, B. (2024). Weaker forms of increasingness of binary operations and their role in the characterization of meet and join operations. FUZZY SETS AND SYSTEMS, 497. https://doi.org/10.1016/j.fss.2024.109116
- Chicago author-date
- Zedam, Lemnaouar, and Bernard De Baets. 2024. “Weaker Forms of Increasingness of Binary Operations and Their Role in the Characterization of Meet and Join Operations.” FUZZY SETS AND SYSTEMS 497. https://doi.org/10.1016/j.fss.2024.109116.
- Chicago author-date (all authors)
- Zedam, Lemnaouar, and Bernard De Baets. 2024. “Weaker Forms of Increasingness of Binary Operations and Their Role in the Characterization of Meet and Join Operations.” FUZZY SETS AND SYSTEMS 497. doi:10.1016/j.fss.2024.109116.
- Vancouver
- 1.Zedam L, De Baets B. Weaker forms of increasingness of binary operations and their role in the characterization of meet and join operations. FUZZY SETS AND SYSTEMS. 2024;497.
- IEEE
- [1]L. Zedam and B. De Baets, “Weaker forms of increasingness of binary operations and their role in the characterization of meet and join operations,” FUZZY SETS AND SYSTEMS, vol. 497, 2024.
@article{01J6VQ5K6115DETSFJH4MXMVSC,
abstract = {{Due to the lack of transitivity of the pseudo-order relation of a proper trellis, its meet and join operations are not increasing. In this paper, we identify weaker forms of increasingness of binary operations that are satisfied by the meet and/or join operation of a trellis or lattice. Some of these forms coincide with the classical notion of increasingness when the trellis is a lattice. Furthermore, we demonstrate the role of these weaker forms in the characterization of the meet and join operations of a trellis, lattice or chain as specific idempotent operations.}},
articleno = {{109116}},
author = {{Zedam, Lemnaouar and De Baets, Bernard}},
issn = {{0165-0114}},
journal = {{FUZZY SETS AND SYSTEMS}},
keywords = {{Binary operation,Increasingness,Join,Lattice,Meet,Trellis,FUZZY MATHEMATICAL MORPHOLOGY,MONOTONICITY,AGGREGATION,FUNDAMENTALS}},
language = {{eng}},
pages = {{18}},
title = {{Weaker forms of increasingness of binary operations and their role in the characterization of meet and join operations}},
url = {{http://doi.org/10.1016/j.fss.2024.109116}},
volume = {{497}},
year = {{2024}},
}
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