A dissection of the monotonicity property of binary operations from a dominance point of view
- Author
- Yuntian Wang, Lemnaouar Zedam (UGent) , Bao Qing Hu and Bernard De Baets (UGent)
- Organization
- Abstract
- In this paper, we expound weaker forms of increasingness of binary operations on a lattice by reducing the number of variables involved in the classical formulation of the increasingness property as seen from the viewpoint of dominance between binary operations. We investigate the relationships among these weaker forms. Furthermore, we demonstrate the role of these weaker forms in characterizing the meet and join operations of a lattice and a chain in particular. Finally, we provide ample generic examples.
- Keywords
- Binary operation, Increasingness, Dominance relation, Lattice, AGGREGATION OPERATORS, NORMS
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Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-01JASKKGYGNMDG1CAC3S0HVH1Q
- MLA
- Wang, Yuntian, et al. “A Dissection of the Monotonicity Property of Binary Operations from a Dominance Point of View.” INTERNATIONAL JOURNAL OF APPROXIMATE REASONING, vol. 175, 2024, doi:10.1016/j.ijar.2024.109304.
- APA
- Wang, Y., Zedam, L., Hu, B. Q., & De Baets, B. (2024). A dissection of the monotonicity property of binary operations from a dominance point of view. INTERNATIONAL JOURNAL OF APPROXIMATE REASONING, 175. https://doi.org/10.1016/j.ijar.2024.109304
- Chicago author-date
- Wang, Yuntian, Lemnaouar Zedam, Bao Qing Hu, and Bernard De Baets. 2024. “A Dissection of the Monotonicity Property of Binary Operations from a Dominance Point of View.” INTERNATIONAL JOURNAL OF APPROXIMATE REASONING 175. https://doi.org/10.1016/j.ijar.2024.109304.
- Chicago author-date (all authors)
- Wang, Yuntian, Lemnaouar Zedam, Bao Qing Hu, and Bernard De Baets. 2024. “A Dissection of the Monotonicity Property of Binary Operations from a Dominance Point of View.” INTERNATIONAL JOURNAL OF APPROXIMATE REASONING 175. doi:10.1016/j.ijar.2024.109304.
- Vancouver
- 1.Wang Y, Zedam L, Hu BQ, De Baets B. A dissection of the monotonicity property of binary operations from a dominance point of view. INTERNATIONAL JOURNAL OF APPROXIMATE REASONING. 2024;175.
- IEEE
- [1]Y. Wang, L. Zedam, B. Q. Hu, and B. De Baets, “A dissection of the monotonicity property of binary operations from a dominance point of view,” INTERNATIONAL JOURNAL OF APPROXIMATE REASONING, vol. 175, 2024.
@article{01JASKKGYGNMDG1CAC3S0HVH1Q,
abstract = {{In this paper, we expound weaker forms of increasingness of binary operations on a lattice by reducing the number of variables involved in the classical formulation of the increasingness property as seen from the viewpoint of dominance between binary operations. We investigate the relationships among these weaker forms. Furthermore, we demonstrate the role of these weaker forms in characterizing the meet and join operations of a lattice and a chain in particular. Finally, we provide ample generic examples.}},
articleno = {{109304}},
author = {{Wang, Yuntian and Zedam, Lemnaouar and Hu, Bao Qing and De Baets, Bernard}},
issn = {{0888-613X}},
journal = {{INTERNATIONAL JOURNAL OF APPROXIMATE REASONING}},
keywords = {{Binary operation,Increasingness,Dominance relation,Lattice,AGGREGATION OPERATORS,NORMS}},
language = {{eng}},
pages = {{25}},
title = {{A dissection of the monotonicity property of binary operations from a dominance point of view}},
url = {{http://doi.org/10.1016/j.ijar.2024.109304}},
volume = {{175}},
year = {{2024}},
}
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