- Author
- Yao Ouyang, Hua-Peng Zhang, Zhudeng Wang and Bernard De Baets (UGent)
- Organization
- Project
- Abstract
- Internal uninorms on a bounded lattice always output one of the two input values and are nothing else but idempotent uninorms when the lattice is a chain. In this paper, we study the existence and representation of internal uninorms with a given neutral element e on a bounded lattice. We obtain a necessary condition for the existence of such an internal uninorm. In the case that those elements that are incomparable with the neutral element (collected in the set ) constitute a chain, we prove that this necessary condition also becomes a sufficient one and allows to represent any internal uninorm on a bounded lattice in terms of an internal uninorm on the bounded chain obtained by deleting from the lattice and an internal quasi-uninorm on connected via a family of lower sets and a family of upper sets indexed by .
- Keywords
- Internal uninorm, Idempotent uninorm, Lattice
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Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-01HXBKCNJJDVERB1SVJFMGTGKA
- MLA
- Ouyang, Yao, et al. “On the Representation of Internal Uninorms on a Bounded Lattice.” FUZZY SETS AND SYSTEMS, vol. 487, 2024, doi:10.1016/j.fss.2024.108994.
- APA
- Ouyang, Y., Zhang, H.-P., Wang, Z., & De Baets, B. (2024). On the representation of internal uninorms on a bounded lattice. FUZZY SETS AND SYSTEMS, 487. https://doi.org/10.1016/j.fss.2024.108994
- Chicago author-date
- Ouyang, Yao, Hua-Peng Zhang, Zhudeng Wang, and Bernard De Baets. 2024. “On the Representation of Internal Uninorms on a Bounded Lattice.” FUZZY SETS AND SYSTEMS 487. https://doi.org/10.1016/j.fss.2024.108994.
- Chicago author-date (all authors)
- Ouyang, Yao, Hua-Peng Zhang, Zhudeng Wang, and Bernard De Baets. 2024. “On the Representation of Internal Uninorms on a Bounded Lattice.” FUZZY SETS AND SYSTEMS 487. doi:10.1016/j.fss.2024.108994.
- Vancouver
- 1.Ouyang Y, Zhang H-P, Wang Z, De Baets B. On the representation of internal uninorms on a bounded lattice. FUZZY SETS AND SYSTEMS. 2024;487.
- IEEE
- [1]Y. Ouyang, H.-P. Zhang, Z. Wang, and B. De Baets, “On the representation of internal uninorms on a bounded lattice,” FUZZY SETS AND SYSTEMS, vol. 487, 2024.
@article{01HXBKCNJJDVERB1SVJFMGTGKA,
abstract = {{Internal uninorms on a bounded lattice always output one of the two input values and are nothing else but idempotent uninorms when the lattice is a chain. In this paper, we study the existence and representation of internal uninorms with a given neutral element e on a bounded lattice. We obtain a necessary condition for the existence of such an internal uninorm. In the case that those elements that are incomparable with the neutral element (collected in the set
) constitute a chain, we prove that this necessary condition also becomes a sufficient one and allows to represent any internal uninorm on a bounded lattice in terms of an internal uninorm on the bounded chain obtained by deleting
from the lattice and an internal quasi-uninorm on
connected via a family of lower sets and a family of upper sets indexed by
.}},
articleno = {{108994}},
author = {{Ouyang, Yao and Zhang, Hua-Peng and Wang, Zhudeng and De Baets, Bernard}},
issn = {{0165-0114}},
journal = {{FUZZY SETS AND SYSTEMS}},
keywords = {{Internal uninorm,Idempotent uninorm,Lattice}},
language = {{eng}},
pages = {{12}},
title = {{On the representation of internal uninorms on a bounded lattice}},
url = {{http://doi.org/10.1016/j.fss.2024.108994}},
volume = {{487}},
year = {{2024}},
}
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