Galois connections between a fuzzy preordered structure and a general fuzzy structure
- Author
- Inma P Cabrera, Pablo Cordero, Francisca Garcia-Pardo, Manuel Ojeda-Aciego and Bernard De Baets (UGent)
- Organization
- Abstract
- We continue the study of (isotone) Galois connections, also called adjunctions, in the framework of fuzzy preordered structures, which generalize fuzzy preposets by considering underlying fuzzy equivalence relations. Specifically, we present necessary and sufficient conditions so that, given amapping f :A -> B from a fuzzy preordered structure A = < A, approximate to(A),rho(A)> into a fuzzy structure < B, approximate to(B)>, it is possible to construct a fuzzy relation rho(B) that induces a suitable fuzzy preorder structure on B and such that there exists a mapping g : B -> A such that the pair (f, g) constitutes an Galois connection.
- Keywords
- Fuzzy sets, Galois connection, preorder, KNOWLEDGE DISCOVERY, CONCEPT LATTICES, ADJUNCTIONS, CLASSIFICATION, CONSTRUCTION, TREES
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Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-8578995
- MLA
- Cabrera, Inma P., et al. “Galois Connections between a Fuzzy Preordered Structure and a General Fuzzy Structure.” IEEE TRANSACTIONS ON FUZZY SYSTEMS, vol. 26, no. 3, 2018, pp. 1274–87, doi:10.1109/tfuzz.2017.2718495.
- APA
- Cabrera, I. P., Cordero, P., Garcia-Pardo, F., Ojeda-Aciego, M., & De Baets, B. (2018). Galois connections between a fuzzy preordered structure and a general fuzzy structure. IEEE TRANSACTIONS ON FUZZY SYSTEMS, 26(3), 1274–1287. https://doi.org/10.1109/tfuzz.2017.2718495
- Chicago author-date
- Cabrera, Inma P, Pablo Cordero, Francisca Garcia-Pardo, Manuel Ojeda-Aciego, and Bernard De Baets. 2018. “Galois Connections between a Fuzzy Preordered Structure and a General Fuzzy Structure.” IEEE TRANSACTIONS ON FUZZY SYSTEMS 26 (3): 1274–87. https://doi.org/10.1109/tfuzz.2017.2718495.
- Chicago author-date (all authors)
- Cabrera, Inma P, Pablo Cordero, Francisca Garcia-Pardo, Manuel Ojeda-Aciego, and Bernard De Baets. 2018. “Galois Connections between a Fuzzy Preordered Structure and a General Fuzzy Structure.” IEEE TRANSACTIONS ON FUZZY SYSTEMS 26 (3): 1274–1287. doi:10.1109/tfuzz.2017.2718495.
- Vancouver
- 1.Cabrera IP, Cordero P, Garcia-Pardo F, Ojeda-Aciego M, De Baets B. Galois connections between a fuzzy preordered structure and a general fuzzy structure. IEEE TRANSACTIONS ON FUZZY SYSTEMS. 2018;26(3):1274–87.
- IEEE
- [1]I. P. Cabrera, P. Cordero, F. Garcia-Pardo, M. Ojeda-Aciego, and B. De Baets, “Galois connections between a fuzzy preordered structure and a general fuzzy structure,” IEEE TRANSACTIONS ON FUZZY SYSTEMS, vol. 26, no. 3, pp. 1274–1287, 2018.
@article{8578995,
abstract = {{We continue the study of (isotone) Galois connections, also called adjunctions, in the framework of fuzzy preordered structures, which generalize fuzzy preposets by considering underlying fuzzy equivalence relations. Specifically, we present necessary and sufficient conditions so that, given amapping f :A -> B from a fuzzy preordered structure A = < A, approximate to(A),rho(A)> into a fuzzy structure < B, approximate to(B)>, it is possible to construct a fuzzy relation rho(B) that induces a suitable fuzzy preorder structure on B and such that there exists a mapping g : B -> A such that the pair (f, g) constitutes an Galois connection.}},
author = {{Cabrera, Inma P and Cordero, Pablo and Garcia-Pardo, Francisca and Ojeda-Aciego, Manuel and De Baets, Bernard}},
issn = {{1063-6706}},
journal = {{IEEE TRANSACTIONS ON FUZZY SYSTEMS}},
keywords = {{Fuzzy sets,Galois connection,preorder,KNOWLEDGE DISCOVERY,CONCEPT LATTICES,ADJUNCTIONS,CLASSIFICATION,CONSTRUCTION,TREES}},
language = {{eng}},
number = {{3}},
pages = {{1274--1287}},
title = {{Galois connections between a fuzzy preordered structure and a general fuzzy structure}},
url = {{http://doi.org/10.1109/tfuzz.2017.2718495}},
volume = {{26}},
year = {{2018}},
}
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