Abstract
We continue the study of different generalizations of the notion of Galois connection. Previously, we had focused on the cases in which both the domain and codomain had the structure of either a transitive digraph or a fuzzy transitive digraph. Here, we extend it to the fuzzy relational framework. Specifically, we present a suitable notion of fuzzy relational Galois connection between fuzzy transitive digraphs where both components are now fuzzy relations and the underlying truth value algebra is a complete Heyting algebra. The resulting notion of fuzzy relational Galois connection inherits interesting characterisations of the notion of (crisp) relational Galois connection.
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Notes
- 1.
For convenience, hereafter, we will always omit the prefix \(\mathbb L\).
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Acknowledgements
Partially supported by the Spanish Ministry of Science, Innovation, and Universities (MCIU), State Agency of Research (AEI), Junta de Andalucía (JA), Universidad de Málaga (UMA) and European Regional Development Fund (FEDER) through the projects PGC2018-095869-B-I00 and TIN2017-89023-P (MCIU/AEI/FEDER), and UMA2018-FEDERJA-001 (JA/UMA/FEDER).
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Cabrera, I.P., Cordero, P., Muñoz-Velasco, E., Ojeda-Aciego, M., De Baets, B. (2022). On the Definition of Fuzzy Relational Galois Connections Between Fuzzy Transitive Digraphs. In: Ciucci, D., et al. Information Processing and Management of Uncertainty in Knowledge-Based Systems. IPMU 2022. Communications in Computer and Information Science, vol 1601. Springer, Cham. https://doi.org/10.1007/978-3-031-08971-8_9
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