Relational Galois connections between transitive digraphs: Characterization and construction

 

Abstract

This paper focuses on a twofold relational generalization of the notion of Galois connection. It is twofold because it is defined between sets endowed with arbitrary transitive relations and, moreover, both components of the connection are relations, not necessarily functions. A characterization theorem of the notion of relational Galois connection is provided and, then, it is proved that a suitable notion of closure can be obtained within this framework. Finally, we state a necessary and sufficient condition that allows to build a relational Galois connection starting from a single transitive digraph and a single binary relation.

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Citation

Please, cite this work as:

[Cab+20] I. P. Cabrera, P. Cordero, E. Muñoz-Velasco, et al. “Relational Galois connections between transitive digraphs: Characterization and construction”. In: Information Sciences 519 (2020). Cited by: 8; All Open Access, Green Open Access, p. 439 – 450. DOI: 10.1016/j.ins.2020.01.034. URL: [https://www.scopus.com/inward/record.uri?eid=2-s2.0-85079160299&doi=10.1016

BibTeX

@ARTICLE{Cabrera2020439,
     author = {Cabrera, Inma P. and Cordero, Pablo and Muñoz-Velasco, Emilio and Ojeda-Aciego, Manuel and De Baets, Bernard},
     title = {Relational Galois connections between transitive digraphs: Characterization and construction},
     year = {2020},
     journal = {Information Sciences},
     volume = {519},
     pages = {439 – 450},
     doi = {10.1016/j.ins.2020.01.034},
     url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85079160299&doi=10.1016%2fj.ins.2020.01.034&partnerID=40&md5=2d80ac2cb125c6e9326073eb92a4f5a4},
     type = {Article},
     publication_stage = {Final},
     source = {Scopus},
     note = {Cited by: 8; All Open Access, Green Open Access}
}

Bibliometric data

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9

CITATIONS

9 Total citations

1 Recent citation

5.45 Field Citation Ratio

n/a Relative Citation Ratio

• Citations
• CrossRef - Citation Indexes: 9
• Scopus - Citation Indexes: 8

• Captures
• Mendeley - Readers: 11

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Cites

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Papers citing this work

The following is a non-exhaustive list of papers that cite this work:

[1] R. G. Aragón, J. Medina, and E. Ramírez-Poussa. “Characterization of the Infimum of Classes Induced by an Attribute Reduction in FCA”. In: Computational Intelligence and Mathematics for Tackling Complex Problems 3. Springer International Publishing, Aug. 2021, p. 73–79. ISBN: 9783030749705. DOI: 10.1007/978-3-030-74970-5_9. URL: http://dx.doi.org/10.1007/978-3-030-74970-5_9.

[2] R. G. Aragón, J. Medina, and E. Ramírez-Poussa. “Identifying Non-Sublattice Equivalence Classes Induced by an Attribute Reduction in FCA”. In: Mathematics 9.5 (Mar. 2021), p. 565. ISSN: 2227-7390. DOI: 10.3390/math9050565. URL: http://dx.doi.org/10.3390/math9050565.

[3] I. P. Cabrera, P. Cordero, E. Muñoz-Velasco, et al. “On the Definition of Fuzzy Relational Galois Connections Between Fuzzy Transitive Digraphs”. In: Information Processing and Management of Uncertainty in Knowledge-Based Systems. Springer International Publishing, 2022, p. 100–106. ISBN: 9783031089718. DOI: 10.1007/978-3-031-08971-8_9. URL: http://dx.doi.org/10.1007/978-3-031-08971-8_9.

[4] I. Cabrera, P. Cordero, E. Muñoz-Velasco, et al. “Fuzzy relational Galois connections between fuzzy transitive digraphs”. In: Fuzzy Sets and Systems 463 (Jul. 2023), p. 108456. ISSN: 0165-0114. DOI: 10.1016/j.fss.2022.12.012. URL: http://dx.doi.org/10.1016/j.fss.2022.12.012.

[5] N. Madrid and M. Ojeda-Aciego. “The f-index of inclusion as optimal adjoint pair for fuzzy modus ponens”. In: Fuzzy Sets and Systems 466 (Aug. 2023), p. 108474. ISSN: 0165-0114. DOI: 10.1016/j.fss.2023.01.009. URL: http://dx.doi.org/10.1016/j.fss.2023.01.009.

[6] S. Nagar, P. Bhanodia, K. K. Sethi, et al. “Cross-Domain and Decision Tree-Based Approach for Human Sentiment Analysis”. In: Data Science and Big Data Analytics. Springer Nature Singapore, 2025, p. 339–355. ISBN: 9789819798551. DOI: 10.1007/978-981-97-9855-1_24. URL: http://dx.doi.org/10.1007/978-981-97-9855-1_24.

[7] M. Ojeda-Hernandez, I. P. Cabrera, P. Cordero, et al. “On (fuzzy) closure systems in complete fuzzy lattices”. In: 2021 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE). IEEE, Jul. 2021, p. 1–6. DOI: 10.1109/fuzz45933.2021.9494404. URL: http://dx.doi.org/10.1109/fuzz45933.2021.9494404.

[8] M. Ojeda-Hernández, I. P. Cabrera, P. Cordero, et al. “Fuzzy closure relations”. In: Fuzzy Sets and Systems 450 (Dec. 2022), p. 118–132. ISSN: 0165-0114. DOI: 10.1016/j.fss.2022.05.016. URL: http://dx.doi.org/10.1016/j.fss.2022.05.016.

[9] M. Ojeda-Hernández, I. P. Cabrera, P. Cordero, et al. “Fuzzy closure structures as formal concepts”. In: Fuzzy Sets and Systems 463 (Jul. 2023), p. 108458. ISSN: 0165-0114. DOI: 10.1016/j.fss.2022.12.014. URL: http://dx.doi.org/10.1016/j.fss.2022.12.014.