Galois Connections Between a Fuzzy Preordered Structure and a General Fuzzy Structure

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Authors

Inma P. Cabrera

Pablo Cordero

Francisca García-Pardo

Manuel Ojeda-Aciego

Bernard De Baets

Published

1 January 2018

Publication details

{IEEE} Trans. Fuzzy Syst. vol. 26 (3), pages 1274–1287.

Links

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 a mapping f : A → B from a fuzzy preordered structure A = 〈A, ≈ _A , _ρA 〉 into a fuzzy structure 〈B, ≈ _B 〉, it is possible to construct a fuzzy relation ρ _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.

Citation

Please, cite this work as:

[Cab+18] I. P. Cabrera, P. Cordero, F. Garc'-Pardo, et al. “Galois Connections Between a Fuzzy Preordered Structure and a General Fuzzy Structure”. In: IEEE Trans. Fuzzy Syst. 26.3 (2018), pp. 1274-1287. DOI: 10.1109/TFUZZ.2017.2718495. URL: https://doi.org/10.1109/TFUZZ.2017.2718495.

BibTeX

@Article{Cabrera2018,
     author = {Inma P. Cabrera and Pablo Cordero and Francisca Garc'-Pardo and Manuel Ojeda-Aciego and Bernard De Baets},
     journal = {{IEEE} Trans. Fuzzy Syst.},
     title = {Galois Connections Between a Fuzzy Preordered Structure and a General Fuzzy Structure},
     year = {2018},
     number = {3},
     pages = {1274–1287},
     volume = {26},
     bibsource = {dblp computer science bibliography, https://dblp.org},
     biburl = {https://dblp.org/rec/journals/tfs/CabreraCGOB18.bib},
     doi = {10.1109/TFUZZ.2017.2718495},
     timestamp = {Sat, 30 Sep 2023 01:00:00 +0200},
     url = {https://doi.org/10.1109/TFUZZ.2017.2718495},
}

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Citations
CrossRef - Citation Indexes: 12
Scopus - Citation Indexes: 24

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Mendeley - Readers: 8

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Papers citing this work

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

[1] Ľ. Antoni, P. Eliaš, S. Krajči, et al. “Heterogeneous formal context and its decomposition by heterogeneous fuzzy subsets”. In: Fuzzy Sets and Systems 451 (Dec. 2022), p. 361–384. ISSN: 0165-0114. DOI: 10.1016/j.fss.2022.05.015. URL: http://dx.doi.org/10.1016/j.fss.2022.05.015.

[2] I. P. Cabrera, P. Cordero, E. Muñoz-Velasco, et al. “A Relational Extension of Galois Connections”. In: Formal Concept Analysis. Springer International Publishing, 2019, p. 290–303. ISBN: 9783030214623. DOI: 10.1007/978-3-030-21462-3_19. URL: http://dx.doi.org/10.1007/978-3-030-21462-3_19.

[3] I. P. Cabrera, P. Cordero, E. Muñoz-Velasco, et al. “Galois Connections Between Unbalanced Structures in a Fuzzy Framework”. In: Information Processing and Management of Uncertainty in Knowledge-Based Systems. Springer International Publishing, 2020, p. 736–747. ISBN: 9783030501532. DOI: 10.1007/978-3-030-50153-2_54. URL: http://dx.doi.org/10.1007/978-3-030-50153-2_54.

[4] I. P. Cabrera, P. Cordero, E. Muñoz-Velasco, et al. “Relational Connections Between Preordered Sets”. In: Applied Physics, System Science and Computers III. Springer International Publishing, 2019, p. 163–169. ISBN: 9783030215071. DOI: 10.1007/978-3-030-21507-1_24. URL: http://dx.doi.org/10.1007/978-3-030-21507-1_24.

[5] 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.

[6] I. P. Cabrera, P. Cordero, E. Muñoz-Velasco, et al. “Relational Galois connections between transitive digraphs: Characterization and construction”. In: Information Sciences 519 (May. 2020), p. 439–450. ISSN: 0020-0255. DOI: 10.1016/j.ins.2020.01.034. URL: http://dx.doi.org/10.1016/j.ins.2020.01.034.

[7] I. P. Cabrera, P. Cordero, E. Muñoz‐Velasco, et al. “Relational Galois connections between transitive fuzzy digraphs”. In: Mathematical Methods in the Applied Sciences 43.9 (Feb. 2020), p. 5673–5680. ISSN: 1099-1476. DOI: 10.1002/mma.6302. URL: http://dx.doi.org/10.1002/mma.6302.

[8] 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.

[9] I. Cabrera, P. Cordero, and M. Ojeda-Aciego. “Galois connections in computational intelligence: A short survey”. In: 2017 IEEE Symposium Series on Computational Intelligence (SSCI). IEEE, Nov. 2017, p. 1–7. DOI: 10.1109/ssci.2017.8285310. URL: http://dx.doi.org/10.1109/ssci.2017.8285310.

[10] M. E. Cornejo, J. Medina, and E. Ramírez-Poussa. “Implication operators generating pairs of weak negations and their algebraic structure”. In: Fuzzy Sets and Systems 405 (Feb. 2021), p. 18–39. ISSN: 0165-0114. DOI: 10.1016/j.fss.2020.01.008. URL: http://dx.doi.org/10.1016/j.fss.2020.01.008.

[11] M. Demirci. “A characterization of categorical many-valued partial orderings by categorical topologies and an application to comma categories”. In: Fuzzy Sets and Systems 469 (Oct. 2023), p. 108629. ISSN: 0165-0114. DOI: 10.1016/j.fss.2023.108629. URL: http://dx.doi.org/10.1016/j.fss.2023.108629.

[12] M. Demirci. “Many-valued partial orders in a closed monoidal category”. In: Fuzzy Sets and Systems 468 (Sep. 2023), p. 108591. ISSN: 0165-0114. DOI: 10.1016/j.fss.2023.108591. URL: http://dx.doi.org/10.1016/j.fss.2023.108591.

[13] B. Farhadinia and F. Chiclana. “Extended Fuzzy Sets and Their Applications”. In: Mathematics 9.7 (Apr. 2021), p. 770. ISSN: 2227-7390. DOI: 10.3390/math9070770. URL: http://dx.doi.org/10.3390/math9070770.

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[18] M. Ojeda-Hernández, I. P. Cabrera, and P. Cordero. “Quasi-closed elements in fuzzy posets”. In: Journal of Computational and Applied Mathematics 404 (Apr. 2022), p. 113390. ISSN: 0377-0427. DOI: 10.1016/j.cam.2021.113390. URL: http://dx.doi.org/10.1016/j.cam.2021.113390.

[19] 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.

[20] M. Ojeda-Hernández, I. P. Cabrera, P. Cordero, et al. “Closure Systems as a Fuzzy Extension of Meet-subsemilattices”. In: Joint Proceedings of the 19th World Congress of the International Fuzzy Systems Association (IFSA), the 12th Conference of the European Society for Fuzzy Logic and Technology (EUSFLAT), and the 11th International Summer School on Aggregation Operators (AGOP). ifsa-eusflat-agop-21. Atlantis Press, 2021. DOI: 10.2991/asum.k.210827.006. URL: http://dx.doi.org/10.2991/asum.k.210827.006.

[21] M. Ojeda-Hernández, I. P. Cabrera, P. Cordero, et al. “Fuzzy closure systems: Motivation, definition and properties”. In: International Journal of Approximate Reasoning 148 (Sep. 2022), p. 151–161. ISSN: 0888-613X. DOI: 10.1016/j.ijar.2022.06.004. URL: http://dx.doi.org/10.1016/j.ijar.2022.06.004.

[22] M. Ojeda-Hernández, I. P. Cabrera, P. Cordero, et al. “Relational Extension of Closure Structures”. In: Information Processing and Management of Uncertainty in Knowledge-Based Systems. Springer International Publishing, 2022, p. 77–86. ISBN: 9783031089718. DOI: 10.1007/978-3-031-08971-8_7. URL: http://dx.doi.org/10.1007/978-3-031-08971-8_7.

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