Relational Galois connections between transitive fuzzy digraphs

 

Abstract

Fuzzy-directed graphs are often chosen as the data structure to model and implement solutions to several problems in the applied sciences. Galois connections have also shown to be useful both in theoretical and in practical problems.

In this paper, the notion of relational Galois connection is extended to be applied between transitive fuzzy directed graphs. In this framework, the components of the connection are crisp relations satisfying certain reasonable properties given in terms of the so-called full powering.

Funding

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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 fuzzy digraphs”. In: Mathematical Methods in the Applied Sciences 43.9 (2020). Cited by: 8, p. 5673 – 5680. DOI: 10.1002/mma.6302. URL: [https://www.scopus.com/inward/record.uri?eid=2-s2.0-85084927857&doi=10.1002

BibTeX

@ARTICLE{Cabrera20205673,
     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 fuzzy digraphs},
     year = {2020},
     journal = {Mathematical Methods in the Applied Sciences},
     volume = {43},
     number = {9},
     pages = {5673 – 5680},
     doi = {10.1002/mma.6302},
     url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85084927857&doi=10.1002%2fmma.6302&partnerID=40&md5=f62ecd3bbabdb3af560c55aac0694690},
     type = {Article},
     publication_stage = {Final},
     source = {Scopus},
     note = {Cited by: 8}
}

Bibliometric data

The following data has been extracted from resources such as OpenAlex, Dimensions, PlumX or Altmetric.

7

CITATIONS

7 Total citations

2 Recent citations

4.48 Field Citation Ratio

n/a Relative Citation Ratio

• Citations
• CrossRef - Citation Indexes: 7
• Scopus - Citation Indexes: 8

• Captures
• Mendeley - Readers: 3

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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] 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.

[2] 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.

[3] 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.

[4] N. Madrid and M. Ojeda‐Aciego. “A measure of consistency for fuzzy logic theories”. In: Mathematical Methods in the Applied Sciences 46.15 (May. 2021), p. 15982–15995. ISSN: 1099-1476. DOI: 10.1002/mma.7470. URL: http://dx.doi.org/10.1002/mma.7470.

[5] 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.

[6] 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.

[7] 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.

[8] 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.

[9] 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.