Fuzzy relational Galois connections between fuzzy transitive digraphs

 

Abstract

We present a fuzzy version of the notion of relational Galois connection between fuzzy transitive directed graphs (fuzzy T-digraphs) on the specific setting in which the underlying algebra of truth values is a complete Heyting algebra. The components of such fuzzy Galois connection are fuzzy relations satisfying certain reasonable properties expressed in terms of the so-called full powering. Moreover, we provide a necessary and sufficient condition under which it is possible to construct a right adjoint for a given fuzzy relation between a fuzzy T-digraph and an unstructured set.

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Please, cite this work as:

[Cab+23] I. Cabrera, P. Cordero, E. Muñoz-Velasco, et al. “Fuzzy relational Galois connections between fuzzy transitive digraphs”. In: Fuzzy Sets and Systems 463 (2023). Cited by: 0; All Open Access, Green Open Access, Hybrid Gold Open Access. DOI: 10.1016/j.fss.2022.12.012. URL: [https://www.scopus.com/inward/record.uri?eid=2-s2.0-85146018750&doi=10.1016

NoteBibTeX

@ARTICLE{Cabrera2023,
     author = {Cabrera, I.P. and Cordero, P. and Muñoz-Velasco, E. and Ojeda-Aciego, M. and De Baets, B.},
     title = {Fuzzy relational Galois connections between fuzzy transitive digraphs},
     year = {2023},
     journal = {Fuzzy Sets and Systems},
     volume = {463},
     doi = {10.1016/j.fss.2022.12.012},
     url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85146018750&doi=10.1016%2fj.fss.2022.12.012&partnerID=40&md5=ab3b57e7c17a2ee95c32bf4300fc353d},
     type = {Article},
     publication_stage = {Final},
     source = {Scopus},
     note = {Cited by: 0; All Open Access, Green Open Access, Hybrid Gold Open Access}
}

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Fuzzy relational Galois connections between fuzzy transitive digraphs

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Papers citing this work

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[1] 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.

[2] F. Pérez-Gámez and C. Bejines. “An exploration of weak Heyting algebras: Characterization and properties”. In: International Journal of Approximate Reasoning 179 (Apr. 2025), p. 109365. ISSN: 0888-613X. DOI: 10.1016/j.ijar.2025.109365. URL: http://dx.doi.org/10.1016/j.ijar.2025.109365.