Fuzzy relational Galois connections between fuzzy transitive digraphs - De-las-Peñas-Cabrera, Inmaculada; Cordero-Ortega, Pablo; Muñoz-Velasco, Emilio José; Ojeda-Aciego, Manuel; De Baets, Bernard (Elsevier, 2022)
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.
Keywords: Galois, Teoría de; Galois connection; Fuzzy transitive digraph