On the definition of suitable orderings to generate adjunctions over an unstructured codomain

García-Pardo, Francisca; Cabrera, Inma P.; Cordero, Pablo; Ojeda‐Aciego, Manuel; Rodríguez, Francisco J.

doi:10.1016/j.ins.2014.07.006

Cited by 18 publications

(1 citation statement)

References 38 publications

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“…In this paper, we continue our research line on the construction of Galois connections between sets with unbalanced structures initiated in Garcia‐Pardo et al, where we attempted to characterize the existence of the right part of a Galois connection of a given mapping between sets with a different structure (it is precisely this condition of different structure that makes this problem to be outside the scope of Freyd's adjoint functor theorem). Since then, we have obtained results in several frameworks: for instance, in Garcia‐Pardo et al, given a mapping from a (pre‐)ordered set

false(A, ⩽_{A} false)

into an unstructured set

B

, we solved the problem of completing the structure of

B

, namely, defining a suitable (pre‐)ordering relation

⩽_{B}

B

, such that there exists a mapping such that the pair of mappings forms an isotone Galois connection (or adjunction) between the (pre‐)ordered sets

false(A, ⩽_{A} false)

and

false(B, ⩽_{B} false)

. Later, in Cabrera et al, we moved to the fuzzy framework by considering the corresponding problem between a fuzzy preposet

false(A, ρ false)

and an unstructured

B

; this work was recently extended in Cabrera et al, by considering that equality is expressed by a fuzzy equivalence relation, so that the problem considers a mapping between a fuzzy preordered structure

false(A, \approx_{A}, ρ false)

and a fuzzy structure

false(B, \approx_{B} false)

.…”

Section: Introductionmentioning

confidence: 99%

Relational Galois connections between transitive fuzzy digraphs

Cabrera

Muñoz‐Velasco

Ojeda‐Aciego

et al. 2020

Math Methods in App Sciences

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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.

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