Francisca García-Pardo

On galois connections and soft computing

After recalling the different interpretations usually assigned to the term Galois connection, both in the crisp and in the fuzzy case, we survey on several of their applications in Computer Science and specifically, in Soft Computing.

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

Given a mappingf:A->B from a (pre-)ordered set A into an unstructured set B, we study the problem of defining a suitable (pre-)ordering relation on B such that there exists a mapping g:B->A such that the pair of mappings (f,g) forms an adjunction between (pre-)ordered sets. The necessary and sufficient conditions obtained are then expressed in terms of closure operators and closure systems.

Generating Isotone Galois Connections on an Unstructured Codomain

Given a mapping f : A → B from a partially ordered set A into an unstructured set B, we study the problem of defining a suitable partial ordering relation on B such that there exists a mapping g : B → A such that the pair of mappings (f,g) forms an isotone Galois connection between partially ordered sets.

On the construction of adjunctions between a fuzzy preposet and an unstructured set

In this work, we focus on adjunctions, also called isotone Galois connections, in the framework of fuzzy preordered sets (hereafter, fuzzy preposets). Specifically, we present necessary and sufficient conditions so that, given a mapping f:A→B from a fuzzy preposet A into an unstructured set B, it is possible to construct a suitable fuzzy preorder relation on B for which there exists a mapping g:B→A such that the pair (f,g) constitutes an adjunction.

On the Existence of Isotone Galois Connections between Preorders

Given a mapping f : A → B from a preordered set A into an unstructured set B, we study the problem of defining a suitable preordering relation on B such that there exists a mapping g : B → A such that the pair (f,g) forms an adjunction between preordered sets.

On Adjunctions between Fuzzy Preordered Sets: Necessary Conditions

There exists a direct relation between fuzzy rough sets and fuzzy preorders. On the other hand, it is well known the existing parallelism between Formal Concept Analysis and Rough Set Theory. In both cases, Galois connections play a central role. In this work, we focus on adjunctions (also named isotone Galois connections) between fuzzy preordered sets; specifically, we study necessary conditions that have to be fulfilled in order such an adjunction to exist.

On Closure Systems and Adjunctions Between Fuzzy Preordered Sets

The aim of this work is providing a characterization in terms of closure systems, for the construction, given a mapping \(f:\mathbb A\rightarrow B\) from a fuzzy preordered set \(\mathbb A\) into an unstructured set B, of a suitable fuzzy preordering on B for which there exists a mapping \(g:B\rightarrow A\) such that the pair (f, g) constitutes an adjunction (isotone Galois connection). This contribution continues our research line on the construction of adjunctions in which the theory of fuzzy closure systems is used in order to provide a more meaningful framework for the extension to the fuzzy case of previous results.

On Fuzzy Preordered Sets and Monotone Galois Connections

In this work, we focus on the study of necessary and sufficient conditions in order to ensure the existence (under some constraints) of monotone Galois connections between fuzzy preordered sets.