Open Access
Application of the L-fuzzy concept analysis in the morphological image and signal processing
(Springer International Publishing, 2014) Alcalde, Cristina; Burusco Juandeaburre, Ana; Fuentes González, Ramón; Automática y Computación; Automatika eta Konputazioa; Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa
In this work we are going to set up a new relationship between the L-fuzzy Concept Analysis and the Fuzzy Mathematical Morphology. Specifically we prove that the problem of finding fuzzy images or signals that remain invariant under a fuzzy morphological opening or under a fuzzy morphological closing, is equal to the problem of finding the L-fuzzy concepts of some L-fuzzy context. Moreover, since the Formal Concept Analysis and the Mathematical Morphology are the particular cases of the fuzzy ones, the showed result has also an interpretation for binary images or signals.
Open Access
Linking mathematical morphology and L-fuzzy concepts
(World Scientific, 2017) Alcalde, Cristina; Burusco Juandeaburre, Ana; Bustince Sola, Humberto; Fuentes González, Ramón; Sesma Sara, Mikel; Automatika eta Konputazioa; Institute of Smart Cities - ISC; Automática y Computación
In this paper we study the relation between L-fuzzy morphology and L-fuzzy concepts over complete lattices. In particular, we show how the erosion and dilation operators of the former can be understood in terms of the derivation operators of the latter, even when the set of objects is different from the set of attributes.
Open Access
The study of fuzzy context sequences
(Atlantis Press and Taylor & Francis, 2013) Alcalde, Cristina; Burusco Juandeaburre, Ana; Fuentes González, Ramón; Automática y Computación; Automatika eta Konputazioa; Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa
In some cases, the relationship between an object set X and an attribute set Y is set up by means of a fuzzy context sequence. A particular case of this situation appears when we want to study the evolution of an L-fuzzy context in time. In this work, we analyze these situations. First we introduce the fuzzy context sequence definition and remind the main results about OWA operators. With the aid of these operators, we propose an exhaustive study of the different contexts values of the sequence using some new relations. In the second part, we also study the fuzzy context sequences establishing tendencies and temporal patterns. Finally, we illustrate all the results by means of examples.
Open Access
The use of two relations in L-fuzzy contexts
(Elsevier, 2015) Alcalde, Cristina; Burusco Juandeaburre, Ana; Fuentes González, Ramón; Automática y Computación; Automatika eta Konputazioa; Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa
In the analysis of relations among the elements of two sets it is usual to obtain different values depending on the point of view from which these relations are measured. The main goal of the paper is the modelization of these situations by means of a generalization of the L-fuzzy concept analysis called L-fuzzy bicontext. We study the L-fuzzy concepts of these L-fuzzy bicontexts obtaining some interesting results. Specifically, we will be able to classify the biconcepts of the L-fuzzy bicontext. Finally, a practical case is developed using this new tool.
Open Access
On the modeling of the concept: “The Contents of the Empty Set" using the activity orderings family (⊑w)w∈L in a distributive lattice ( L, ≤ ). An interpretation of those order relations ⊑w as alternative inclusions (“w-Inclusions") and of its associated inf- operators ⨅w as additional intersections (“w-Intersections”), both in the Intuitive set theory and in the L-fuzzy set theory. (In Spanish)
(2018) Fuentes González, Ramón; Ingeniería Matemática e Informática; Matematika eta Informatika Ingeniaritza
A mathematical model is presented to define new inclusions, intersections and unions as alternatives to the usual ones between crisp and fuzzy subsets. In particular, the concept of “the non-trivial content of the empty set ∅” is analyzed. This proposed model is based on the interconnection of two consolidated mathematical concepts in specialized literature: One, (which belongs to the field of image processing using Mathematical Morphology techniques), is that of order of activity and that we use here in the general context of lattices (L, ≤) and in particular in that of Boolean Algebras. The other consists of a version in distributive lattices (L, ≤) of the symmetric difference operator Δ, a classic concept in Set Theory. The utility of the model is illustrated in the following fields: analysis of risk maps, (areas of avalanches, risk of fires, landslides, earthquakes, ...), as well as maps with contour lines: (isochrons, isotherms, salinity , rainfall, intensity of earthquakes, ...). Also in data pre-processing for “Data Mining” tasks and in “Data Analysis with Uncertainty”. A special section is dedicated to the application of the model in Digital Image Processing using Mathematical Morphology techniques. Finally, it is justified that the model can be useful in other fields such as Analysis of Formal Concepts, Probability and in theoretical contexts such as Topology.