Open Access
Multivalued contexts associated with criteria
(Taylor & Francis, 2018) Alcalde, Cristina; Burusco Juandeaburre, Ana; Automatika eta Konputazioa; Institute of Smart Cities - ISC; Automática y Computación; Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa
We are interested in the study of L-fuzzy contexts taking into account different criteria. These contexts arise when we want to analyze the relationship between objects and attributes from different points of view. Furthermore, in some occasions, these L-fuzzy contexts have several values for every pair object attribute. We will see how both the WOWA operators and the Choquet integrals will be interesting tools for the aggregation processes that we are going to carry out.
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
Evolution in time of L-fuzzy context sequences
(Elsevier, 2016) Alcalde, Cristina; Burusco Juandeaburre, Ana; Bustince Sola, Humberto; Jurío Munárriz, Aránzazu; Sanz Delgado, José Antonio; Automatika eta Konputazioa; Institute of Smart Cities - ISC; Automática y Computación; Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa
In this work, we consider a complete lattice L and we study L-fuzzy context sequences which represent the evolution in time of an L-fuzzy context. To carry out this study, in the first part of the paper, we consider n-ary OWA operators in complete lattices, which enable us to make a general analysis and a temporal analysis at any moment in time of L-fuzzy context sequences. After that, evolution in time of the relationship between the objects and the attributes is considered. In particular, we analyze the concepts of Trend and Persistent formal contexts. Finally, we illustrate our results with an example where we consider the particular lattice L = J ([0, 1]).
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
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
New measures for comparing matrices and their application to image processing
(Elsevier, 2018) Sesma Sara, Mikel; Miguel Turullols, Laura de; Pagola Barrio, Miguel; Burusco Juandeaburre, Ana; Mesiar, Radko; Bustince Sola, Humberto; Automatika eta Konputazioa; Institute of Smart Cities - ISC; Automática y Computación; Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa
In this work we present the class of matrix resemblance functions, i.e., functions that measure the difference between two matrices. We present two construction methods and study the properties that matrix resemblance functions satisfy, which suggest that this class of functions is an appropriate tool for comparing images. Hence, we present a comparison method for grayscale images whose result is a new image, which enables to locate the areas where both images are equally similar or dissimilar. Additionally, we propose some applications in which this comparison method can be used, such as defect detection in industrial manufacturing processes and video motion detection and object tracking.
Open Access
Fuzzy concept lattices and fuzzy relation equations in the retrieval processing of images and signals
(World Scientific, 2017) Alcalde, Cristina; Burusco Juandeaburre, Ana; Díaz Moreno, Juan Carlos; Medina, Jesús; Automática y Computación; Automatika eta Konputazioa; Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa
This paper considers the introduced relations between fuzzy property-oriented concept lattices and fuzzy relation equations, on the one hand, and mathematical morphology, on the other hand, in the retrieval processing of images and signals. In the first part, it studies how the original images and signals can be retrieved using fuzzy propertyoriented concept lattices and fuzzy relation equations. In the second one we analyze two of the most important tools in fuzzy mathematical morphology from the point of view of the fuzzy property-oriented concepts and the aforementioned study. Both parts are illustrated with practical examples.
Open Access
Reduction of the size of L-fuzzy contexts. A tool for differential diagnoses of diseases
(Taylor & Francis, 2019) Alcalde, Cristina; Burusco Juandeaburre, Ana; Estatistika, Informatika eta Matematika; Institute of Smart Cities - ISC; Estadística, Informática y Matemáticas
Information extraction from an L-fuzzy context becomes a hard problem when we work with a large set of objects and/or attributes. The goal of this paper is to present two different and complementary techniques to reduce the size of the context. First, using overlap indexes, we will establish rankings among the elements of the context that will allow us to determine those that do not provide relevant information and eliminate them. Second, by means of Choquet integrals, we will aggregate some objects or attributes of the context in order to jointly use the provided information. One interesting application of the developed theory consists on helping in the differential diagnoses of diseases that share a large number of symptoms and, therefore, that are difficult of distinguish.
Open Access
Concept lattices associated with interval-valued L-fuzzy contexts
(Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences, 1995) Burusco Juandeaburre, Ana; Fuentes González, Ramón; Automática y Computación; Automatika eta Konputazioa
In 1882 Wille published the paper titled Restructuring lattice theory: an approach based on hierarchies of concepts, where he developed a new theory called formal concept theory. In that paper he analyzes 0/1 relations between the object and attribute sets. Applying the L-fuzzy set theory to Wille’s results, we have developed the L-fuzzy concept theory dealing with L-fuzzy relations inside 0/1 relations. The final purpose of our theory is knowledge acquisition and classification. Taking as departure point the L-fuzzy concept theory, in this paper we study contexts defined by interval-valued L-fuzzy relations between the object and attribute sets. We give a new definition of L-fuzzy concept valid for this case and analyze the structure of the L-fuzzy concept set. We apply these results to a medical example.