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
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
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
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
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
Use of Choquet integrals in multivalued contexts
(Springer, 2020) Burusco Juandeaburre, Ana; Alcalde, Cristina; Estatistika, Informatika eta Matematika; Institute of Smart Cities - ISC; Estadística, Informática y Matemáticas
In this work, multivalued contexts are studied, in which the different observations are related to each other. Continuing the studies already carried out in previous works, the use of Choquet integrals can be an adequate tool for this situations. If in addition the set of objects or attributes of these contexts represent a temporal sequence, we can also represent these contexts as sequences of contexts that evolve in time and we can use tools in this field to extract information. Finally, as illustrative application, the developed theory is used to measure student progress in learning.
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
Evolution of L-fuzzy contexts associated with criteria
(Springer, 2020) Alcalde, Cristina; Burusco Juandeaburre, Ana; Estatistika, Informatika eta Matematika; Institute of Smart Cities - ISC; Estadística, Informática y Matemáticas
This paper will delve deeper into the general study of the L-fuzzy contexts associated with criteria analyzing situations with a known evolution over time. These criteria may be independent or dependent on each other. We propose two different studies: to build an aggregated context looking for a simplification of the process and to keep the sequence obtaining interesting nuances over time. In both cases, aggregation operators will be used in order to address the problem. Finally, a practical example about ratings obtained by different tourist accommodations illustrates the results.
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
In search of L-Fuzzy contexts adaptable to variable information: a tool for time-varying data analysis
(MDPI, 2025-01-27) Alcalde, Cristina; Burusco Juandeaburre, Ana; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika
This paper sheds light on the study of a new structure, called L-fuzzy hypercontext, which provides an extension of the range of applications of fuzzy concept analysis. The advantage of working with L-fuzzy hypercontexts lies in the fact that we can establish relation among elements such that their values are, in turn, other relations. Thus, they are easily adaptable to different situations that vary over time. The usefulness of the developed theory is illustrated by a practical case in which the valuation made by the different clients of a hotel company is analyzed.