Open Access
A generalization of the Sugeno integral to aggregate interval-valued data: an application to brain computer interface and social network analysis
(Elsevier, 2022) Fumanal Idocin, Javier; Takáč, Zdenko; Horanská, Lubomíra; Da Cruz Asmus, Tiago; Pereira Dimuro, Graçaliz; Vidaurre Arbizu, Carmen; Fernández Fernández, Francisco Javier; Bustince Sola, Humberto; Institute of Smart Cities - ISC
Intervals are a popular way to represent the uncertainty related to data, in which we express the vagueness of each observation as the width of the interval. However, when using intervals for this purpose, we need to use the appropriate set of mathematical tools to work with. This can be problematic due to the scarcity and complexity of interval-valued functions in comparison with the numerical ones. In this work, we propose to extend a generalization of the Sugeno integral to work with interval-valued data. Then, we use this integral to aggregate interval-valued data in two different settings: first, we study the use of intervals in a brain-computer interface; secondly, we study how to construct interval-valued relationships in a social network, and how to aggregate their information. Our results show that interval-valued data can effectively model some of the uncertainty and coalitions of the data in both cases. For the case of brain-computer interface, we found that our results surpassed the results of other interval-valued functions.
Open Access
VCI-LSTM: Vector choquet integral-based long short-term memory
(IEEE, 2022) Ferrero Jaurrieta, Mikel; Takáč, Zdenko; Fernández Fernández, Francisco Javier; Horanská, Lubomíra; Pereira Dimuro, Graçaliz; Montes Rodríguez, Susana; Díaz, Irene; Bustince Sola, Humberto; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika
Choquet integral is a widely used aggregation operator on one-dimensional and interval-valued information, since it is able to take into account the possible interaction among data. However, there are many cases where the information taken into account is vectorial, such as Long Short-Term Memories (LSTM). LSTM units are a kind of Recurrent Neural Networks that have become one of the most powerful tools to deal with sequential information since they have the power of controlling the information flow. In this paper, we first generalize the standard Choquet integral to admit an input composed by $n$-dimensional vectors, which produces an $n$-dimensional vector output. We study several properties and construction methods of vector Choquet integrals. Then, we use this integral in the place of the summation operator, introducing in this way the new VCI-LSTM architecture. Finally, we use the proposed VCI-LSTM to deal with two problems: sequential image classification and text classification.
Open Access
A generalization of the Choquet integral defined in terms of the Mobius transform
(IEEE, 2020) Fernández Fernández, Francisco Javier; Bustince Sola, Humberto; Horanská, Lubomíra; Mesiar, Radko; Stupñanová, Andrea; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika
In this article, we propose a generalization of the Choquet integral, starting fromits definition in terms of the Mobius transform. We modify the product on R considered in the Lovasz extension form of the Choquet integral into a function F, and we discuss the properties of this new functional. For a fixed n, a complete description of all F yielding an n-ary aggregation function with a fixed diagonal section, independent of the considered fuzzy measure, is given, and several particular examples are presented. Finally, all functions F yielding an aggregation function, independent of the number n of inputs and of the considered fuzzy measure, are characterized, and related aggregation functions are shown to be just the Choquet integrals over the distorted inputs.
Open Access
Generalized decomposition integral
(Elsevier, 2020) Horanská, Lubomíra; Bustince Sola, Humberto; Fernández Fernández, Francisco Javier; Mesiar, Radko; Estatistika, Informatika eta Matematika; Institute of Smart Cities - ISC; Estadística, Informática y Matemáticas
In this paper we propose two different generalizations of the decomposition integral introduced by Even and Lehrer. We modify the product operator merging a given capacity and the decomposition coefficients by some more general functions F and G and compare properties of the obtained functionals with properties of the original decomposition integral. Generalized decomposition integrals corresponding to the particular decomposition systems, being generalizations of Shilkret, Choquet and concave integrals, are studied and exemplified.
Open Access
Sugeno integral generalization applied to improve adaptive image binarization
(Elsevier, 2021) Bardozzo, Francesco; Osa Hernández, Borja de la; Horanská, Lubomíra; Fumanal Idocin, Javier; Priscoli, Mattia delli; Troiano, Luigi; Tagliaferri, Roberto; Fernández Fernández, Francisco Javier; Bustince Sola, Humberto; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika; Gobierno de Navarra / Nafarroako Gobernua, PI043-2019; Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa, PC093-094 TFIPDL
Classic adaptive binarization methodologies threshold pixels intensity with respect to adjacent pixels exploiting integral images. In turn, integral images are generally computed optimally by using the summed-area-table algorithm (SAT). This document presents a new adaptive binarization technique based on fuzzy integral images. Which, in turn, this technique is supported by an efficient design of a modified SAT for generalized Sugeno fuzzy integrals. We define this methodology as FLAT (Fuzzy Local Adaptive Thresholding). Experimental results show that the proposed methodology produced a better image quality thresholding than well-known global and local thresholding algorithms. We proposed new generalizations of different fuzzy integrals to improve existing results and reaching an accuracy ≈0.94 on a wide dataset. Moreover, due to high performances, these new generalized Sugeno fuzzy integrals created ad hoc for adaptive binarization, can be used as tools for grayscale processing and more complex real-time thresholding applications.
Open Access
Enhancing LSTM for sequential image classification by modifying data aggregation
(IEEE, 2021) Takáč, Zdenko; Ferrero Jaurrieta, Mikel; Horanská, Lubomíra; Krivonakova, Nada; Pereira Dimuro, Graçaliz; Bustince Sola, Humberto; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika
Recurrent Neural Networks (RNN) model sequential information and are commonly used for the analysis of time series. The most usual operation to fuse information in RNNs is the sum. In this work, we use a RNN extended type, Long Short-Term Memory (LSTM) and we use it for image classification, to which we give a sequential interpretation. Since the data used may not be independent to each other, we modify the sum operator of an LSTM unit using the n-dimensional Choquet integral, which considers possible data coalitions. We compare our methods to those based on usual aggregation functions, using the datasets Fashion-MNIST and MNIST.
Open Access
Fuzzy clustering to encode contextual information in artistic image classification
(Springer, 2022) Fumanal Idocin, Javier; Takáč, Zdenko; Horanská, Lubomíra; Bustince Sola, Humberto; Cordón, Óscar; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika
Automatic art analysis comprises of utilizing diverse processing methods to classify and categorize works of art. When working with this kind of pictures, we have to take under consideration different considerations compared to classical picture handling, since works of art alter definitely depending on the creator, the scene delineated or their aesthetic fashion. This extra data improves the visual signals gotten from the images and can lead to better performance. However, this information needs to be modeled and embed alongside the visual features of the image. This is often performed utilizing deep learning models, but they are expensive to train. In this paper we utilize the Fuzzy C-Means algorithm to create a embedding strategy based on fuzzy memberships to extract relevant information from the clusters present in the contextual information. We extend an existing state-of-the-art art classification system utilizing this strategy to get a new version that presents similar results without training additional deep learning models.
Embargo
Degree of totalness: how to choose the best admissible permutation for vector fuzzy integration
(Elsevier, 2023-08-30) Ferrero Jaurrieta, Mikel; Horanská, Lubomíra; Lafuente López, Julio; Mesiar, Radko; Pereira Dimuro, Graçaliz; Takáč, Zdenko; Gómez Fernández, Marisol; Fernández Fernández, Francisco Javier; Bustince Sola, Humberto; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika
The use of aggregation operators that require ordering of the data brings a problem when the structures to be aggregated are multi-valued, since there may be several admissible orders. To addressing this problem, the concept of admissible permutation was introduced for intervals. In this paper we extend this concept to vector domain. However, the problem of selecting the best possible permutation is still an open problem. In this paper we present a novel concept in order to choose the best admissible permutation for vectors: the degree of totalness. This concept allows us to represent to which degree the admissible permutation reorder given vectors as a chain with respect to the partial order. Finally, from the best admissible permutation we construct the Choquet integral.