Open Access
Neuro-inspired edge feature fusion using Choquet integrals
(Elsevier, 2021) Marco Detchart, Cedric; Lucca, Giancarlo; López Molina, Carlos; Miguel Turullols, Laura de; Pereira Dimuro, Graçaliz; Bustince Sola, Humberto; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika; Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa
It is known that the human visual system performs a hierarchical information process in which early vision cues (or primitives) are fused in the visual cortex to compose complex shapes and descriptors. While different aspects of the process have been extensively studied, such as lens adaptation or feature detection, some other aspects, such as feature fusion, have been mostly left aside. In this work, we elaborate on the fusion of early vision primitives using generalizations of the Choquet integral, and novel aggregation operators that have been extensively studied in recent years. We propose to use generalizations of the Choquet integral to sensibly fuse elementary edge cues, in an attempt to model the behaviour of neurons in the early visual cortex. Our proposal leads to a fully-framed edge detection algorithm whose performance is put to the test in state-of-the-art edge detection datasets.
Open Access
Pre-aggregation functions: construction and an application
(IEEE, 2015) Lucca, Giancarlo; Sanz Delgado, José Antonio; Pereira Dimuro, Graçaliz; Bedregal, Benjamin; Mesiar, Radko; Kolesárová, Anna; Bustince Sola, Humberto; Automática y Computación; Automatika eta Konputazioa
In this work we introduce the notion of preaggregation function. Such a function satisfies the same boundary conditions as an aggregation function, but, instead of requiring monotonicity, only monotonicity along some fixed direction (directional monotonicity) is required. We present some examples of such functions. We propose three different methods to build pre-aggregation functions. We experimentally show that in fuzzy rule-based classification systems, when we use one of these methods, namely, the one based on the use of the Choquet integral replacing the product by other aggregation functions, if we consider the minimum or the Hamacher product t-norms for such construction, we improve the results obtained when applying the fuzzy reasoning methods obtained using two classical averaging operators like the maximum and the Choquet integral.
Open Access
Aggregation functions based on the Choquet integral applied to image resizing
(Atlantis Press, 2019) Bueno, Jéssica C. S.; Dias, Camila A.; Pereira Dimuro, Graçaliz; Santos, Helida; Bustince Sola, Humberto; Estatistika, Informatika eta Matematika; Institute of Smart Cities - ISC; Estadística, Informática y Matemáticas
The rising volume of data and its high complexity has brought the need of developing increasingly efficient knowledge extraction techniques, which demands efficiency both in computational cost and in accuracy. Most of problems that are handled by these techniques has complex information to be identified. So, machine learning methods are frequently used, where a variety of functions can be applied in the different steps that are employed in their architecture. One of them is the use of aggregation functions aiming at resizing images. In this context, we introduce a study of aggregation functions based on the Choquet integral, whose main characteristic in comparison with other aggregation functions is that it considers, through fuzzy measure, the interaction between the elements to be aggregated. Thus, our main goal is to present an evaluation study of the performance of the standard Choquet integral the and copula-based generalization of the Choquet integral in relation to the maximum and mean functions, looking for results that may be better than the aggregation functions commonly applied. The results of such comparisons are promising, when evaluated through image quality metrics.
Open Access
Dissimilarity based choquet integrals
(Springer, 2020) Bustince Sola, Humberto; Mesiar, Radko; Fernández Fernández, Francisco Javier; Galar Idoate, Mikel; Paternain Dallo, Daniel; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika
In this paper, in order to generalize the Choquet integral, we replace the difference between inputs in its definition by a restricted dissimilarity function and refer to the obtained function as d-Choquet integral. For some particular restricted dissimilarity function the corresponding d-Choquet integral with respect to a fuzzy measure is just the ‘standard’ Choquet integral with respect to the same fuzzy measure. Hence, the class of all d-Choquet integrals encompasses the class of all 'standard' Choquet integrals. This approach allows us to construct a wide class of new functions, d-Choquet integrals, that are possibly, unlike the 'standard' Choquet integral, outside of the scope of aggregation functions since the monotonicity is, for some restricted dissimilarity function, violated and also the range of such functions can be wider than [0, 1], in particular it can be [0, n].
Open Access
A supervised fuzzy measure learning algorithm for combining classifiers
(Elsevier, 2023) Uriz Martín, Mikel Xabier; Paternain Dallo, Daniel; Bustince Sola, Humberto; Galar Idoate, Mikel; Institute of Smart Cities - ISC; Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa
Fuzzy measure-based aggregations allow taking interactions among coalitions of the input sources into account. Their main drawback when applying them in real-world problems, such as combining classifier ensembles, is how to define the fuzzy measure that governs the aggregation and specifies the interactions. However, their usage for combining classifiers has shown its advantage. The learning of the fuzzy measure can be done either in a supervised or unsupervised manner. This paper focuses on supervised approaches. Existing supervised approaches are designed to minimize the mean squared error cost function, even for classification problems. We propose a new fuzzy measure learning algorithm for combining classifiers that can optimize any cost function. To do so, advancements from deep learning frameworks are considered such as automatic gradient computation. Therefore, a gradient-based method is presented together with three new update policies that are required to preserve the monotonicity constraints of the fuzzy measures. The usefulness of the proposal and the optimization of cross-entropy cost are shown in an extensive experimental study with 58 datasets corresponding to both binary and multi-class classification problems. In this framework, the proposed method is compared with other state-of-the-art methods for fuzzy measure learning.
Open Access
Funções de agregação baseadas em integral de Choquet aplicadas em redimensionalização de imagens
(Universidade Passo Fundo, 2019) Bueno, Jéssica C. S.; Dias, Camila A.; Pereira Dimuro, Graçaliz; Borges, Eduardo N.; Botelho, Silvia S. C.; Mattos, Viviane L. D. de; Bustince Sola, Humberto; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika
The increasing data volume, coupled with the high complexity of these data, has generated the need to develop increasingly efficient knowledge extraction techniques, both in computational cost and precision. Most of the problems that are addressed by these techniques have complex information to be identified. For this, machine learning methods are used, where these methods use a variety of functions inside the different steps that are employed in their architectures. One of these consists in the use of aggregation functions to resize images. In this context, a study of aggregation functions based on the Choquet integral is presented, where the main feature of Choquet integral, in comparison with other aggregation functions, resides in the fact that it considers, through the fuzzy measure, the interaction between the elements to be aggregated. Thus, an evaluation study of the performance of the standard Choquet integral functions is presented (Choquet integral based on Copula in relation to the maximum and average functions) looking for results that may be better than the usual applied aggregation functions. The results of such comparisons are promising when evaluated through measures of image quality.
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
d-XC integrals: on the generalization of the expanded form of the Choquet integral by restricted dissimilarity functions and their applications
(IEEE, 2022) Wieczynski, Jonata; Fumanal Idocin, Javier; Lucca, Giancarlo; Borges, Eduardo N.; Da Cruz Asmus, Tiago; Emmendorfer, Leonardo R.; Bustince Sola, Humberto; Pereira Dimuro, Graçaliz; Automática y Computación; Automatika eta Konputazioa; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika
Restricted dissimilarity functions (RDFs) were introduced to overcome problems resulting from the adoption of the standard difference. Based on those RDFs, Bustince et al. introduced a generalization of the Choquet integral (CI), called d-Choquet integral, where the authors replaced standard differences with RDFs, providing interesting theoretical results. Motivated by such worthy properties, joint with the excellent performance in applications of other generalizations of the CI (using its expanded form, mainly), this paper introduces a generalization of the expanded form of the standard Choquet integral (X-CI) based on RDFs, which we named d-XC integrals. We present not only relevant theoretical results but also two examples of applications. We apply d-XC integrals in two problems in decision making, namely a supplier selection problem (which is a multi-criteria decision making problem) and a classification problem in signal processing, based on motor-imagery brain-computer interface (MI-BCI). We found that two d-XC integrals provided better results when compared to the original CI in the supplier selection problem. Besides that, one of the d-XC integrals performed better than any previous MI-BCI results obtained with this framework in the considered signal processing problem.
Open Access
Using the Choquet integral in the fuzzy reasoning method of fuzzy rule-based classification systems
(MDPI, 2013) Barrenechea Tartas, Edurne; Bustince Sola, Humberto; Fernández Fernández, Francisco Javier; Paternain Dallo, Daniel; Sanz Delgado, José Antonio; Automática y Computación; Automatika eta Konputazioa
In this paper we present a new fuzzy reasoning method in which the Choquet integral is used as aggregation function. In this manner, we can take into account the interaction among the rules of the system. For this reason, we consider several fuzzy measures, since it is a key point on the subsequent success of the Choquet integral, and we apply the new method with the same fuzzy measure for all the classes. However, the relationship among the set of rules of each class can be different and therefore the best fuzzy measure can change depending on the class. Consequently, we propose a learning method by means of a genetic algorithm in which the most suitable fuzzy measure for each class is computed. From the obtained results it is shown that our new proposal allows the performance of the classical fuzzy reasoning methods of the winning rule and additive combination to be enhanced whenever the fuzzy measure is appropriate for the tackled problem.