Embargo
Non-symmetric over-time pooling using pseudo-grouping functions for convolutional neural networks
(Elsevier, 2024-07-01) Ferrero Jaurrieta, Mikel; Paiva, Rui; Cruz, Anderson; Bedregal, Benjamin; Miguel Turullols, Laura de; Takáč, Zdenko; López Molina, Carlos; Bustince Sola, Humberto; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika; Institute of Smart Cities - ISC
Convolutional Neural Networks (CNNs) are a family of networks that have become state-of-the-art in several fields of artificial intelligence due to their ability to extract spatial features. In the context of natural language processing, they can be used to build text classification models based on textual features between words. These networks fuse local features to generate global features in their over-time pooling layers. These layers have been traditionally built using the maximum function or other symmetric functions such as the arithmetic mean. It is important to note that the order of input local features is significant (i.e. the symmetry is not an inherent characteristic of the model). While this characteristic is appropriate for image-oriented CNNs, where symmetry might make the network robust to image rigid transformations, it seems counter-productive for text processing, where the order of the words is certainly important. Our proposal is, hence, to use non-symmetric pooling operators to replace the maximum or average functions. Specifically, we propose to perform over-time pooling using pseudo-grouping functions, a family of non-symmetric aggregation operators that generalize the maximum function. We present a construction method for pseudo-grouping functions and apply different examples of this family to over-time pooling layers in text-oriented CNNs. Our proposal is tested on seven different models and six different datasets in the context of engineering applications, e.g. text classification. The results show an overall improvement of the models when using non-symmetric pseudo-grouping functions over the traditional pooling function.
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
Directional monotonicity of multidimensional fusion functions with respect to admissible orders
(Elsevier, 2023-03-09) Sesma Sara, Mikel; Bustince Sola, Humberto; Mesiar, Radko; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika; Institute of Smart Cities - ISC; Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa, PJUPNA25-2022
The notion of directional monotonicity emerged as a relaxation of the monotonicity condition of aggregation functions. As the extension of aggregation functions to fuse more complex information than numeric data, directional monotonicity was extended to the framework of multidimensional data, with respect to the product order, which is a partial order. In this work, we present the notion of admissible order for multidimensional data and we define the concept of directional monotonicity for multidimensional fusion functions with respect to an admissible order. Moreover, we study the main properties of directionally monotone functions in this new context. We conclude that, while some of the properties are still valid (e.g. the set of directions of increasingness is still closed under convex combinations), some of the main ones no longer hold (e.g. there does not exist a finite set of directions that characterize standard monotonicity in terms of directional monotonicity).
Open Access
A rule-based approach for interpretable intensity-modulated radiation therapy treatment selection
(IEEE, 2024-08-05) González García, Xabier; Fumanal Idocin, Javier; Nunez do Rio, Joan M.; Bustince Sola, Humberto; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika
Artificial Intelligence (AI) methods are becoming essential in healthcare. In the context of Intensity-Modulated Radiation Therapy (IMRT), Knowledge-Based Planning (KBP) methodologies have enabled the modification of treatments in real-time to accommodate morphological changes in patients. KBP for IMRT is a data-driven approach that utilises real-time medical imaging to adjust the radiation dose for a patient as needed for the different stages of an illness. In this work we present an interpretable AI model that selects the best IMRT treatment alternatives and determines which is the best. We use an Adaptive Neuforuzzy Adaptive Inference System (ANFIS), which combines the potential of a neural network with the interpretability of a rule based system. We train the model in a supervised manner using the OpenKBP challenge data repository. For this purpose, we also developed a data augmentation method that is supported by Diffusion Probabilistic Models. This approach enables the generation of a wider spectrum of treatment qualities and aids regularisation. The primary advantage of this framework resides in its ability to offer explanations, which is essential in the deployment of medical procedures in real life. Moreover, it serves as a valuable means to test hypotheses concerning the quality of IMRT treatments. Our study reveals that the developed tool has substantial potential to establish itself as a reference in the realm of explainable IMRT treatment selection tools.
Open Access
Reduction of complexity using generators of pseudo-overlap and pseudo-grouping functions
(2024) Ferrero Jaurrieta, Mikel; Paiva, Rui; Cruz, Anderson; Bedregal, Benjamin; Zhang, Xiaohong; Takáč, Zdenko; López Molina, Carlos; Bustince Sola, Humberto; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika
Overlap and grouping functions can be used to measure events in which we must consider either the maximum or the minimum lack of knowledge. The commutativity of overlap and grouping functions can be dropped out to introduce the notions of pseudo-overlap and pseudo-grouping functions, respectively. These functions can be applied in problems where distinct orders of their arguments yield different values, i.e., in non-symmetric contexts. Intending to reduce the complexity of pseudo-overlap and pseudo-grouping functions, we propose new construction methods for these functions from generalized concepts of additive and multiplicative generators. We investigate the isomorphism between these families of functions. Finally, we apply these functions in an illustrative problem using them in a time series prediction combined model using the IOWA operator to evidence that using these generators and functions implies better performance.
Embargo
Fuzzy dissimilarities and the fuzzy choquet integral of triangular fuzzy numbers on [0,1]
(Elsevier, 2025-04-01) Roldán López de Hierro, Antonio Francisco; Cruz, Anderson; Santiago, Regivan; Roldán, Concepción; García-Zamora, Diego; Neres, Fernando; Bustince Sola, Humberto; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika; Institute of Smart Cities - ISC
Having in mind the huge amount of data daily registered in the world, it is becoming increasingly important to summarize the information included in a data set. In Statistics and Computer Science, this task is successfully carried out by aggregation functions. One of the most widely applied methodologies of aggregating data is the Choquet integral. The main aim of this paper is to introduce an appropriate notion of Choquet integral in the context of fuzzy numbers. To do this, we face three challenges: the underlying uncertainty when handling fuzzy numbers, the way to order fuzzy numbers by appropriate binary relations and the way to compute the dissimilarity among fuzzy numbers. Illustrative examples are given by involving the α-order on the family of all triangular fuzzy numbers with support on [0,1].
Open Access
On the notion of fuzzy dispersion measure and its application to triangular fuzzy numbers
(Elsevier, 2023) Roldán López de Hierro, Antonio Francisco; Bustince Sola, Humberto; Rueda, María del Mar; Roldán, Concepción; Miguel Turullols, Laura de; Guerra Errea, Carlos; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika
In this paper, based on the analysis of the most widely used dispersion measure in the real context (namely, the variance), we introduce the notion of fuzzy dispersion measure associated to a finite set of data given by fuzzy numbers. This measure is implemented as a fuzzy number, so there is no loss of information caused by any defuzzification. The proposed concept satisfies the usual properties in a genuinely fuzzy sense and it avoids limitations in terms of its geometric shape or its analytical properties: under this conception, it could have a piece of its support in the negative part of the real line. This novel notion can be interpreted as a way of fusing the information included in a fuzzy data set in order to make a decision based on its dispersion. To illustrate the main characteristics of this approach, we present an example of a fuzzy dispersion measure that allows to conclude that this new way to deal this problem is coherent, at least, from the point of view of human intuition.
Open Access
Admissible OWA operators for fuzzy numbers
(Elsevier, 2024) García-Zamora, Diego; Cruz, Anderson; Neres, Fernando; Santiago, Regivan; Roldán López de Hierro, Antonio Francisco; Paiva, Rui; Pereira Dimuro, Graçaliz; Martínez López, Luis; Bedregal, Benjamin; Bustince Sola, Humberto; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika; Institute of Smart Cities - ISC
Ordered Weighted Averaging (OWA) operators are some of the most widely used aggregation functions in classic literature, but their application to fuzzy numbers has been limited due to the complexity of defining a total order in fuzzy contexts. However, the recent notion of admissible order for fuzzy numbers provides an effective method to totally order them by refining a given partial order. Therefore, this paper is devoted to defining OWA operators for fuzzy numbers with respect to admissible orders and investigating their properties. Firstly, we define the OWA operators associated with such admissible orders and then we show their main properties. Afterward, an example is presented to illustrate the applicability of these AOWA operators in linguistic decision-making. In this regard, we also develop an admissible order for trapezoidal fuzzy numbers that can be efficiently applied in practice.
Open Access
Generalizando el pooling maximo por funciones (a, b)-grouping en redes neuronales convolucionales
(CAEPIA, 2024) Rodríguez Martínez, Iosu; Da Cruz Asmus, Tiago; Pereira Dimuro, Graçaliz; Herrera, Francisco; Takáč, Zdenko; Bustince Sola, Humberto; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika; Institute of Smart Cities - ISC; Gobierno de Navarra / Nafarroako Gobernua
Este artículo es un resumen del trabajo publicado en la revista Information Fusion [1]. En este artículo explorábamos el reemplazo del operador de pooling máximo comunmente empleado en redes neuronales convolucionales (CNNs) por funciones (a, b)-grouping. Estas funciones extienden el concepto de función de grouping clásica [2] a un intervalo cerrado [a, b], siguiendo la filosofía de [3]. En el contexto del operador de pooling, estas nuevas funciones ayudan a la optimización de los modelos suavizando los gradientes en el proceso de retropropagación y obteniendo resultados competitivos con métodos más complejos
Open Access
On fuzzy implications derived from general overlap functions and their relation to other classes
(MDPI, 2023) Pinheiro, Jocivania; Santos, Helida; Pereira Dimuro, Graçaliz; Bedregal, Benjamin; Santiago, Regivan; Fernández Fernández, Francisco Javier; Bustince Sola, Humberto; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika; Institute of Smart Cities - ISC
There are distinct techniques to generate fuzzy implication functions. Despite most of them using the combination of associative aggregators and fuzzy negations, other connectives such as (general) overlap/grouping functions may be a better strategy. Since these possibly non-associative operators have been successfully used in many applications, such as decision making, classification and image processing, the idea of this work is to continue previous studies related to fuzzy implication functions derived from general overlap functions. In order to obtain a more general and flexible context, we extend the class of implications derived by fuzzy negations and t-norms, replacing the latter by general overlap functions, obtaining the so-called (GO, N)-implication functions. We also investigate their properties, the aggregation of (GO, N)-implication functions, their characterization and the intersections with other classes of fuzzy implication functions.