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.
Open Access
Systematic review of aggregation functions applied to image edge detection
(MDPI, 2023) Amorim, Miqueias; Pereira Dimuro, Graçaliz; Borges, Eduardo N.; Dalmazo, Bruno L.; Marco Detchart, Cedric; Lucca, Giancarlo; Bustince Sola, Humberto; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika
Edge detection is a crucial process in numerous stages of computer vision. This field of study has recently gained momentum due to its importance in various applications. The uncertainty, among other characteristics of images, makes it difficult to accurately determine the edge of objects. Furthermore, even the definition of an edge is vague as an edge can be considered as the maximum boundary between two regions with different properties. Given the advancement of research in image discontinuity detection, especially using aggregation and pre-aggregation functions, and the lack of systematic literature reviews on this topic, this paper aims to gather and synthesize the current state of the art of this topic. To achieve this, this paper presents a systematic review of the literature, which selected 24 papers filtered from 428 articles found in computer databases in the last seven years. It was possible to synthesize important related information, which was grouped into three approaches: (i) based on both multiple descriptor extraction and data aggregation, (ii) based on both the aggregation of distance functions and fuzzy C-means, and (iii) based on fuzzy theory, namely type-2 fuzzy and neutrosophic sets. As a conclusion, this review provides interesting gaps that can be explored in future work.
Open Access
Additively generated (a,b)-implication functions*
(IEEE, 2023) Santos, Helida; Pereira Dimuro, Graçaliz; Bedregal, Benjamin; Paiva, Rui; Lucca, Giancarlo; Moura, Bruno; Cruz, Anderson; Bustince Sola, Humberto; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika
Some problems involving classification through neural networks are known to use inputs out of the scope of the unit interval. Therefore, defining operations on arbitrary closed real intervals may be an interesting strategy to tackle this issue and enhance those application environments. In this paper we follow the ideas already discussed in the literature regarding (a,b)-fusion functions, and (a,b)-negations, to provide a new way to construct implication functions. The main idea is to construct an operator using additively generated functions that preserve the properties required by implication functions.
Open Access
A study on the suitability of different pooling operators for convolutional neural networks in the prediction of COVID-19 through chest x-ray image analysis
(Elsevier, 2024) Rodríguez Martínez, Iosu; Ursúa Medrano, Pablo; Fernández Fernández, Francisco Javier; Takáč, Zdenko; Bustince Sola, Humberto; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika; Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa
The 2019 coronavirus disease outbreak, caused by the severe acute respiratory syndrome type-2 virus (SARS-CoV-2), was declared a pandemic in March 2020. Since its emergence to the present day, this disease has brought multiple countries to the brink of health care collapse during several waves of the disease. One of the most common tests performed on patients is chest x-ray imaging. These images show the severity of the patient's illness and whether it is indeed covid or another type of pneumonia. Automated assessment of this type of imaging could alleviate the time required for physicians to treat and diagnose each patient. To this end, in this paper we propose the use of Convolutional Neural Networks (CNNs) to carry out this process. The aim of this paper is twofold. Firstly, we present a pipeline adapted to this problem, covering all steps from the preprocessing of the datasets to the generation of classification models based on CNNs. Secondly, we have focused our study on the modification of the information fusion processes of this type of architectures, in the pooling layers. We propose a number of aggregation theory functions that are suitable to replace classical processes and have shown their benefits in past applications, and study their performance in the context of the x-ray classification problem. We find that replacing the feature reduction processes of CNNs leads to drastically different behaviours of the final model, which can be beneficial when prioritizing certain metrics such as precision or recall.
Open Access
Supervised penalty-based aggregation applied to motor-imagery based brain-computer-interface
(Elsevier, 2024) Fumanal Idocin, Javier; Vidaurre Arbizu, Carmen; Fernández Fernández, Francisco Javier; Gómez Fernández, Marisol; Andreu-Pérez, Javier; Prasad, M.; Bustince Sola, Humberto; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika; Institute for Advanced Materials and Mathematics - INAMAT2; Institute of Smart Cities - ISC
In this paper we propose a new version of penalty-based aggregation functions, the Multi Cost Aggregation choosing functions (MCAs), in which the function to minimize is constructed using a convex combination of two relaxed versions of restricted equivalence and dissimilarity functions instead of a penalty function. We additionally suggest two different alternatives to train a MCA in a supervised classification task in order to adapt the aggregation to each vector of inputs. We apply the proposed MCA in a Motor Imagery-based Brain- Computer Interface (MI-BCI) system to improve its decision making phase. We also evaluate the classical aggregation with our new aggregation procedure in two publicly available datasets. We obtain an accuracy of 82.31% for a left vs. right hand in the Clinical BCI challenge (CBCIC) dataset, and a performance of 62.43% for the four-class case in the BCI Competition IV 2a dataset compared to a 82.15% and 60.56% using the arithmetic mean. Finally, we have also tested the goodness of our proposal against other MI-BCI systems, obtaining better results than those using other decision making schemes and Deep Learning on the same datasets.
Open Access
Data stream clustering: introducing recursively extendable aggregation functions for incremental cluster fusion processes
(IEEE, 2025-03-07) Urío Larrea, Asier; Camargo, Heloisa A.; Lucca, Giancarlo; Asmus, Tiago da Cruz; Marco Detchart, Cedric; Schick, L.; López Molina, Carlos; Andreu-Pérez, Javier; Bustince Sola, Humberto; Dimuro, Graçaliz Pereira; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika; Institute of Smart Cities - ISC
In data stream (DS) learning, the system has to extract knowledge from data generated continuously, usually at high speed and in large volumes, making it impossible to store the entire set of data to be processed in batch mode. Hence, machine learning models must be built incrementally by processing the incoming examples, as data arrive, while updating the model to be compatible with the current data. In fuzzy DS clustering, the model can either absorb incoming data into existing clusters or initiate a new cluster. As the volume of data increases, there is a possibility that the clusters will overlap to the point where it is convenient to merge two or more clusters into one. Then, a cluster comparison measure (CM) should be applied, to decide whether such clusters should be combined, also in an incremental manner. This defines an incremental fusion process based on aggregation functions that can aggregate the incoming inputs without storing all the previous inputs. The objective of this article is to solve the fuzzy DS clustering problem of incrementally comparing fuzzy clusters on a formal basis. First, we formalize and operationalize incremental fusion processes of fuzzy clusters by introducing recursively extendable (RE) aggregation functions, studying construction methods and different classes of such functions. Second, we propose two approaches to compare clusters: 1) similarity and 2) overlapping between clusters, based on RE aggregation functions. Finally, we analyze the effect of those incremental CMs on the online and offline phases of the well-known fuzzy clustering algorithm d-FuzzStream, showing that our new approach outperforms the original algorithm and presents better or comparable performance to other state-of-the-art DS clustering algorithms found in the literature.