Open Access
De funciones de equivalencia restringida en Lⁿ a medidas de similitud entre multiconjuntos difusos
(CAEPIA, 2024) Ferrero Jaurrieta, Mikel; Rodríguez Martínez, Iosu; Bernardini, Ángela; Fernández Fernández, Francisco Javier; López Molina, Carlos; Bustince Sola, Humberto; Takáč, Zdenko; Marco Detchart, Cedric; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika; Institute of Smart Cities - ISC
Este artículo es un resumen del trabajo publicado en la revista IEEE Transactions on Fuzzy Systems. En este trabajo, presentamos una contribución a la teoría de las Funciones de Equivalencia Restringida (REF), que permite comparar elementos multivaluados. Extendemos el concepto de REF de L a Ln y presentamos una nueva construcción de similitud en Ln. A partir de esta filosofía se construyen medidas de similitud entre multiconjuntos difusos y se presenta un ejemplo aplicado en el contexto de la difusión anisotrópica de imágenes en color.
Open Access
Fuzzy integrals for edge detection
(Springer, 2023) Marco Detchart, Cedric; Lucca, Giancarlo; Pereira Dimuro, Graçaliz; Da Cruz Asmus, Tiago; López Molina, Carlos; Borges, Eduardo N.; Rincón Arango, Jaime Andrés; Julian, Vicente; Bustince Sola, Humberto; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika
In this work, we compare different families of fuzzy integrals in the context of feature aggregation for edge detection. We analyze the behaviour of the Sugeno and Choquet integral and some of its generalizations. In addition, we study the influence of the fuzzy measure over the extracted image features. For testing purposes, we follow the Bezdek Breakdown Structure for edge detection and compare the different fuzzy integrals with some classical feature aggregation methods in the literature. The results of these experiments are analyzed and discussed in detail, providing insights into the strengths and weaknesses of each approach. The overall conclusion is that the configuration of the fuzzy measure does have a paramount effect on the results by the Sugeno integral, but also that satisfactory results can be obtained by sensibly tuning such parameter. The obtained results provide valuable guidance in choosing the appropriate family of fuzzy integrals and settings for specific applications. Overall, the proposed method shows promising results for edge detection and could be applied to other image-processing tasks.
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
From restricted equivalence functions on Ln to similarity measures between fuzzy multisets
(IEEE, 2023) Ferrero Jaurrieta, Mikel; Takáč, Zdenko; Rodríguez Martínez, Iosu; Marco Detchart, Cedric; Bernardini, Ángela; Fernández Fernández, Francisco Javier; López Molina, Carlos; Bustince Sola, Humberto; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika
Restricted equivalence functions are well-known functions to compare two numbers in the interval between 0 and 1. Despite the numerous works studying the properties of restricted equivalence functions and their multiple applications as support for different similarity measures, an extension of these functions to an n-dimensional space is absent from the literature. In this paper, we present a novel contribution to the restricted equivalence function theory, allowing to compare multivalued elements. Specifically, we extend the notion of restricted equivalence functions from L to L n and present a new similarity construction on L n . Our proposal is tested in the context of color image anisotropic diffusion as an example of one of its many applications.
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.