# Person: Da Cruz Asmus, Tiago

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Da Cruz Asmus

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Tiago

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Estadística, Informática y Matemáticas

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0000-0002-7066-7156

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811596

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Publication Open Access Generalizing max pooling via (a, b)-grouping functions for convolutional neural networks(Elsevier, 2023) 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; Universidad Pública de Navarra / Nafarroako Unibertsitate PublikoaShow more Due to their high adaptability to varied settings and effective optimization algorithm, Convolutional Neural Networks (CNNs) have set the state-of-the-art on image processing jobs for the previous decade. CNNs work in a sequential fashion, alternating between extracting significant features from an input image and aggregating these features locally through ‘‘pooling" functions, in order to produce a more compact representation. Functions like the arithmetic mean or, more typically, the maximum are commonly used to perform this downsampling operation. Despite the fact that many studies have been devoted to the development of alternative pooling algorithms, in practice, ‘‘max-pooling" still equals or exceeds most of these possibilities, and has become the standard for CNN construction. In this paper we focus on the properties that make the maximum such an efficient solution in the context of CNN feature downsampling and propose its replacement by grouping functions, a family of functions that share those desirable properties. In order to adapt these functions to the context of CNNs, we present (𝑎��, 𝑏��)- grouping functions, an extension of grouping functions to work with real valued data. We present different construction methods for (𝑎, 𝑏)-grouping functions, and demonstrate their empirical applicability for replacing max-pooling by using them to replace the pooling function of many well-known CNN architectures, finding promising results.Show more Publication Open Access Constructing interval-valued fuzzy material implication functions derived from general interval-valued grouping functions(IEEE, 2022) Pereira Dimuro, Graçaliz; Santos, Helida; Da Cruz Asmus, Tiago; Wieczynski, Jonata; Pinheiro, Jocivania; Callejas Bedregal, Benjamin; Bustince Sola, Humberto; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika; Institute of Smart Cities - ISCShow more Grouping functions and their dual counterpart, overlap functions, have drawn the attention of many authors, mainly because they constitute a richer class of operators compared to other types of aggregation functions. Grouping functions are a useful theoretical tool to be applied in various problems, like decision making based on fuzzy preference relations. In pairwise comparisons, for instance, those functions allow one to convey the measure of the amount of evidence in favor of either of two given alternatives. Recently, some generalizations of grouping functions were proposed, such as (i) the n-dimensional grouping functions and the more flexible general grouping functions, which allowed their application in n-dimensional problems, and (ii) n-dimensional and general interval-valued grouping functions, in order to handle uncertainty on the definition of the membership functions in real-life problems. Taking into account the importance of interval-valued fuzzy implication functions in several application problems under uncertainty, such as fuzzy inference mechanisms, this paper aims at introducing a new class of interval-valued fuzzy material implication functions. We study their properties, characterizations, construction methods and provide examples.Show more Publication Open Access General grouping functions(Springer, 2020) Santos, Helida; Pereira Dimuro, Graçaliz; Da Cruz Asmus, Tiago; Sanz Delgado, José Antonio; Fernández Fernández, Francisco Javier; Bustince Sola, Humberto; Estatistika, Informatika eta Matematika; Institute of Smart Cities - ISC; Estadística, Informática y MatemáticasShow more Some aggregation functions that are not necessarily associative, namely overlap and grouping functions, have called the attention of many researchers in the recent past. This is probably due to the fact that they are a richer class of operators whenever one compares with other classes of aggregation functions, such as t-norms and t-conorms, respectively. In the present work we introduce a more general proposal for disjunctive n-ary aggregation functions entitled general grouping functions, in order to be used in problems that admit n dimensional inputs in a more flexible manner, allowing their application in different contexts. We present some new interesting results, like the characterization of that operator and also provide different construction methods.Show more Publication Open Access On construction methods of (interval-valued) general grouping functions(Springer, 2022) Pereira Dimuro, Graçaliz; Da Cruz Asmus, Tiago; Pinheiro, Jocivania; Santos, Helida; Borges, Eduardo N.; Lucca, Giancarlo; Rodríguez Martínez, Iosu; Mesiar, Radko; Bustince Sola, Humberto; Estadística, Informática y Matemáticas; Estatistika, Informatika eta MatematikaShow more Recently, several theoretical and applied studies on grouping functions and overlap functions appeared in the literature, mainly because of their flexibility when comparing them with the popular aggregation operators t-conorms and t-norms, respectively. Additionally, they constitute richer classes of disjunction/conjunction operations than t-norms and t-conorms. In particular, grouping functions have been applied as the disjunction operator in several problems, like decision making based on fuzzy preference relations. In this case, when performing pairwise comparisons, grouping functions allow one to evaluate the measure of the amount of evidence in favor of either of two given alternatives. However, grouping functions are not associative. Then, in order to allow them to be applied in n-dimensional problems, such as the pooling layer of neural networks, some generalizations were introduced, namely, n-dimensional grouping functions and the more flexible general grouping functions, the latter for enlarging the scope of applications. Then, in order to h andle uncertainty on the definition of the membership functions in real-life problems, n-dimensional and general interval-valued grouping functions were proposed. This paper aims at providing new constructions methods of general (interval-valued) grouping functions, also providing some examples.Show more