# 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 Enhancing the efficiency of the interval-valued fuzzy rule-based classifier with tuning and rule selection(Springer, 2020) Sanz Delgado, José Antonio; Da Cruz Asmus, Tiago; Osa Hernández, Borja de la; Bustince Sola, Humberto; Institute of Smart Cities - ISC; Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa, PJUPNA1926Show more Interval-Valued fuzzy rule-based classifier with TUning and Rule Selection, IVTURS, is a state-of-the-art fuzzy classifier. One of the key point of this method is the usage of interval-valued restricted equivalence functions because their parametrization allows one to tune them to each problem, which leads to obtaining accurate results. However, they require the application of the exponentiation several times to obtain a result, which is a time demanding operation implying an extra charge to the computational burden of the method. In this contribution, we propose to reduce the number of exponentiation operations executed by the system, so that the efficiency of the method is enhanced with no alteration of the obtained results. Moreover, the new approach also allows for a reduction on the search space of the evolutionary method carried out in IVTURS. Consequently, we also propose four different approaches to take advantage of this reduction on the search space to study if it can imply an enhancement of the accuracy of the classifier. The experimental results prove: 1) the enhancement of the efficiency of IVTURS and 2) the accuracy of IVTURS is competitive versus that of the approaches using the reduced search space.Show more Publication Open Access N-dimensional admissibly ordered interval-valued overlap functions and its influence in interval-valued fuzzy rule-based classification systems(IEEE, 2021) Da Cruz Asmus, Tiago; Sanz Delgado, José Antonio; Pereira Dimuro, Graçaliz; Callejas Bedregal, Benjamin; Fernández Fernández, Francisco Javier; Bustince Sola, Humberto; Estatistika, Informatika eta Matematika; Institute of Smart Cities - ISC; Estadística, Informática y MatemáticasShow more Overlap functions are a type of aggregation functions that are not required to be associative, generally used to indicate the overlapping degree between two values. They have been successfully used as a conjunction operator in several practical problems, such as fuzzy rulebased classification systems (FRBCSs) and image processing. Some extensions of overlap functions were recently proposed, such as general overlap functions and, in the interval-valued context, n-dimensional interval-valued overlap functions. The latter allow them to be applied in n-dimensional problems with interval-valued inputs, like interval-valued classification problems, where one can apply interval-valued FRBCSs (IV-FRBCSs). In this case, the choice of an appropriate total order for intervals, like an admissible order, can play an important role. However, neither the relationship between the interval order and the n-dimensional interval-valued overlap function (which may or may not be increasing for that order) nor the impact of this relationship in the classification process have been studied in the literature. Moreover, there is not a clear preferred n-dimensional interval-valued overlap function to be applied in an IV-FRBCS. Hence, in this paper we: (i) present some new results on admissible orders, which allow us to introduce the concept of n-dimensional admissibly ordered interval-valued overlap functions, that is, n-dimensional interval-valued overlap functions that are increasing with respect to an admissible order; (ii) develop a width-preserving construction method for this kind of function, derived from an admissible order and an n-dimensional overlap function, discussing some of its features; (iii) analyze the behaviour of several combinations of admissible orders and n-dimensional (admissibly ordered) interval-valued overlap functions when applied in IV-FRBCSs. All in all, the contribution of this paper resides in pointing out the effect of admissible orders and n-dimensional admissibly ordered interval-valued overlap functions, both from a theoretical and applied points of view, the latter when considering classification problems.Show more Publication Embargo A generalization of the Sugeno integral to aggregate interval-valued data: an application to brain computer interface and social network analysis(Elsevier, 2022) Fumanal Idocin, Javier; Takáč, Zdenko; Horanská, Lubomíra; Da Cruz Asmus, Tiago; Pereira Dimuro, Graçaliz; Vidaurre Arbizu, Carmen; Fernández Fernández, Francisco Javier; Bustince Sola, Humberto; Institute of Smart Cities - ISCShow more Intervals are a popular way to represent the uncertainty related to data, in which we express the vagueness of each observation as the width of the interval. However, when using intervals for this purpose, we need to use the appropriate set of mathematical tools to work with. This can be problematic due to the scarcity and complexity of interval-valued functions in comparison with the numerical ones. In this work, we propose to extend a generalization of the Sugeno integral to work with interval-valued data. Then, we use this integral to aggregate interval-valued data in two different settings: first, we study the use of intervals in a brain-computer interface; secondly, we study how to construct interval-valued relationships in a social network, and how to aggregate their information. Our results show that interval-valued data can effectively model some of the uncertainty and coalitions of the data in both cases. For the case of brain-computer interface, we found that our results surpassed the results of other interval-valued functions.Show more Publication Open Access General admissibly ordered interval-valued overlap functions(CEUR Workshop Proceedings (CEUR-WS.org), 2021) Da Cruz Asmus, Tiago; Pereira Dimuro, Graçaliz; Sanz Delgado, José Antonio; Wieczynski, Jonata; Lucca, Giancarlo; Bustince Sola, Humberto; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika; Universidad Pública de Navarra / Nafarroako Unibertsitate PublikoaShow more Overlap functions are a class of aggregation functions that measure the verlapping degree between two values. They have been successfully applied in several problems in which associativity is not required, such as classification and image processing. Some generalizations of overlap functions were proposed for them to be applied in problems with more than two classes, such as 𝑛- dimensional and general overlap functions. To measure the overlapping of interval data, interval-valued overlap functions were defined, and, later, they were also generalized in the form of 𝑛-dimensional and general interval-valued overlap functions. In order to apply some of those concepts in problems with interval data considering the use of admissible orders, which are total orders that refine the most used partial order for intervals, 𝑛-dimensional admissibly ordered interval-valued overlap functions were recently introduced, proving to be suitable to be applied in classification problems. However, the sole construction method presented for this kind of function do not allow the use of the well known lexicographical orders. So, in this work we combine previous developments to introduce general admissibly ordered interval-valued overlap functions, while also presenting different construction methods and the possibility to combine such methods, showcasing the flexibility and adaptability of this approach, while also being compatible with the lexicographical orders.Show more Publication Open Access dCF-integrals: generalizing CF-integrals by means of restricted dissimilarity functions(IEEE, 2022) Wieczynski, Jonata; Lucca, Giancarlo; Pereira Dimuro, Graçaliz; Borges, Eduardo N.; Sanz Delgado, José Antonio; Da Cruz Asmus, Tiago; Fernández Fernández, Francisco Javier; Bustince Sola, Humberto; Estatistika, Informatika eta Matematika; Institute of Smart Cities - ISC; Estadística, Informática y Matemáticas; Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa, PJUPNA1926Show more The Choquet integral (CI) is an averaging aggregation function that has been used, e.g., in the fuzzy reasoning method (FRM) of fuzzy rule-based classification systems (FRBCSs) and in multicriteria decision making in order to take into account the interactions among data/criteria. Several generalizations of the CI have been proposed in the literature in order to improve the performance of FRBCSs and also to provide more flexibility in the different models by relaxing both the monotonicity requirement and averaging conditions of aggregation functions. An important generalization is the CF -integrals, which are preaggregation functions that may present interesting nonaveraging behavior depending on the function F adopted in the construction and, in this case, offering competitive results in classification. Recently, the concept of d-Choquet integrals was introduced as a generalization of the CI by restricted dissimilarity functions (RDFs), improving the usability of CIs, as when comparing inputs by the usual difference may not be viable. The objective of this article is to introduce the concept of dCF -integrals, which is a generalization of CF -integrals by RDFs. The aim is to analyze whether the usage of dCF -integrals in the FRM of FRBCSs represents a good alternative toward the standard CF -integrals that just consider the difference as a dissimilarity measure. For that, we consider six RDFs combined with five fuzzy measures, applied with more than 20 functions F . The analysis of the results is based on statistical tests, demonstrating their efficiency. Additionally, comparing the applicability of dCF -integrals versus CF -integrals, the range of the good generalizations of the former is much larger than that of the latter.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 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 MatematikaShow more 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.Show more Publication Open Access A framework for general fusion processes under uncertainty modeling control, with an application in interval-valued fuzzy rule-based classification systems(2022) Da Cruz Asmus, Tiago; Sanz Delgado, José Antonio; Pereira Dimuro, Graçaliz; Estadística, Informática y Matemáticas; Estatistika, Informatika eta MatematikaShow more La fusión de información es el proceso de combinar varios valores numéricos en uno solo que los represente. En problemas con algún tipo de modelado difuso, este proceso generalmente se realiza mediante funciones de fusión o, su subclase más importante, las funciones de agregación. Estas funciones se han aplicado ampliamente en varias técnicas para resolver problemas de clasificación, en particular, en los Sistemas de Clasificación Basados en Reglas Difusas (SCBRDs). En este tipo de clasificador, se han aplicado de forma exitosa las funciones de solapamiento (que son funciones de agregación bivariadas con propiedades deseables) y sus generalizaciones n-dimensionales. Cuando hay incertidumbre con respecto al modelado de las funciones de pertenencia en los SCBRDs, generalmente asociados con términos lingüísticos, se pueden aplicar conjuntos difusos intervalo-valorados. El modelado de etiquetas lingüísticas a través de conjuntos difusos intervalo-valorados en los SCBRDs origino a los Sistemas de Clasificación Basados en Reglas Difusas Intervalo-valorados (IV-SCBRDs). En estos sistemas, los procesos de fusión se calculan mediante funciones de agregación definidas en el contexto intervalar, mientras que las amplitudes de los intervalos de pertenencia asignados están intrínsecamente relacionadas con la incertidumbre con respecto a los valores que están aproximando y, luego, con la calidad de la información que representan. Sin embargo, no existe una guía en la literatura que muestre cómo definir y construir funciones de fusión con valores intervalares que tomen en consideración el control de la calidad de la información. Por todo ello, en esta tesis, desarrollamos un marco para definir funciones de fusión intervalo-valoradas n-dimensionales generalizadas considerando los órdenes admisibles y el control de la calidad de la información. Aplicamos los conceptos desarrollados en un IV-SCBRD considerado como estado del arte (es decir, IVTURS), desarrollando nuestra propia versión basada en operadores de solapamiento con control de la calidad de la información, demostrando que nuestro enfoque mejora el rendimiento del clasificador. Finalmente, desarrollamos un marco para definir funciones de fusión n-dimensionales que actúan en un intervalo real cerrado arbitrario como homólogas de clases conocidas de funciones de fusión que actúan sobre el intervalo unitario, para expandir la aplicabilidad de las funciones de fusión con propiedades deseables a problemas que no involucren un modelado difuso.Show more 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