BUSCADOR RECOLECTA

J. Baz is partially supported by Programa Severo Ochoa of Principality of Asturias (BP21042). H. Bustince and M. Ferrero-Jaurrieta are supported by Agencia Estatal de Investigación (PID2019-108392GB-I00, AEI/10.13039/501100011033). J. Baz, S. Montes and I. Díaz are supported by the Ministry of Science and Innovation (PDI2022-139886NB-l00). The work of G. Beliakov was supported by the Australian Research
Council Discovery project DP210100227.

[EN] Most of the strategies for boundary image evaluation involve the comparison of computer-generated images with ground truth solutions. While this can be done in different manners, recent years have seen a dominance of techniques based on the use of confusion matrices. That is, techniques that, at the evaluation stage, interpret boundary detection as a classification problem. These techniques require a correspondence between the boundary pixels in the candidate image and those in the ground truth; that correspondence is further used to create the confusion matrix, from which evaluation statistics can be computed. The correspondence between boundary images faces different challenges, mainly related to the matching of potentially displaced boundaries. Interestingly, boundary image comparison relates to many other fields of study in literature, from object tracking to biometrical identification. In this work, we survey all existing strategies for boundary matching, we propose a taxonomy to embrace them all, and perform a usability-driven quantitative analysis of their behaviour., The authors gratefully acknowledge the financial support of the Spanish Ministry of Science (PID2019-108392GB-I00, AEI/10.13039/50110 0 011033), ass well as that of the Research Foundation Flanders (FWO project 3G.0838.12.N)

[EN] 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 stud-
ied, 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 prim-
itives 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., The authors gratefully acknowledge the financial support of the Spanish Ministry of Science and Technology (project
PID2019-108392GB-I00 (AEI/10.13039/501100011033), the Research Services of Universidad Pública de Navarra, CNPq
(307781/2016-0, 301618/2019-4), FAPERGS (19/2551-0001660) and PNPD/CAPES (464880/2019-00).

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., The authors are grateful to their universities. This paper has been supported by FEDER/Junta de Andalucía-Consejería de Transformación Económica, Industria, Conocimiento y Universidades by Project A-FQM-170-UGR20, and also by Ministerio de Ciencia e Innovación by Projects PID2020-119478GB-I00 and PID2019-108392GB-I00 (AEI/ 10.13039/501100011033).

En este trabajo proponemos un nuevo enfoque del algoritmo de clustering gravitacional basado en lo que Einstein considero su 'mayor error': la constante cosmológica. De manera similar al algoritmo de clustering gravitacional, nuestro enfoque está inspirado en principios y leyes del cosmos, y al igual que ocurre con la teoría de la relatividad de Einstein y la teoría de la gravedad de Newton, nuestro enfoque puede considerarse una generalización del agrupamiento gravitacional, donde, el algoritmo de clustering gravitacional se recupera como caso límite. Además, se desarrollan e implementan algunas mejoras que tienen como objetivo optimizar la cantidad de iteraciones finales, y de esta forma, se reduce el tiempo de ejecución tanto para el algoritmo original como para nuestra versión., Este trabajo ha sido respaldado por los proyectos PID2019-
108392GB-I00 (AEI/10.13039/ 501100011033) de la Agencia
Estatal de Investigación.

En muchos problemas reales no se pueden tomar medidas de forma exacta. Así, los conjuntos difusos surgieron como una forma de intentar tratar con la incertidumbre de la forma más eficiente posible. Por otro lado, debe señalarse que la ‘convexidad es un concepto interesante en varias áreas dentro de las matemáticas. Teniendo esto en cuenta, en este documento proponemos una extensión del concepto de convexidad para conjuntos difusos intervalo-valuados basada en el uso de t-normas para intervalos. Para ello, y teniendo en consideración la literatura científica existente respecto de t-normas, presentamos una definición de t-norma aplicada a intervalos. Por último, comprobamos que nuestra definición de convexidad, utilizando t-normas, preserva la convexidad a través de intersecciones, es decir, que la intersección de dos conjuntos difusos intervalo-valuados convexos es también convexa., Este estudio ha sido parcialmente patrocinado por el programa español MINECO
(TIN-2017-87600-P: P. Alonso; PGC2018-098623-B-I00: P. Huidobro
and S. Montes), MICIN (PID2019!108392GB!I00: H. Bustince), la ayuda
no. 1/0150/21 proporcionada por la agencia de subvenciones eslovaca VEGA
(V. Janis) y el programa de ayudas Severo Ochoa PA-20PF-BP19-169 (P.
Huidobro).

Object segmentation is a prominent low-level task in image processing and computer vision. A technique of special relevance within segmentation algorithms is active contour modeling. An active contour is a closed contour on an image which can be evolved to progressively fit the silhouette of certain area or object. Active contours shall be initialized as a closed contour at some position of the image, further evolving to precisely fit to the silhouette of the object of interest. While the evolution of the contour has been deeply studied in literature [5, 11], the study of strategies to define the initial location of the contour is rather absent from it. Typically, such contour is created as a small closed curve around an inner position in the object. However, literature contains no general-purpose algorithms to determine those inner positions, or to quantify their fitness. In fact, such points are frequently set manually by human experts, hence turning the segmentation process into a semi-supervised one. In this work, we present a method to find inner points in relevant object using spatial-tonal fuzzy clustering. Our proposal intends to detect dominant clusters of bright pixels, which are further used to identify candidate points or regions around which active contours can be initialized., The authors gratefully acknowledge the financial support of the grants PID2019-108392GB-I00 funded by MCIN/AEI/10.13039/501100011033, as well as that by the Government of Navarra (PC082-083-084 EHGNA). A. Mir acknowledges the financial support of the grant PID2020-113870GB-I00 funded by MCIN/AEI/10.13039/ 501100011033/.

In this paper we study the aggregation of fuzzy preferences on non-necessarily finite societies. We characterize in terms of possibility and impossibility a family of models of strongly-connected preferences in which the transitivity is defined for any t-norm. For that purpose, we have described each model by means of some crisp binary relations and we have applied the results obtained by Kirman and Sondermann about ultrafilters and Arrovian models., This work is partially supported by the research project PID2019-108392GB-I00 and a predoctoral grant from the UPNA research institutes.

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., Mikel Uriz has been supported by the CDTI and the Spanish Ministry of Science and Innovation under Neotec 2021 (SNEO-20211147). This work was also supported by the Spanish Ministry of Science and Innovation under project PID2019-108392 GB-I00 (AEI/10.13039/501100011033) and by the Public University of Navarre under project PJUPNA25-2022.

Automatic art analysis comprises of utilizing diverse processing methods to classify and categorize works of art. When working with this kind of pictures, we have to take under consideration different considerations compared to classical picture handling, since works of art alter definitely depending on the creator, the scene delineated or their aesthetic fashion. This extra data improves the visual signals gotten from the images and can lead to better performance. However, this information needs to be modeled and embed alongside the visual features of the image. This is often performed utilizing deep learning models, but they are expensive to train. In this paper we utilize the Fuzzy C-Means algorithm to create a embedding strategy based on fuzzy memberships to extract relevant information from the clusters present in the contextual information. We extend an existing state-of-the-art art classification system utilizing this strategy to get a new version that presents similar results without training additional deep learning models., Javier Fumanal Idocin and Humberto Bustince’s research has been supported by the project PID2019-108392GB I00 (AEI/10.13039/501100011033). Zdenko Takác and Lúbomíra Horanská’s research has been supported by the grant VEGA 1/0267/21.

The study of orders is a constantly evolving topic, not only for its interest from a theoretical point of view, but also for its possible applications. Recently, one of the hot lines of research has been the construction of admissible orders in different frameworks. Following this direction, this paper presents a new representation theorem in the field of discrete fuzzy numbers that enables the construction of two families of admissible orders in the set of discrete fuzzy numbers whose support is a closed interval of a finite chain, leading to the first admissible orders introduced in this framework., This work has been partially supported by the Spanish Grants FEDER/Ministerio de Economía, Industria y Competitividad-AEI/TIN2016-75404-P and PID2019-108392GB-I00 (AEI/10.13039/501100011033).

In this paper we propose an extension of the notion of deviation-based aggregation function tailored to aggregate multidimensional data. Our objective is both to improve the results obtained by other methods that try to select the best aggregation function for a particular set of data, such as penalty functions, and to reduce the temporal complexity required by such approaches. We discuss how this notion can be defined and present three illustrative examples of the applicability of our new proposal in areas where temporal constraints can be strict, such as image processing, deep learning and decision making, obtaining favourable results in the process., The research done by Humberto Bustince, Iosu Rodríguez Martínez and Javier Fumanal Idocin has been funded by the project PID2019-108392GB-I00: 3031138640/AEI/10.13039/501100011033. The work of Martin Papčo was supported by the Slovak Research and Development Agency under the contract No. APVV-16-0073.

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)., This work has been funded by the Spanish ministry MCIN , with the project PID2019-108392GB-I00/AEI/10.13039/501100011033, by the Public University of Navarra under the project PJUPNA25-2022 and by the grant APVV-18-0052 by the Slovak Research and Development Agency .

The fuzzy implication on bounded lattices was introduced by Palmeira et al., and the method of extending fuzzy implications on bounded lattices by using retraction was provided. However, we find that the extension of fuzzy implications on bounded lattices can also be realized through homomorphism. In order to get better results, we will continue to study this topic in this paper. In particular, we will focus on the construction methods of fuzzy implications on bounded posets. More precisely, we will give some construction methods of fuzzy implications via 0,1-homomorphism on bounded posets. Then we further study two special kinds of fuzzy implications, (Q,N)-implications and RQ-implications on bounded posets, where Q is a quasi-overlap function. Finally, we discuss the distributive laws and the importation laws of (Q,N)-implications and RQ-implications over a quasi-overlap function Q., This work is supported by NNSFC (12271319) and by grant PID2019-108392GB-I00 financed by AEI/10.13039/501100011033.

The detection of building footprints and road networks has many useful applications including the monitoring of urban development, real-time navigation, etc. Taking into account that a great deal of human attention is required by these remote sensing tasks, a lot of effort has been made to automate them. However, the vast majority of the approaches rely on very high-resolution satellite imagery (<2.5 m) whose costs are not yet affordable for maintaining up-to-date maps. Working with the limited spatial resolution provided by high-resolution satellite imagery such as Sentinel-1 and Sentinel-2 (10 m) makes it hard to detect buildings and roads, since these labels may coexist within the same pixel. This paper focuses on this problem and presents a novel methodology capable of detecting building and roads with sub-pixel width by increasing the resolution of the output masks. This methodology consists of fusing Sentinel-1 and Sentinel-2 data (at 10 m) together with OpenStreetMap to train deep learning models for building and road detection at 2.5 m. This becomes possible thanks to the usage of OpenStreetMap vector data, which can be rasterized to any desired resolution. Accordingly, a few simple yet effective modifications of the U-Net architecture are proposed to not only semantically segment the input image, but also to learn how to enhance the resolution of the output masks. As a result, generated mappings quadruplicate the input spatial resolution, closing the gap between satellite and aerial imagery for building and road detection. To properly evaluate the generalization capabilities of the proposed methodology, a data-set composed of 44 cities across the Spanish territory have been considered and divided into training and testing cities. Both quantitative and qualitative results show that high-resolution satellite imagery can be used for sub-pixel width building and road detection following the proper methodology., Christian Ayala was partially supported by the Goverment of Navarra under the industrial PhD program 2020 reference 0011-1408-2020-000008. Mikel Galar was partially supported by Tracasa Instrumental S.L. under projects OTRI 2018-901-073, OTRI 2019-901-091, and OTRI 2020-901-050, and by the Spanish MICIN (PID2019-108392GB-I00/AEI/10.13039/501100011033).

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., This research was funded by CNPq (grant numbers: 312053/2018-5, 301618/2019-4, 311429/2020-3), FAPERGS (grant number: 19/2551-0001660-3), CAPES-Print (grant number: 88887.363001/2019-00), Spanish Ministry Science and Tech. (grant numbers: TIN2016-77356-P, PID2019-108392GB I00 (AEI/10.13039/501100011033)), and Fundación “La Caixa” (grant number: LCF/PR/PR13/51080004).

Precise and reliable identification of specific plant diseases is a challenge within precision agriculture nowadays. This is the case of esca, a complex grapevine trunk disease, that represents a major threat to modern viticulture as it is responsible for large economic losses annually. The lack of effective control strategies and the complexity of esca disease expression make essential the identification of affected plants, before symptoms become evident, for a better management of the vineyard. This study evaluated the suitability of a near-infrared hyperspectral imaging (HSI) system to detect esca disease in asymptomatic grapevine leaves of Tempranillo red-berried cultivar. For this, 72 leaves from an experimental vineyard, naturally infected with esca, were collected and scanned with a lab-scale HSI system in the 900-1700 nm spectral range. Then, effective image processing and multivariate analysis techniques were merged to develop pixel-based classification models for the distinction of healthy, asymptomatic and symptomatic leaves. Automatic and interval partial least squares variable selection methods were tested to identify the most relevant wavelengths for the detection of esca-affected vines using partial least squares discriminant analysis and different pre-processing techniques. Three-class and two-class classifiers were carried out to differentiate healthy, asymptomatic and symptomatic leaf pixels, and healthy from asymptomatic pixels, respectively. Both variable selection methods performed similarly, achieving good classification rates in the range of 82.77-97.17% in validation datasets for either three-class or two-class classifiers. The latter results demonstrated the capability of hyperspectral imaging to distinguish two groups of seemingly identical leaves (healthy and asymptomatic). These findings would ease the annual monitoring of disease incidence in the vineyard and, therefore, better crop management and decision making., This research was supported by Public University of Navarre postgraduate scholarships (FPI-UPNA-2017), by the Spanish Ministry of Economy and Competitiveness (AGL2017-83738-C3-1R, AEI/EU-FEDER), and by the Spanish Ministry of Science, Innovation and Universities (PID2019-108392GB-I00, AEI/10.13039/ 501100011033).

In this work we generalize the notion of restricted equivalence function for type-2 fuzzy sets, leading to the notion of extended restricted equivalence functions. We also study how under suitable conditions, these new functions recover the standard axioms for restricted equivalence functions in the real setting. Extended restricted equivalence functions allow us to compare any two general type-2 fuzzy sets and to generate a similarity measure for type-2 fuzzy sets. The result of this similarity is a fuzzy set on the same referential set (i.e., domain) as the considered type-2 fuzzy set. The latter is crucial for applications such as explainable AI and decision making, as it enables an intuitive interpretation of the similarity within the domain-specific context of the fuzzy sets. We show how this measure can be used to compare type-2 fuzzy sets with different membership functions in such a way that the uncertainty linked to type-2 fuzzy sets is not lost. This is achieved by generating a fuzzy set rather than a single numerical value. Furthermore, we
also show how to obtain a numerical value for discrete referential sets., This work has been supported by the Research Services of Universidad Pública de Navarra as well as by the Projects PID2019-108392GBI00, financed by MCIN/AEI/10.13039/501100011033), TIN2017-89517-P, by grant VEGA 1/0267/21 and UK EPSRC grant EP/P011918/1.

Demographic biases in source datasets have been shown as one of the causes of unfairness and discrimination in the predictions of Machine Learning models. One of the most prominent types of demographic bias are statistical imbalances in the representation of demographic groups in the datasets. In this paper, we study the measurement of these biases by reviewing the existing metrics, including those that can be borrowed from other disciplines. We develop a taxonomy for the classification of these metrics, providing a practical guide for the selection of appropriate metrics. To illustrate the utility of our framework, and to further understand the practical characteristics of the metrics, we conduct a case study of 20 datasets used in Facial Emotion Recognition (FER), analyzing the biases present in them. Our experimental results show that many metrics are redundant and that a reduced subset of metrics may be sufficient to measure the amount of demographic bias. The paper provides valuable insights for researchers in AI and related fields to mitigate dataset bias and improve the fairness and accuracy of AI models., This work was supported in part by a predoctoral fellowship from the Research Service of the Universidad Pública de Navarra through open access funding, in part by the Spanish MICIN under Grants PID2019-108392GB-I00, PID2020-118014RB-I00, and PID2022-136627NB-I00/AEI/10.13039/501100011033 FEDER, UE, and in part by the Government of Navarre under Grant 0011-1411-2020-000079 - Emotional Films.

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., The authors gratefully acknowledge the financial support of the Spanish Ministry of Science and Technology (project PID2019-108392GB-I00 (AEI/10.13039/501100011033), the Research Services of Universidad Pública de Navarra, CNPq (307781/2016-0, 301618/2019-4), FAPERGS (19/2551-0001660) and PNPD/CAPES (464880/2019-00).

En este trabajo presentamos el modelado de redes
sociales y detección de comunidades utilizando como base un evento histórico real, las conquistas de César Borgia en el siglo XV. Para ello, proponemos un nuevo conjunto de funciones, llamadas funciones de afinidad, disenadas para capturar la 'naturaleza de las interacciones locales entre cada par de actores
en una red. Utilizando estas funciones, desarrollamos un nuevo algoritmo de detección de comunidades, el Borgia Clustering, donde las comunidades surgen naturalmente de un proceso de simulación de interacción de múltiples agentes en la red. También discutimos los efectos del tamaño y la escala de cada
comunidad, y como pueden ser tomadas en cuenta en el proceso de simulación. Finalmente, comparamos nuestra detección de comunidades con otros algoritmos representativos, encontrando
resultados favorables a nuestra propuesta., El trabajo de Javier Fumanal Idocin y Humberto Bustince
ha sido financiado por el proyecto PID2019-108392GB-I00
(AEI/10.13039/ 501100011033).
El trabajo de Oscar Cordón ha sido financiado por el
Gobierno de España, EXASOCO (PGC2018-101216-B-I00),
incluyendo fondos de desarrollo regional europeo (ERDF). La investigación de Amparo Alonso Betanzos ha sido
parcialmente financiado por el Ministerio de Economía y
Competitividad de España (TIN2015-65069-C2-1-R), por los
fondos europeos FEDER y por la Consellería de Industria de
la Xunta de Galicia (GRC2014 /035).
El trabajo de María Minárová ha sido financiado por los
proyectos APVV-17-0066, and APVV-18-0052.

Social network analysis is a popular discipline among the social and behavioural sciences, in which the relationships between different social entities are modelled as a network. One of the most popular problems in social network analysis is finding communities in its network structure. Usually, a community in a social network is a functional sub-partition of the graph. However, as the definition of community is somewhat imprecise, many algorithms have been proposed to solve this task, each of them focusing on different social characteristics of the actors and the communities. In this work we propose to use novel combinations of affinity functions, which are
designed to capture different social mechanics in the network interactions. We use them to extend already existing community detection algorithms in order to
combine the capacity of the affinity functions to model different social interactions than those exploited by the original algorithms., Javier Fumanal Idocin and Humberto
Bustince’s re-search has been supported
by the project PID2019-108392GBI00
(AEI/10.13039/501100011033).
Maria Minarová research has been funded by the project work was supported by the projects APVV-17-0066 andAPVV-18-0052.
Oscar Cordon’s research was supported by the Spanish Ministry of Science, Innovation and Universities under grant EXASOCO (PGC2018-101216-B-I00), including, European Regional Development Funds (ERDF).

Ordered Weighted Averaging (OWA) operators have been integrated in Convolutional Neural Networks (CNNs) for image classification through the OWA layer. This layer lets the CNN integrate global information about the image in the early stages, where most CNN architectures only allow for the exploitation of local information. As a side effect of this integration, the OWA layer becomes a practical method for the determination of OWA operator weights, which is usually a difficult task that complicates the integration of these operators in other fields. In this paper, we explore the weights learned for the OWA operators inside the OWA layer, characterizing them through their basic properties of orness and dispersion. We also compare them to some families of OWA operators, namely the Binomial OWA operator, the Stancu OWA operator and the expo-nential RIM OWA operator, finding examples that are currently impossible to generalize through these parameterizations., This work was funded by a predoctoral fellowship of the Research Service of Universidad Pública de Navarra, the Universidad Pública de Navarra under project PJUPNA1926, and the Spanish MICIN (PID2019-108392GB-I00 / AEI / 10.13039/501100011033).

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., This work was supported by Navarra de Servicios y Tecnologías, S.A. (NASERTIC), FAPERGS-Brazil (19/2551-0001279-9, 19/2551-0001660), CNPq-Brazil (301618/2019-4, 305805/2021-5), the Spanish Ministry of Science and Technology (TIN2016-77356-P, PID2019-108392GB-I00 (MCIN/AEI/10.13039/501100011033)).

Automatic image detection is one of the most im- portant areas in computing due to its potential application in numerous real-world scenarios. One important tool to deal with that is called overlap indices. They were introduced as a procedure to provide the maximum lack of knowledge when comparing two fuzzy objects. They have been successfully applied in the following fields: image processing, fuzzy rule-based systems, decision making and computational brain interfaces. This notion of overlap indices is also necessary for applications in which type-2 fuzzy sets are required. In this paper we introduce the notion of type-(2, k) overlap index (k 0, 1, 2) in the setting of type-2 fuzzy sets. We describe both the reasons that have led to this notion and the relationships that naturally arise among the algebraic underlying structures. Finally, we illustrate how type- (2, k) overlap indices can be employed in the setting of fuzzy rule-based systems when the involved objects are type-2 fuzzy sets., This manuscript has been partially supported by Junta de Andalucía by Projects A-FQM-170-UGR20 (Program FEDER Andalucía 2014-2020) and FQM-365 (Andalusian CICYE), and also by Projects PID2020-119478GBI00 and PID2019-108392GB-I00 (AEI/10.13039/501100011033, Ministerio
de Ciencia e Innovación), by CNPq (301618/2019-4), FAPERGS (19/2551- 0001660) and grant VEGA 1/0267/21.

En este trabajo proponemos un nuevo enfoque del
algoritmo de clustering gravitacional basado en lo que Einstein considero su 'mayor error': la constante cosmológica. De manera similar al algoritmo de clustering gravitacional, nuestro enfoque
está inspirado en principios y leyes del cosmos, y al igual que ocurre con la teoría de la relatividad de Einstein y la teoría de la gravedad de Newton, nuestro enfoque puede considerarse
una generalización del agrupamiento gravitacional, donde, el algoritmo de clustering gravitacional se recupera como caso límite. Además, se desarrollan e implementan algunas mejoras que tienen como objetivo optimizar la cantidad de iteraciones finales, y de esta forma, se reduce el tiempo de ejecución tanto para el algoritmo original como para nuestra versión., Este trabajo ha sido respaldado por los proyectos PID2019-108392GB-I00 (AEI/10.13039/ 501100011033) de la Agencia Estatal de Investigación.

Las redes convolucionales llevan a cabo un proceso automatico de extracción y fusión de características mediante el cual obtienen la información más relevante de una imagen dada. El proceso de submuestreo mediante el cual se fusionan características localmente próximas, conocido como ‘pooling’, se lleva a cabo tradicionalmente con funciones sencillas como el máximo o la media aritmética, ignorando otras opciones muy populares en el campo de la teoría de agregaciones. En este trabajo proponemos reemplazar dichas funciones por otra serie de ordenes estadísticos, así como por la integral de Sugeno y una nueva generalización de la misma. Además, basándonos en trabajos que emplean la combinación convexa del máximo y la media, presentamos una nueva capa que permite combinar varias de las nuevas agregaciones, mejorando sus resultados individuales., Este trabajo ha sido financiado por los proyectos de investigación PID2019-108392GB-I00 (AEI/10.13039/501100011033) de la Agencia Estatal de Investigación, PC095-096 FUSIPROD y P18-FR-4961.

Denoising Diffusion Probabilistic Models have exhibited impressive performance for generative modelling of images. This paper aims to explore the potential of diffusion models for semantic segmentation tasks in the context of remote sensing. The major challenge of employing these models for semantic segmentation tasks is the generative nature of the model, which produces an arbitrary segmentation mask from a random noise input. Therefore, the diffusion process needs to be constrained to produce a segmentation mask that matches the target image. To address this issue, the denoising process is conditioned by utilizing the input image as a reference. In the experimental study, the proposed model is compared against other state-of-the-art semantic segmentation architectures using the Massachusetts Buildings Aerial dataset. The results of this study provide valuable insights into the potential of diffusion models for semantic segmentation tasks in the field of remote sensing., Thanks to the Government of Navarre for supporting under the industrial PhD program 2020 reference 0011-1408-2020-000008 Thanks to the Spanish Ministry of Science and Innovation for supporting under project PID2019-108392GB-I00 (AEI/10.13039/501100011033) and the Public University of Navarre under project PJUPNA25-2022.

At present, in the field of aggregation of various input values, attention is focused on the construction of aggregation functions using other functions that can affect the resulting aggregated value. This resulting value should characterize the properties of the individual input values as accurately as possible. Attention is also paid to aggregation using the so-called moderate deviation function. Using this function in aggregation ensures that all properties of aggregation functions are preserved. This work offers constructions of the moderate deviation functions using negations and automorphisms on the symmetric interval [−1, 1] and a general closed interval [a, b] ⊂ [−∞, ∞]., The work of Jana Špirková has been supported by the Slovak Scientific Grant Agency VEGA no. 1/0150/21. The work of Humberto Bustince, Javier Fernandez and Mikel Sesma-Sara has been supported by grand PID2019-108392GB-I00 (AEI/10.13039/501100011033).

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., This work was supported by the Spanish Ministry of Economy and Competitiveness through the Spanish National Research (project PID2019-108392GB-I00/ financed by MCIN/AEI/10.13039/501100011033 and the grant VEGA 1/0267/21 ).

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., The authors gratefully acknowledge the financial support of Tracasa Instrumental (iTRACASA) and of the Gobierno de Navarra -
Departamento de Universidad, Innovación y Transformación Digital,
as well as that of the Spanish Ministry of Science (project PID2019-108392GB-I00 (AEI/10.13039/501100011033)) and the project
PC095-096 FUSIPROD. T. Asmus and G.P. Dimuro are supported by the
projects CNPq (301618/2019-4) and FAPERGS (19/2551-0001279-9).
F. Herrera is supported by the Andalusian Excellence project P18-FR4961. Z. Takáč is supported by grant VEGA 1/0267/21. Open access
funding provided by Universidad Pública de Navarra.

In this article, we go deeper into the study of some types of decompositions defined by triangular norms and conorms. We work in the spirit of the classical Arrovian models in the fuzzy setting and their possible extensions. This allows us to achieve characterizations of existence and uniqueness for such decompositions. We provide rules to obtain them under some specific conditions. We conclude by applying the results achieved to the study of fuzzy preferences., This work has been partially supported by the research projects whose references are PID2019-108392GB-I00 (AEI/10.13039/501100011033), PID2021-127799NB-I00 and PID2022-1366274NBI00 from the Ministry of Science and Innovation of Spain, as well as the Ayudas para la Recualificación del Sistema Universitario Español para 2021-2023, UPNA. Modalidad Margarita Salas funded by the European Union-NextGenerationEU and a predoctoral grant from the UPNA Research Institutes.

Throughout this paper, our main idea is to analyze from a theoretical and normative point of view different methods to aggregate individual rankings. To do so, first we introduce the concept of a general mean on an abstract set. This new concept conciliates the social choice where well-known impossibility results as the Arrovian ones are encountered and the decision-making approaches where the necessity of fusing rankings is unavoidable. Moreover it gives rise to a reasonable definition of the concept of a ranking fusion function that does indeed satisfy the axioms of a general mean. Then we will introduce some methods to build ranking fusion functions, paying a special attention to the use of score functions, and pointing out the equivalence between ranking and scoring. To conclude, we prove that any ranking fusion function introduces a partial order on rankings implemented on a finite set of alternatives. Therefore, this allows us to compare rankings and different methods of aggregation, so that in practice one should look for the maximal elements with respect to such orders defined on rankings IEEE., This work is partially supported by the research projects ECO2015-65031-R, MTM2015-63608-P (MINECO/ AEI-FEDER, UE), TIN2016-77356-P (MINECO/ AEI-FEDER, UE), PID2019-108392GB-I00 (AEI/10.13039/501100011033), and Brazilian National Council for Scientific and Technological Development CNPq (Proc. 307781/2016-0).

This work aims to evaluate explainable classification methods for the detection of fish species from hydroacoustic data acquired by echo sounders at a region near the coastline of south and southeastern Brazil. Decision trees and fuzzy rule-based methods were adopted. The fitted models were evaluated by quality measures based on the performance of the classifiers and also by an expert which analyzed the usefulness of the rules on describing the schools. The models learned by the algorithms performed well for the available data and were able to represent the documented behavior of the species considered in the studied region, according to the literature., This study was supported by the Spanish Ministry of Science (TIN2016-77356-P, PID2019-108392GB-I00 AEI/10.13039/501100011033), PNPD/CAPES (464880/2019-00), CNPq (301618/2019-4), FAPERGS (19/2551-0001660), and CAPES Financial Code 001.

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., The authors gratefully acknowledge the financial support of the grant PID2019-108392GB-I00 funded by
MCIN/AEI/10.13039/50110001103, as well as grant VEGA
1/0545/20. Also, the financial support of Consellería
d’Innovacio, Universitats, Ciencia i Societat Digital from Comunitat Valenciana (APOSTD/2021/227) and the European Social Fund (Investing In Your Future) and to Tracasa Instrumental and the Immigration Policy and Justice Department of
the Government of Navarre.

Imbalanced classification problems are attracting the attention of the research community because they are prevalent in real-world problems and they impose extra difficulties for learning methods. Fuzzy rule-based classification systems have been applied to cope with these problems, mostly together with sampling techniques. In this paper, we define a new fuzzy association rule-based classifier, named FARCI, to tackle directly imbalanced classification problems. Our new proposal belongs to the algorithm modification category, since it is constructed on the basis of the state-of-the-art fuzzy classifier FARC–HD. Specifically, we modify its three learning stages, aiming at boosting the number of fuzzy rules of the minority class as well as simplifying them and, for the sake of handling unequal fuzzy rule lengths, we also change the matching degree computation, which is a key step of the inference process and it is also involved in the learning process. In the experimental study, we analyze the effectiveness of each one of the new components in terms of performance, F-score, and rule base size. Moreover, we also show the superiority of the new method when compared versus FARC–HD alongside sampling techniques, another algorithm modification approach, two cost-sensitive methods and an ensemble., This work was supported in part by the Spanish Ministry of Economy and Competitiveness through the Spanish National Research (project PID2019-108392GB-I00/AEI/10.13039/501100011033) and by the Public University of Navarre under the project PJUPNA1926.

The relaxation of the property of monotonicity is a trend in the theory of aggregation and fusion functions and several generalized forms of monotonicity have been introduced, most of which are based on the notion of directional monotonicity. In this paper, we propose a general framework for generalized monotonicity that encompasses the different forms of monotonicity that we can find in the literature. Additionally, we introduce various new forms of monotonicity that are not based on directional monotonicity. Specifically, we introduce dilative monotonicity, which requires that the function increases when the inputs have increased by a common factor, and a general form of monotonicity that is dependent on a function T and a subset of the domain Z. This two new generalized monotonicities are the basis to propose a set of different forms of monotonicity. We study the particularities of each of the new proposals and their links to the previous relaxed forms of monotonicity. We conclude that the introduction of dilative monotonicity complements the conditions of weak monotonicity for fusion functions and that (T,Z)-monotonicity yields a condition that is slightly stronger than weak monotonicity. Finally, we present an application of the introduced notions of monotonicity in sentiment analysis., This work has been funded by the Spanish ministry MCIN, with the project PID2019-108392GB-I00/AEI/10.13039/501100011033, by the Public University of Navarra under the project PJUPNA25-2022 and by the grant APVV-18-0052 by the Slovak Research and Development Agency. Open access funding provided by Universidad Pública de Navarra.

Choosing the proper ground sampling distance (GSD) is a vital decision in remote sensing, which can determine the success or failure of a project. Higher resolutions may be more suitable for accurately detecting objects, but they also come with higher costs and require more computing power. Semantic segmentation is a common task in remote sensing where GSD plays a crucial role. In semantic segmentation, each pixel of an image is classified into a predefined set of classes, resulting in a semantic segmentation map. However, comparing the results of semantic segmentation at different GSDs is not straightforward. Unlike scene classification and object detection tasks, which are evaluated at scene and object level, respectively, semantic segmentation is typically evaluated at pixel level. This makes it difficult to match elements across different GSDs, resulting in a range of methods for computing metrics, some of which may not be adequate. For this reason, the purpose of this work is to set out a clear set of guidelines for fairly comparing semantic segmentation results obtained at various spatial resolutions. Additionally, we propose to complement the commonly used scene-based pixel-wise metrics with region-based pixel-wise metrics, allowing for a more detailed analysis of the model performance. The set of guidelines together with the proposed region-based metrics are illustrated with building and swimming pool detection problems. The experimental study demonstrates that by following the proposed guidelines and the proposed region-based pixel-wise metrics, it is possible to fairly compare segmentation maps at different spatial resolutions and gain a better understanding of the model's performance. To promote the usage of these guidelines and ease the computation of the new region-based metrics, we create the seg-eval Python library and make it publicly available at https://github.com/itracasa/ seg-eval., The work of Christian Ayala was supported in part by the Government of Navarre through the Industrial Ph.D. Program 2020 Reference under Grant 0011-1408-2020-000008. The work of Mikel Galar was supported in part by the Spanish Ministry of Science and Innovation (MCIN/Agencia Estatal de Investigación
(AEI)/10.13039/501100011033) under Project PID2019-108392GB-I00 and Project PID2022-136627NB-I00 and in part by the Public University of Navarre under Project PJUPNA25-2022.

This paper presents a modification of a Michigan-style fuzzy rule based classifier by applying the Choquet-like Copula-based aggregation function, which is based on the minimum t-norm and satisfies all the conditions required for an aggregation function. The proposed new version of the algorithm aims at improving the accuracy in comparison to the original algorithm and involves two main modifications: replacing the fuzzy reasoning method of the winning rule by the one based on Choquet-like Copula-based aggregation function and changing the calculus of the fitness of each fuzzy rule. The modification proposed, as well as the original algorithm, uses a (1+1) evolutionary strategy for learning the fuzzy rulebase and it shows promising results in terms of accuracy, compared to the original algorithm, over ten classification datasets with different sizes and different numbers of variables and clases., This work was supported by the Universidad Nacional de San Agustin de Arequipa under Project IBAIB-06-2019-UNSA and in part by the Spanish Ministry of Economy and Competitiveness through the Spanish National Research (project PID2019-108392GB-I00 / AEI / 10.13039/501100011033) and by the Public University of Navarre under the project PJUPNA1926.

Overlap and grouping functions are important aggregation operators, especially in information fusion, classification and decision-making problems. However, when we do more in-depth application research (for example, non-commutative fuzzy reasoning, complex multi-attribute decision making and image processing), we find overlap functions as well as grouping functions are required to be commutative (or symmetric), which limit their wide applications. For the above reasons, this paper expands the original notions of overlap functions and grouping functions, and the new concepts of pseudo overlap functions and pseudo grouping functions are proposed on the basis of removing the commutativity of the original functions. Some examples and construction methods of pseudo overlap functions and pseudo grouping functions are presented, and the residuated implication (co-implication) operators derived from them are investigated. Not only that, some applications of pseudo overlap (grouping) functions in multi-attribute (group) decision-making, fuzzy mathematical morphology and image processing are discussed. Experimental results show that, in many application fields, pseudo overlap functions and pseudo grouping functions have greater flexibility and practicability., This research was funded by National Natural Science Foundation of China (No. 12271319) and research project No. PID2019-108392GB-I00 (AEI/10.13039/501100011033). The Major Program of the National Social Science Foundation of China under Grant No. 20&ZD047.

Semantic segmentation of remote sensing images has many practical applications such as urban planning or disaster assessment.
Deep learning-based approaches have shown their usefulness in automatically segmenting large remote sensing images, helping
to automatize these tasks. However, deep learning models require large amounts of labeled data to generalize well to unseen
scenarios. The generation of global-scale remote sensing datasets with high intraclass variability presents a major challenge. For
this reason, data augmentation techniques have been widely applied to artificially increase the size of the datasets. Among them,
photometric data augmentation techniques such as random brightness, contrast, saturation, and hue have been traditionally applied
aiming at improving the generalization against color spectrum variations, but they can have a negative effect on the model due
to their synthetic nature. To solve this issue, sensors with high revisit times such as Sentinel-1 and Sentinel-2 can be exploited
to realistically augment the dataset. Accordingly, this paper sets out a novel realistic multi-temporal color data augmentation
technique. The proposed methodology has been evaluated in the building and road semantic segmentation tasks, considering a
dataset composed of 38 Spanish cities. As a result, the experimental study shows the usefulness of the proposed multi-temporal
data augmentation technique, which can be further improved with traditional photometric transformations., Christian Ayala was partially supported by the Government
of Navarra under the industrial Ph.D. program 2020 reference
0011-1408-2020-000008. Mikel Galar was partially supported
by Tracasa Instrumental S.L. under the project OTRI 2020-
901-156, and by the Spanish MICIN (PID2019-108392GB-I00
/ AEI / 10.13039/501100011033).

Este trabajo es un resumen del artículo [1] publicado
en Mathematics para su presentación en la Multiconferencia CAEPIA’21 KeyWorks., Este trabajo ha estado parcialmente financiado por los proyectos FEDER/Ministerio de Economía, Industria y Competitividad - AEI/TIN2016-75404-P y PID2019-108392GBI00 (AEI/10.13039/501100011033).

In this work, we introduce the notion of dG-Choquet integral, which generalizes the discrete Choquet integral replacing, in the first place, the difference between inputs represented by closed subintervals of the unit interval [0,1] by a dissimilarity function; and we also replace the sum by more general appropriate functions. We show that particular cases of dG-Choquet integral are both the discrete Choquet integral and the d-Choquet integral. We define interval-valued fuzzy measures and we show how they can be used with dG-Choquet integrals to define an interval-valued discrete Choquet integral which is monotone with respect to admissible orders. We finally study the validity of this interval-valued Choquet integral by means of an illustrative example in a classification problem. © 2021, This work was supported in part by the Spanish Ministry of Science and Technology, under project PID2019-108392GB-I00 (AEI/10.13039/501100011033), by the project PJUPNA-1926 of the Public University of Navarre and by the project VEGA 1/0267/21 .

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., The authors gratefully acknowledge the partial support of Brazilian funding agencies CNPq (301618/2019-4, 200282/2022-0, 409696/2022-6), CNPq/FAPERGS (23/2551-0000126-8), Agencia Estatal de Investigación from the Government of Spain (PID2019-108392GB-I00 (AEI/10.13039/ 501100011033)), and Fundación La Caixa.

An effective way to cope with classification problems, among others, is by using Fuzzy Rule-Based Classification Systems (FRBCSs). These systems are composed by two main components, the Knowledge Base (KB) and the Fuzzy Reasoning Method (FRM). The FRM is responsible for performing the classification of new examples based on the information stored in the KB. A key point in the FRM is how the information given by the fired fuzzy rules is aggregated. Precisely, the aggregation function is the component that differs from the two most widely used FRMs in the specialized literature. In this paper we provide a revision of the literature discussing the generalizations of the Choquet integral that has been applied in the FRM of a FRBCS. To do so, we consider an analysis of different generalizations, by t-norms, copulas, and by F functions. Also, the main contributions of each generalization are discussed., Supported by PNPD/CAPES (process. 464880/2019-00), FAPERGS (19/2551-0001279-9, 19/2551-0001660), CNPq (301618/2019-4), the Spanish Ministry of Science and Technology (TIN2016-77356-P, PID2019-108392GB I00 (AEI/10.13039/501100 011033)).

In this paper we propose a new generalization for the notion of homogeneous functions. We show some properties and how it appears in some scenarios. Finally we show how this generalization can be used in order to provide a new paradigm for decision making theory called consistent influenced/disturbed decision making. In order to illustrate the applicability of this new paradigm, we provide a toy example., Supported by CNPq (312053/2018-5, 311429/2020-3, 301618/2019-4), CAPES (88887.363001/2019-00), FAPERGS (19/2551-0001279-9, 19/2551-0001660-3) and by Research project PID2019-108392GBI00 (3031138640/AEI/10.13039/501100011033).

Overlap functions are a class of aggregation functions that measure the overlapping degree between two values. They have been successfully applied as a fuzzy conjunction operation in several problems in which associativity is not required, such as image processing and classification. Interval-valued overlap functions were defined as an extension to express the overlapping of interval-valued data, and they have been usually applied when there is uncertainty regarding the assignment of membership degrees, as in interval-valued fuzzy rule-based classification systems. In this context, the choice of a total order for intervals can be significant, which motivated the recent developments on interval-valued aggregation functions and interval-valued overlap functions that are increasing to a given admissible order, that is, a total order that refines the usual partial order for intervals. Also, width preservation has been considered on these recent works, in an intent to avoid the uncertainty increase and guarantee the information quality, but no deeper study was made regarding the relation between the widths of the input intervals and the output interval, when applying interval-valued functions, or how one can control such uncertainty propagation based on this relation. Thus, in this paper we: (i) introduce and develop the concepts of width-limited interval-valued functions and width limiting functions, presenting a theoretical approach to analyze the relation between the widths of the input and output intervals of bivariate interval-valued functions, with special attention to interval-valued aggregation functions; (ii) introduce the concept of (a,b)-ultramodular aggregation functions, a less restrictive extension of one-dimension convexity for bivariate aggregation functions, which have an important predictable behaviour with respect to the width when extended to the interval-valued context; (iii) define width-limited interval-valued overlap functions, taking into account a function that controls the width of the output interval and a new notion of increasingness with respect to a pair of partial orders (≤1,≤2); (iv) present and compare three construction methods for these width-limited interval-valued overlap functions, considering a pair of orders (≤1,≤2), which may be admissible or not, showcasing the adaptability of our developments., Supported by CNPq (311429/2020-3, 301618/2019-4), FAPERGS (19/2551-0001660) and the Spanish Ministries of Science and Technology and of Economy and Competitiveness (TIN2016-77356-P, PID2019-108392GB I00 (AEI/10.13039/501100011033) ), by UPNA (PJUPNA1926) and the Grant APVV-0052-18.

The impreciseness of numeric input data can be expressed by intervals. On the other hand, the normalization of numeric data is a usual process in many applications. How do we match the normalization with impreciseness on numeric data? A straightforward answer is that it is enough to apply a correct interval arithmetic, since the normalized exact value will be enclosed in the resulting 'normalized' interval. This paper shows that this approach is not enough since the resulting 'normalized' interval can be even wider than the input intervals. So, we propose a pair of axioms that must be satisfied by an interval arithmetic in order to be applied in the normalization of intervals. We show how some known interval arithmetics behave with respect to these axioms. The paper ends with a discussion about the current paradigm of interval computations., This study was funded by National Council for Scientific and Technological Development (CNPq) within the project 312053/2018-5, by Coordination for the Improvement of Higher Education Personnel (CAPES) within the project Capes-Print 88887.363001/2019-00. Ministerio de Ciencia y innovación within the project PID2019-108392GB-I00 (AEI/10.13039/501100011033).

The aggregation of several predictors in time series forecasting has been used intensely in the last decade in order to construct a better resulting model. Some of the most used alternatives are the ones related to the Induced Ordered Weighted Averaging (IOWA), in which the prediction values are ordered using a secondary vector, often related to the accuracy of the prediction model in the last prediction. Although the time series study has been historically a subject related to statistics and stochastic processes, the random behaviour of the aggregation process is typically not considered. In addition, extensions of aggregation functions with a weaker notion of monotonicity, pre-aggregation functions, are appearing as better alternative for some topics such us classification. In this paper, a pre-aggregation extension of the IOWA operator, the Induced Ordered Linear Fusion (IOLF), is defined as a way to aggregate time series model predictions and its behaviour is studied from a probabilistic point of view. The IOLF operator over random vectors is defined, its properties studied and the relation between some averaging aggregation functions established. The expressions of the optimal weights according to statistical criteria are derived. The advantages and consequences of the use of the IOLF operator are studied, and its behaviour is compared to the usual procedures. Numerical results illustrate its performance on a practical example., J. Baz is partially supported by Programa Severo Ochoa of Principality of Asturias (BP21042). H. Bustince and M. Ferrero-Jaurrieta are supported by Agencia Estatal de Investigación (PID2019-108392GB-I00 , AEI/10.13039/501100011033). J. Baz, S. Montes and I. Díaz are supported by the Ministry of Science and Innovation (PDI2022-139886NB-l00). The work of G. Beliakov was supported by the Australian Research Council Discovery project DP210100227.

Throughout this paper, our main idea is to analyze the concepts of a strong negation and a restricted equivalence function, that appear in a natural way when dealing with theory and applications of fuzzy sets and fuzzy logic. Here we will use an analytical and topological approach, showing how to construct them in an easy way. In particular, we will also analyze some classical functional equation related to those key concepts., This work has been partially supported by the research projects TIN2016-77356-P ( MINECO/AEI-FEDER , UE) and PID2019-108392GB-I00 financed by MCIN/AEI /10.13039/501100011033.