Rodríguez Martínez, Iosu
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Rodríguez Martínez
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Iosu
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Estadística, Informática y Matemáticas
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Publication Embargo Extremal values-based aggregation functions(Elsevier, 2024-10-01) Halaš, Radomír; Mesiar, Radko; Kolesárová, Anna; Saadati, Reza; Herrera, Francisco; Rodríguez Martínez, Iosu; Bustince Sola, Humberto; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika; Institute of Smart Cities - ISCWe introduce and study aggregation functions based on extremal values, namely extended (𝑙, 𝑢)- aggregation functions whose outputs only depend on a fixed number 𝑙 of extremal lower input values and a fixed number 𝑢 of extremal upper input values, independently of the arity of the input 𝑛-tuples (𝑛 ≥ 𝑙 + 𝑢). We discuss several general properties of (𝑙, 𝑢)-aggregation functions and we study special (𝑙, 𝑢)-aggregation functions with neutral element, including t-conorms, t-norms and uninorms. We also study (𝑙, 𝑢)-aggregation functions defined by means of integrals with respect to discrete fuzzy measures, as well as (𝑙, 𝑢)-ordered weighted quasi-arithmetic means based on appropriate weighting vectors. We also stress some generalizations based on recently introduced new types of monotonicity. Some possible applications are sketched, too.Publication Open Access Affine construction methodology of aggregation functions(Elsevier, 2020) Roldán López de Hierro, Antonio Francisco; Roldán, Concepción; Bustince Sola, Humberto; Fernández Fernández, Francisco Javier; Rodríguez Martínez, Iosu; Fardoun, Habib; Lafuente López, Julio; Estadística, Informática y Matemáticas; Estatistika, Informatika eta MatematikaAggregation functions have attracted much attention in recent times because of its potential use in many areas such us data fusion and decision making. In practice, most of the aggregation functions that scientists use in their studies are constructed from very simple (usually affine or polynomial) functions. However, these are distinct in nature. In this paper, we develop a systematic study of these two classes of functions from a common point of view. To do this, we introduce the class of affine aggregation functions, which cover both the aforementioned families and most of examples of aggregation functions that are used in practice, including, by its great applicability, the symmetric case. Our study allows us to characterize when a function constructed from affine or polynomial functions is, in fact, a new aggregation function. We also study when sums or products of this kind of functions are again an aggregation function.Publication Open Access A new family of aggregation functions for intervals(Springer, 2024) Díaz-Vázquez, Susana; Torres-Manzanera, Emilio; Rico, Noelia; Mesiar, Radko; Rodríguez Martínez, Iosu; Lafuente López, Julio; Díaz, Irene; Montes Rodríguez, Susana; Bustince Sola, Humberto; Estadística, Informática y Matemáticas; Estatistika, Informatika eta MatematikaAggregation operators are unvaluable tools when different pieces of information have to be taken into account with respect to the same object. They allow to obtain a unique outcome when different evaluations are available for the same element/object. In this contribution we assume that the opinions are not given in form of isolated values, but intervals. We depart from two “classical” aggregation functions and define a new operator for aggregating intervals based on the two original operators. We study under what circumstances this new function is well defined and we provide a general characterization for monotonicity. We also study the behaviour of this operator when the departing functions are the most common aggregation operators. We also provide an illustrative example demonstrating the practical application of the theoretical contribution to ensemble deep learning models.