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Pereira Dimuro, Graçaliz

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https://academica-e.unavarra.es/handle/2454/49759

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Pereira Dimuro

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Graçaliz

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Automática y Computación

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0000-0001-6986-9888

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811336

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2020 - 20222
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Subject: Grouping functions × Subject: General grouping functions × Start date: 2020 × End date: 2022 ×

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    PublicationOpen 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 Matemáticas
    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.
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    PublicationOpen 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 Matematika
    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.