Pereira Dimuro, Graçaliz
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Pereira Dimuro
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Graçaliz
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Automática y Computación
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Publication Open Access On fuzzy implications derived from general overlap functions and their relation to other classes(MDPI, 2023) Pinheiro, Jocivania; Santos, Helida; Pereira Dimuro, Graçaliz; Bedregal, Benjamin; Santiago, Regivan; Fernández Fernández, Francisco Javier; Bustince Sola, Humberto; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika; Institute of Smart Cities - ISCThere 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.Publication Open Access Aggregation functions based on the Choquet integral applied to image resizing(Atlantis Press, 2019) Bueno, Jéssica C. S.; Dias, Camila A.; Pereira Dimuro, Graçaliz; Santos, Helida; Bustince Sola, Humberto; Estatistika, Informatika eta Matematika; Institute of Smart Cities - ISC; Estadística, Informática y MatemáticasThe rising volume of data and its high complexity has brought the need of developing increasingly efficient knowledge extraction techniques, which demands efficiency both in computational cost and in accuracy. Most of problems that are handled by these techniques has complex information to be identified. So, machine learning methods are frequently used, where a variety of functions can be applied in the different steps that are employed in their architecture. One of them is the use of aggregation functions aiming at resizing images. In this context, we introduce a study of aggregation functions based on the Choquet integral, whose main characteristic in comparison with other aggregation functions is that it considers, through fuzzy measure, the interaction between the elements to be aggregated. Thus, our main goal is to present an evaluation study of the performance of the standard Choquet integral the and copula-based generalization of the Choquet integral in relation to the maximum and mean functions, looking for results that may be better than the aggregation functions commonly applied. The results of such comparisons are promising, when evaluated through image quality metrics.Publication Open Access Additively generated (a,b)-implication functions*(IEEE, 2023) Santos, Helida; Pereira Dimuro, Graçaliz; Bedregal, Benjamin; Paiva, Rui; Lucca, Giancarlo; Moura, Bruno; Cruz, Anderson; Bustince Sola, Humberto; Estadística, Informática y Matemáticas; Estatistika, Informatika eta MatematikaSome 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.