(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 - ISC
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.
(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 Matematika
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.
