(IEEE, 2022) Pereira Dimuro, Graçaliz; Santos, Helida; Da Cruz Asmus, Tiago; Wieczynski, Jonata; Pinheiro, Jocivania; Bedregal, Benjamin; Bustince Sola, Humberto; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika; Institute of Smart Cities - ISC
Grouping functions and their dual counterpart,
overlap functions, have drawn the attention of many authors,
mainly because they constitute a richer class of operators compared to other types of aggregation functions. Grouping functions
are a useful theoretical tool to be applied in various problems, like
decision making based on fuzzy preference relations. In pairwise
comparisons, for instance, those functions allow one to convey
the measure of the amount of evidence in favor of either of two
given alternatives. Recently, some generalizations of grouping
functions were proposed, such as (i) the n-dimensional grouping
functions and the more flexible general grouping functions, which
allowed their application in n-dimensional problems, and (ii)
n-dimensional and general interval-valued grouping functions,
in order to handle uncertainty on the definition of the membership functions in real-life problems. Taking into account
the importance of interval-valued fuzzy implication functions in
several application problems under uncertainty, such as fuzzy
inference mechanisms, this paper aims at introducing a new
class of interval-valued fuzzy material implication functions. We
study their properties, characterizations, construction methods
and provide examples.
