(IEEE, 2022) Botelho, Cecilia; Galvao, Alessandra; Santos, Helida; Pinheiro, Jocivania; Bedregal, Benjamin; Yamin, Adenauer; Reiser, Renata; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika
Firstly, this work discusses the main conditions
guarantying that general overlap (grouping) functions can be
obtained from n-dimensional overlap (grouping) functions. Focusing on QL-implications, which are usually generated by strong
negations together with t-norms and t-conorms, we consider a
non-restrictive construction, by relaxing not only the associativity
and the corresponding neutral elements (NE) but also the reverse
construction of other properties. Thus, the main properties of the
QL-implication class are studied, considering a tuple (G,N,O)
generated from grouping and overlap functions together with
the greatest fuzzy negation. In addition, in order to provide more
flexibility, we define a subclass of QL-implications generated from
general overlap and general grouping functions. Some examples
are introduced, illustrating the constructive methods to generate
such operators.