Generalized OWA functions
Aggregation Functions, Pre-Aggregation Functions, OWA Functions, Choquet Integrals, Fuzzy Logic,
Mixture Functions, Bounded Mixture Functions, Bounded Generalized Mixture Functions, t-norms,
t-conorms, DYOWA Functions, Partial Orders, Lattices.
In the literature it is quite common to find problems that need efficient mechanisms in accomplishing
the task of combining entries of the same nature in a value of the same type as the inputs. The
aggregation functions are quite efficient in the accomplishment of this work, being able to be used,
for example, to model the connectives of the fuzzy logic and also in problems of decision making. An
important family of aggregations, belonging to the middle class of functions, was introduced by Yager
in 1988, who called them ordered weighted averaging functions (OWA). These functions are a kind of
weighted average, whose weights are not associated with the particular inputs, but their respective
magnitudes, that is, the importance of an input is determined by their value. More recently, it has
been found that non-aggregate class functions may also be able to combine inputs, such as pre-
aggregations and mixture functions, which may not satisfy the mandatory monotonicity condition for
aggregation functions. Thus, the objective of this work is to present a detailed study on aggregations
and preaggregations, in order to provide a good theoretical basis in an area that has a wide possibility
of applications. We present a detailed study of generalized mixing functions - GM, which extend the
Yager OWA functions, and propose some ways to generalize the GM functions: limited generalized mixing
functions and dynamic ordered weighted averaging functions.