Funções mistura generalizada e aplicações

Abstract

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 of the inputs values. The aggregation functions, such as the Ordered Weighted Averaging - OWA, are efficient mathematical models for solving these problems. However, other types of functions, which do not require the mandatory monotonicity condition for aggregation functions, can also be used, as for example, Pre-aggregations, Mixture and Generalized Mixture - GM functions. In this work, is presented a detailed study on the generalized mixture functions, which are an extension of the concept concept of OWA, but unlike of OWAs, have weights capable of adapting to each input vector of this Function. In addition, it is proposed an extension to the generalized mixiture functions called Functions Generalized Bounded Generalized Mixture (BGM). Later, we introduce some class of weighted averaging functions with dynamic weigths and lattice domains: Dynamic Ordered Weighted Averaging (DYOWA) the OWA and OWA functions based on admissible orders and the Mixed Reticle functions - LGM. Finally, two applications for generalized mixture functions are presented: a method of image reduction and a strategy of combining multiple algorithms of classifier ensembles.