Some Properties of Generalized Mixture Functions

Generalized Mixture (GM) functions beyond to generalize the Mixture functions, also generalizes an important type of aggregation functions, called Ordered Weighted Averaging (OWA). An OWA is a parametrized average, it uses previously defined weights. A GM is also parametrized average, but with a not fixed predefined vector of weights. Whereas applications of OWA depends on the determination of the best vector of weights to be applied, the vector of weights for GM's is determined as a function of input arguments. In this paper we present the notion of GM, show some of their proprieties and build a way to create GM functions starting from any other function of the form: Theta : [0, 1](n) -> [0, 1].