‎On Generalized Mixture Functions

In the literature it is very common to see problems in which it is necessary to aggregate a set of data into a single one‎. ‎An important tool able to deal with these issues is the aggregation functions‎, ‎which we can highlight as the OWA functions‎. ‎However‎, ‎there are other functions that are also capable of performing these tasks‎, ‎such as the preaggregation function and mixture functions‎. ‎In this paper we investigate two special types of functions‎, ‎the Generalized Mixture functions and Bounded Generalized Mixture functions‎, ‎which generalize both OWA and Mixture functions‎. ‎We also prove some properties‎, ‎constructions and examples of these functions‎. ‎Both the Generalized and Bounded Generalized Mixture functions are developed in such a way that the weight vectors are variables that depend on the input vector‎, ‎which generalizes the aggregation functions‎: ‎ Minimum‎, ‎Maximum‎, Arithmetic Mean and Median, ‎and are extensively used in image processing‎. ‎Finally‎, ‎we propose a Generalized Mixture function‎, ‎denoted by \mathbf{H}‎, ‎and we show that \mathbf{H} satisfies a series of properties in order to apply this function in an illustrative example of application‎: ‎The image reduction process‎.

Keywords:

Aggregation functions‎ , ‎Preaggregation functions‎ , ‎OWA functions‎ , ‎Generalized Mixture functions‎ , ‎Image reduction‎