In literature, it is common to find problems which require a way to encode a finite set of information into a single data; usually means are used for that. An important generalization of means are the so called Aggregation Functions, with a noteworthy subclass called OWA functions. There are, however, further functions which are able to provide such codification which do not satisfy the definition of aggregation functions; this is the case of pre-aggregation and mixture functions. In this paper we investigate two special types of functions: Generalized Mixture and Bounded Generalized Mixture functions. They generalize both: OWA and Mixture functions. Both Generalized and Bounded Generalized Mixture functions are developed in such way that the weight vectors are variables depending on the input vector. A special generalized mixture operator, H, is provided and applied in a simple toy example.