Bounded Generalized Mixture Functions

TL;DR

This paper introduces Bounded Generalized Mixture functions, a new class of functions that generalize existing aggregation methods like OWA and Mixture functions, with weights depending on input data.

Contribution

It proposes Bounded Generalized Mixture functions that extend aggregation functions by allowing input-dependent weights, enhancing data encoding flexibility.

Findings

Defined a new class of functions called Bounded Generalized Mixture functions.

Developed a generalized mixture operator H and demonstrated its application.

Showed potential for improved data aggregation in simple examples.

Abstract

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.