Cardinality-limiting extended pre-aggregation functions

Abstract Aggregation functions, which are at the heart of a number of information fusion processes, allow summarisation of multiple inputs into a single representative value. Extended aggregation functions are defined such that the input data can be of varying cardinality, with the implication that there is some consistency across the methods of calculation. This article formalises an approach to extended aggregation such that contributions of repeated inputs or regions of high density are limited in their ability to influence the final value. We establish important definitions and properties, in particular around whether such functions will be monotone or directionally monotone. We then propose a powerful construction method for extended pre-aggregation functions. Illustrative examples are provided throughout.