Generalized Pre-aggregations

Abstract

In this paper we propose an extension of the concept of pre-aggregation at two diferent levels. On the one hand, we extend the definition of pre-aggregation to a more general framework where the space [0, 1] is replaced by a totally ordered set T with maximum and minimum value. On the other hand, since T could be even discrete, we generalize the concept of monotonicity for functions going from Tn into T. In order to do so we introduce the concept of conditioned monotonicity based on the chains in Tn and generalizing that of directional monotonicity.