Generalized Pre-aggregations.

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 T-n into T. In order to do so we introduce the concept of conditioned monotonicity based on the chains in T-n and generalizing that of directional monotonicity.