Kernel aggregation functions on finite scales. Constructions from their marginals

The study of discrete aggregation functions (those defined on a finite chain) with some kind of smoothness has been extensively developed in last years. Many different kinds of aggregation functions have been characterized in this context. In this paper discrete aggregation functions with the kernel property (which implies the smoothness property) are investigated. Some properties and characterizations, as well as some construction methods for this kind of discrete aggregation functions are studied. It is also investigated when the marginal functions of a discrete kernel aggregation function fully determine it.