F-transforms, aggregations, partitions
Irina Perfilieva · 2017
A relationship between real-valued and lattice-valued F-transforms and aggregation functions is analyzed. For each direct F-transform, we find an axiomatic characterization of the corresponding mapping. We show that the real-valued F-transform is a set of images of linear aggregation functions and that the lattice-valued F-transforms are images of linear-like maps. In all cases, the involved maps respect certain partitions of the universe.