Super- and subadditive constructions of aggregation functions

•Transformation of partially given aggregation function.•Generalization of decomposition integral.•Subadditive and superadditive fusion of information.

Two construction methods for aggregation functions based on a restricted a priori known decomposition set and decomposition weighing function are introduced and studied. The outgoing aggregation functions are either superadditive or subadditive. Several examples, including illustrative figures, show the potential of the introduced construction methods. Our approach generalizes several known constructions and optimization methods, including decomposition and superdecomposition integrals. We present also an economic applications of the introduced concepts.