On linear and quadratic constructions of aggregation functions

In the paper we introduce and discuss linear and quadratic constructions of aggregation functions based on an a priori given aggregation function. We focus our attention on linear and quadratic constructions transforming any aggregation function from the considered class of aggregation functions into a new aggregation function belonging to the same class. We study quadratic constructions of distinguished classes of aggregation functions with neutral element ϵ∈{0,1}ϵ∈{0,1}, in particular, semi-copulas, quasi-copulas, copulas, triangular norms and their duals. In all cases, the final results fully characterize quadratic functions which are universal for quadratic constructions of aggregation functions of the considered type.