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 epsilon is an element of{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. (C) 2014 Elsevier B.V. All rights reserved.