On linear and quadratic constructions of aggregation functions

Abstract 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 } , 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.

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