Abstract
Inspired by the Grabisch idea of k–additive measures, we introduce and study k–additive aggregation functions. The Owen multilinear extension of a k–additive capacity is shown to be a particular k–additive aggregation function. We clarify the relation between k–additive aggregation functions and polynomials of a degree not exceeding k. We also describe \(n^2 + 2n\) basic 2–additive n–ary aggregation functions whose convex closure forms the class of all 2–additive n–ary aggregation functions.
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