On k–additive Aggregation Functions

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9880)

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.

Keywords

Aggregation function k–additive aggregation function k–additive capacity 

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Faculty of Chemical and Food TechnologySlovak University of TechnologyBratislavaSlovakia
  2. 2.School of ScienceCommunication University of ChinaBeijingPeople’s Republic of China
  3. 3.Faculty of Civil EngineeringSlovak University of TechnologyBratislavaSlovakia

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