k-additive aggregation functions and their characterization

Anna Kolesárová, Jun Li and Radko Mesiar

European Journal of Operational Research, 2018, vol. 265, issue 3, 985-992

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 with degree not exceeding k. We also describe all basic 2-additive n-dimensional aggregation functions whose convex closure forms the class of all 2-additive n-dimensional aggregation functions. Moreover, we define k-arithmetic means and completely characterize 2-arithmetic means and idempotent 2-arithmetic means as well. Finally, we introduce notions of k-ordered weighted averaging operators and k-Choquet integrals.

Keywords: Multiple criteria analysis; k-additive aggregation function; k-additive capacity; Owen extension; k-OWA operators (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:265:y:2018:i:3:p:985-992

DOI: 10.1016/j.ejor.2017.08.036

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