Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6895246 | European Journal of Operational Research | 2018 | 26 Pages |
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.
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Physical Sciences and Engineering
Computer Science
Computer Science (General)
Authors
Anna Kolesárová, Jun Li, Radko Mesiar,