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Published in:
2016 | OriginalPaper | Chapter
Aggregation of Choquet Integrals
Authors : Radko Mesiar, Ladislav Šipeky, Alexandra Šipošová
Published in: Information Processing and Management of Uncertainty in Knowledge-Based Systems
Publisher: Springer International Publishing
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Abstract
Aggregation functions acting on the lattice of all Choquet integrals on a fixed measurable space \((\mathrm {X},\mathcal {A})\) are discussed. The only direct aggregation of Choquet integrals resulting into a Choquet integral is linked to the convex sums, i.e., to the weighted arithmetic means. We introduce and discuss several other approaches, for example one based on compatible aggregation systems. For \(\mathrm {X}\) finite, the related aggregation of OWA operators is obtained as a corollary. The only exception, with richer structure of aggregation functions, is the case \(card \ \mathrm {X} = 2\), when the lattice of all OWA operators forms a chain.