Additive representations of non-additive measures and the choquet integral

descriptionPublicationkeyboard_double_arrow_right Article , Research , Preprint 01 Mar 1994 English Publisher:Springer Science and Business Media LLCJournal:Annals of Operations Research, volume 52, pages 43-65 (issn: 0254-5330, eissn: 1572-9338,

Copyright policy )

Authors: Itzhak Gilboa; David Schmeidler;

doi: 10.1007/bf02032160

handle: 10419/221343

Additive representations of non-additive measures and the choquet integral

- Summary
- Subjects
- Metrics

Abstract

Real-valued mappings \(v\) defined on a finite algebra are considered satisfying the condition \(v(\emptyset)= 0\) (so-called non-additive measures or capacities). Various properties of the Choquet integral with respect to \(v\) are considered. Especially, a Radon-Nikodým derivative is defined and Bayesian update of a non-additive measure is derived from an additive one. Interpretations of the results are presented and their relation to the theory of expected utility maximization is discussed.

Related Organizations

Keywords

ddc:330, Fuzzy measure theory, Non-additive probabilities, Choquet, Radon-Nikodým, utility maximization, [SHS.ECO.ECO] Humanities and Social Sciences/Economics and Finance/domain_shs.eco.eco, fuzzy integrals, fuzzy measure, Choquet integral, non-additive measures, capacities

Impact byBIP!

	selected citations These citations are derived from selected sources. This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	193
	popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.	Top 10%
	influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	Top 1%
	impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.	Top 10%