Additive representations of non-additive measures and the Choquet integral
type: Item
instance of: scholarly article
title: Additive representations of non-additive measures and the Choquet integral
zbMATH Open document ID: 0814.28010
DOI: 10.1007/BF02032160
author: Itzhak Gilboa
author: David Schmeidler
published in: Annals of Operations Research
publication date: 1995-06-18T00:00:00Z
review text: 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.
reviewed by: Beloslav Riečan
Mathematics Subject Classification ID: 28E10
zbMATH DE Number: 698931
zbMATH Keywords: fuzzy measure
zbMATH Keywords: fuzzy integrals
zbMATH Keywords: non-additive measures
zbMATH Keywords: capacities
zbMATH Keywords: Choquet
zbMATH Keywords: Radon-Nikodým
zbMATH Keywords: utility maximization
Wikidata QID: Q92183874
MaRDI profile type: Publication
cites work: Le Comportement de l'Homme Rationnel devant le Risque: Critique des Postulats et Axiomes de l'Ecole Americaine
cites work: A Definition of Subjective Probability
cites work: Values of Non-Atomic Games
cites work: Linear measures, the Gini index, and the income-equality trade-off
cites work: Upper and Lower Probabilities Induced by a Multivalued Mapping
cites work: Q5556137
cites work: Uncertainty Aversion, Risk Aversion, and the Optimal Choice of Portfolio
cites work: Nash equilibrium under Knightian uncertainty: Breaking down backward induction
cites work: Evidence measures based on fuzzy information
cites work: Stochastic dominance with nonadditive probabilities
cites work: Risk, ambiguity and the Savage axioms
cites work: Intertemporal Asset Pricing under Knightian Uncertainty
cites work: Q3979388
cites work: Q5615833
cites work: Expected utility with purely subjective non-additive probabilities
cites work: Expectation and Variation in Multi-Period Decisions
cites work: Additivizations of Nonadditive Measures
cites work: Duality in non-additive expected utility theory
cites work: Global games
cites work: Maxmin expected utility with non-unique prior
cites work: Updating ambiguous beliefs
cites work: Canonical Representation of Set Functions
cites work: Two views of belief: Belief as generalized probability and belief as evidence
cites work: Minimax tests and the Neyman-Pearson lemma for capacities
cites work: Linear utility theory for belief functions
cites work: Bayesian updating and belief functions
cites work: Prospect Theory: An Analysis of Decision under Risk
cites work: A Simple Axiomatization of Nonadditive Expected Utility
cites work: Q5826088
cites work: Integral Representation Without Additivity
cites work: Subjective Probability and Expected Utility without Additivity
cites work: Q4131415
cites work: The degree of belief in a fuzzy event
cites work: Q5844986
cites work: Continuous subjective expected utility with non-additive probabilities
cites work: Towards a frequentist theory of upper and lower probability
cites work: Belief function representations of statistical evidence
cites work: Belief functions and statistical inference
cites work: Bayes' theorem for Choquet capacities
cites work: The iterative law of expectation and non-adaptive probability measure
full work available at URL: https://doi.org/10.1007/bf02032160
OpenAlex ID: W3125552691
description: scientific article; zbMATH DE number 698931