The symmetric and asymmetric Choquet integrals on finite spaces for decision making

DOI10.1007/s00362-001-0085-4zbMath1058.91020OpenAlexW2053448769MaRDI QIDQ1402917

Michel Grabisch, Christophe Labreuche

Publication date: 31 August 2003

Published in: Statistical Papers (Search for Journal in Brave)

Full work available at URL: https://halshs.archives-ouvertes.fr/halshs-00273184/file/statistical_letter.pdf

zbMATH Keywords

capacities

Mathematics Subject Classification ID

Decision theory (91B06) Fuzzy measure theory (28E10)

Related Items (19)

Entropy of bi-capacities ⋮ Quadratic distances for capacity and bi-capacity approximation and identification ⋮ A weight-based approach to the measurement of the interaction among criteria in the framework of aggregation by the bipolar Choquet integral ⋮ An interval-valued inversion of the non-additive interval-valued F-transform: use for upsampling a signal ⋮ Towards interval-based non-additive deconvolution in signal processing ⋮ Imprecise expectations for imprecise linear filtering ⋮ Maximal chain-based Choquet-like integrals ⋮ Entropy for non-additive measures in continuous domains ⋮ The symmetric Sugeno integral. ⋮ Belief functions on distributive lattices ⋮ Generalized Choquet-like aggregation functions for handling bipolar scales ⋮ Bi-capacities. I: Definition, Möbius transform and interaction ⋮ Bi-capacities. II: The Choquet integral ⋮ Belief functions on lattices ⋮ Theory of inclusion-exclusion integral ⋮ Towards a Robust Imprecise Linear Deconvolution ⋮ Bases and Transforms of Set Functions ⋮ Cooperative Game as Non-Additive Measure ⋮ A fairness relation based on the asymmetric Choquet integral and its application in network resource allocation problems

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Default reasoning and possibility theory
• Some characterizations of lower probabilities and other monotone capacities through the use of Möbius inversion
• Advances in prospect theory: cumulative representation of uncertainty
• The application of fuzzy integrals in multicriteria decision making
• \(k\)-order additive discrete fuzzy measures and their representation
• Continuous-from-above possibility measures and f-additive fuzzy measures on separable metric spaces: Characterization and regularity
• Non-additive measure and integral
• On the extension of pseudo-Boolean functions for the aggregation of interacting criteria.
• Interaction transform of set functions over a finite set
• Theory of capacities
• Alternative Representations of Discrete Fuzzy Measures for Decision Making
• Subjective Probability and Expected Utility without Additivity
• Prospect Theory: An Analysis of Decision under Risk
• Integral Representation Without Additivity
• Relating decision under uncertainty and multicriteria decision making models
• Upper and Lower Probabilities Induced by a Multivalued Mapping

This page was built for publication: The symmetric and asymmetric Choquet integrals on finite spaces for decision making