Interaction transform of set functions over a finite set

DOI10.1016/S0020-0255(99)00099-7zbMath1020.91005OpenAlexW1992545095MaRDI QIDQ1969694

Dieter Denneberg, Michel Grabisch

Publication date: 5 October 2003

Published in: Information Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0020-0255(99)00099-7

zbMATH Keywords

Möbius transforminteraction index

Mathematics Subject Classification ID

Decision theory (91B06) Cooperative games (91A12)

Related Items (13)

Computational aspects of the coarsening at random model and the Shapley value ⋮ Max-min (\(\sigma\)-)additive representation of monotone measures ⋮ The symmetric and asymmetric Choquet integrals on finite spaces for decision making ⋮ Shifted sums of the Bernoulli numbers, reciprocity, and denominators ⋮ A decade of application of the Choquet and Sugeno integrals in multi-criteria decision aid ⋮ A decade of application of the Choquet and Sugeno integrals in multi-criteria decision aid ⋮ Bases and linear transforms of TU-games and cooperation systems ⋮ A definition of subjective possibility ⋮ Canonical sequences of monotone measures ⋮ On the extension of pseudo-Boolean functions for the aggregation of interacting criteria. ⋮ Conditional expectation for monotone measures, the discrete case ⋮ How to share when context matters: the Möbius value as a generalized solution for cooperative games ⋮ Exact bounds of the Möbius inverse of monotone set functions

Cites Work

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• Characterizations of monotone and 2-monotone capacities
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• The application of fuzzy integrals in multicriteria decision making
• Representation of the Choquet integral with the \(\sigma\)-additive Möbius transform
• \(k\)-order additive discrete fuzzy measures and their representation
• Non-additive measure and integral
• An axiomatic approach to the concept of interaction among players in cooperative games
• Ambiguity Aversion and Incompleteness of Financial Markets
• On ordered weighted averaging aggregation operators in multicriteria decisionmaking
• [https://portal.mardi4nfdi.de/wiki/Publication:5731810 On the foundations of combinatorial theory I. Theory of M�bius Functions]

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