Articlegreen2000

Equivalent Representations of Set Functions

Michel Grabisch B · Jean‐Luc Marichal · Marc Roubens B

190 citations0/0 files storedMathematics of Operations Research

No readable copy stored yet — this record is metadata only.

Game Theory and Voting Systems Complexity and Algorithms in Graphs Advanced Combinatorial Mathematics

Abstract

This paper introduces four alternative representations of a set function: the Möbius transformation, the co-Möbius transformation, and the interactions between elements of any subset of a given set as extensions of Shapley and Banzhaf values. The links between the five equivalent representations of a set function are emphasized in this presentation.

Citations in this library

Stored only when both papers are in the corpus — 190 citations exist upstream.

References

195317. A Value for n-Person Games 1988A value for n -person games 1997k-order additive discrete fuzzy measures and their representation 2015Values of Non-Atomic Games 1991The Shapley value : essays in honor of Lloyd S. Shapley 1979Mathematical Properties of the Banzhaf Power Index 1988Probabilistic values for games 1972Multilinear Extensions of Games

Cited by

2005Axiomatic characterizations of probabilistic and cardinal-probabilistic interaction indices 2015Robust Ordinal Regression and Stochastic Multiobjective Acceptability Analysis in multiple criteria hierarchy process for the Choquet integral preference model 2005Fuzzy Measures and Integrals in MCDA 2003Estimation of the weights of interacting criteria from the set of profiles by means of information-theoretic functionals 2018On the Choquet multiple criteria preference aggregation model: Theoretical and practical insights from a real-world application 2000The influence of variables on pseudo-Boolean functions with applications to game theory and multicriteria decision making

Imported from OpenAlex (CC0) — nothing here is generated.