A study of the $k$-additive core of capacities through achievable families

Michel GRABISCH; Pedro MIRANDA

doi:10.14864/softscis.2006.0.1420.0

SCIS & ISIS 2006

Session ID : FR-G4-3

DOI https://doi.org/10.14864/softscis.2006.0.1420.0

Conference information

Host: Japan SOciety for Fuzzy Theory and intelligent informatics

Co-host: The Korea Fuzzy Logic and Intelligent Systems Society, IEEE Computational Intelligence Society, The International Fuzzy Systems Association, 21th Century COE Program "Creation of Agent-Based Social Systems Sciences"

FR-G4 Fuzzy Measures and Cooperative Games

A study of the $k$-additive core of capacities through achievable families

*Michel GRABISCH, Pedro MIRANDA

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Keywords: fuzzy measure, core, game theory

CONFERENCE PROCEEDINGS FREE ACCESS

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Abstract

We investigate in this paper about the set of $k$-additive capacities dominating a given capacity, which we call the $k$-additive core. We study its structure through achievable families, which play the role of maximal chains in the classical case ($k=1$), and show that associated capacities are element (possibly a vertex) of the $k$-additive core when the capacity is $(k+1)$-monotone. The problem of finding all vertices of the $k$-additive core is still an open question.

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