The interaction transform for functions on lattices

Abstract : The paper proposes a general approach of interaction between players or attributes. It generalizes the notion of interaction defined for players modeled by games, by considering functions defined on distributive lattices. A general definition of the interaction transform is provided, as well as the construction of operators establishing transforms between games, their M¨obius transforms and their interaction indices.
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Fabien Lange, Michel Grabisch. The interaction transform for functions on lattices. Discrete Mathematics, Elsevier, 2009, 309 (12), pp.4037-4048. ⟨10.1016/j.disc.2008.12.007⟩. ⟨hal-00496545⟩

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