The interaction transform for functions on lattices

Fabien Lange (1) , Michel Grabisch (2)

1 Keleti Faculty of Economics
2 CES - Centre d'économie de la Sorbonne

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.

Mots clés: Lattice function; Möbius transform; Interaction transform; Group action

Domaines: Mathématique discrète [cs.DM]; Recherche opérationnelle [math.OC]; Combinatoire [math.CO]

Fabien Lange, Michel Grabisch. The interaction transform for functions on lattices. Discrete Mathematics, 2009, 309 (12), pp.4037-4048. ⟨10.1016/j.disc.2008.12.007⟩. ⟨hal-00496545⟩