The interaction transform for functions on lattices

Abstract

International audienceThe 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

Representations of Importance and Interaction of Fuzzy Measures, Capacities, Games and Its Extensions: A Survey

“…The antecessor x of x ∈ L is defined as [18]). Let f be a game on a product lattice L, x ∈ L, and X :…”

An Axiomatisation of the Banzhaf Value and Interaction Index for Multichoice Games

“…To our knowledge, there is no definition of an interaction index for multichoice games. Nevertheless, Lange and Grabisch [17] have provided a general form of interaction index for games on lattices. This does not fit our analycis, that focuses on interaction index defined for groups of criteria.…”