  The paper proposes a general notion of interaction between attributes, which
can be applied to many fields in decision making and data analysis. It
generalizes the notion of interaction defined for criteria modelled by
capacities, by considering functions defined on lattices. For a given problem,
the lattice contains for each attribute the partially ordered set of remarkable
points or levels. The interaction is based on the notion of derivative of a
function defined on a lattice, and appears as a generalization of the Shapley
value or other probabilistic values.
