The representation of importance and interaction of features by fuzzy measures
Pattern Recognition Letters - Special issue on fuzzy set technology in pattern recognition
International Journal of Game Theory
k-order additive discrete fuzzy measures and their representation
Fuzzy Sets and Systems - Special issue on fuzzy measures and integrals
An axiomatic approach of the discrete Choquet integral as a tool to aggregate interacting criteria
IEEE Transactions on Fuzzy Systems
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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.