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The Choquet integral and the Owen extension (or multilinear extension) arethe most popular tools in multicriteria decision making to take into accountthe interaction between criteria. It is known that the interaction transformand the Banzhaf interaction transform arise as the average total variation ofthe Choquet integral and multilinear extension respectively. We consider inthis note another approach to define interaction, by using the Sobol' indiceswhich are related to the analysis of variance of a multivariate model. We provethat the Sobol' indices of the multilinear extension gives the square of theFourier transform, a well-known concept in computer sciences. We also relatethe latter to the Banzhaf interaction transform and compute the Sobol' indicesfor the 2-additive Choquet integral.

A note on the Sobol' indices and interactive criteria