The Choquet integral as a linear interpolator
Résumé
We show that the Choquet integral is the unique linear interpolator between vertices of the $[0, 1]^n$ hypercube, using the least possible number of vertices. Related results by Lovasz and Singer are discussed, as well as other interpolations. We show that the Choquet integral for bi-capacities can be also casted into this framework. Lastly, we discuss the case of Sugeno integral.