The Choquet integral as a linear interpolator

  title={The Choquet integral as a linear interpolator},
  author={Michel Grabisch},
We show that the Choquet integral is the unique linear interpolator between vertices of the [0, 1] hypercube, using the least possible number of vertices. Related results by Lovász 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. 

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