The discrete Choquet integral is a nonlinear transformation that integrates a real function with respect to a fuzzy measure. We show that the discrete Choquet integral defines a metric if and only if the corresponding measure satisfies certain monotonicity constraints, thereby completely characterizing the class of measures that induce a metric with the Choquet integral.
['Jeremy Bolton', 'Paul D. Gader', 'Joseph N. Wilson']
Discrete Choquet Integral as a Distance Metric