Discrete Choquet Integral as a Distance Metric

Authors:
J. Bolton;P. Gader;J. N. Wilson
Affiliations:
Dept. of Comput. & Inf. Sci. & Eng., Univ. of Florida, Gainesville, FL;-;-
Venue:
IEEE Transactions on Fuzzy Systems
Year:
2008

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Abstract

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.