Title :
Discrete Choquet Integral as a Distance Metric
Author :
Bolton, Jeremy ; Gader, Paul ; Wilson, J.N.
Author_Institution :
Dept. of Comput. & Inf. Sci. & Eng., Univ. of Florida, Gainesville, FL
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.
Keywords :
fuzzy set theory; transforms; discrete Choquet integral; distance metric; fuzzy measure; monotonicity constraints; nonlinear transformation; Choquet integral; Distance measure; distance measure; fuzzy measure; metric; nonlinear metric;
Journal_Title :
Fuzzy Systems, IEEE Transactions on
DOI :
10.1109/TFUZZ.2008.924347