Discrete Choquet Integral as a Distance Metric

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 characteriz...

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Bibliographic Details
Published in:IEEE transactions on fuzzy systems 2008-08, Vol.16 (4), p.1107-1110
Main Authors: Bolton, J., Gader, P., Wilson, J.N.
Format: Article
Language:English
Subjects:
Bioinformatics
Choquet integral
distance measure
Fuzzy
Fuzzy logic
fuzzy measure
Fuzzy set theory
Fuzzy systems
Genomics
Image retrieval
Integral equations
Integrals
metric
Military computing
nonlinear metric
Nonlinearity
Stochastic processes
Sufficient conditions
Terminology
Transformations
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Summary: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.
ISSN:1063-6706
1941-0034
DOI:10.1109/TFUZZ.2008.924347