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Integration on finite sets
Date Issued
2006
ISSN
1098111X
Citation
International Journal of Intelligent Systems, 2006, vol. 21 (10), pp. 1073 - 1092
Type
Peer Reviewed Journal Article
Abstract
Various types of integrals with respect to signed fuzzy measures on finite sets with cardinality n can be presented as corresponding rules for partitioning the integrand. The partition can be expressed as an n-dimensional vector, whereas the signed fuzzy measure is also an n-dimensional vector. Thus, the integration value is the inner product of these two vectors. Two pairs of extremes, the Lebesgue-like integral versus the Choquet integral and the upper integral versus the lower integral, are discussed in detail. © 2006 Wiley Periodicals, Inc.
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