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Integration on finite sets

✍ Scribed by Zhenyuan Wang; Kwong-Sak Leung; George J. Klir

Publisher: John Wiley and Sons
Year: 2006
Tongue: English
Weight: 186 KB
Volume: 21
Category: Article
ISSN: 0884-8173
DOI: 10.1002/int.20179

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✦ Synopsis

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.

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