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Integration on finite sets
Author(s) -
Wang Zhenyuan,
Leung KwongSak,
Klir George J.
Publication year - 2006
Publication title -
international journal of intelligent systems
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.291
H-Index - 87
eISSN - 1098-111X
pISSN - 0884-8173
DOI - 10.1002/int.20179
Subject(s) - mathematics , cardinality (data modeling) , choquet integral , lebesgue integration , partition (number theory) , lebesgue measure , measure (data warehouse) , fuzzy measure theory , fuzzy logic , product (mathematics) , discrete mathematics , pure mathematics , fuzzy set , fuzzy number , combinatorics , computer science , artificial intelligence , geometry , data mining
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. Int J Int Syst 21: 1073–1092, 2006.