Wang, ZhenyuanZhenyuanWangProf. LEUNG Kwong SakKlir, George J.George J.Klir2023-03-242023-03-242006International Journal of Intelligent Systems, 2006, vol. 21 (10), pp. 1073 - 10921098111Xhttp://hdl.handle.net/20.500.11861/7579Various 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.enPeer Reviewed Journal Article10.1002/int.20179