A decomposition of k-additive Choquet and k-maxitive Sugeno integrals
Previous work has shown that the Choquet integral w.r.t. a symmetric k-order additive fuzzy measure is characterized as a weighted sum, with possibly negative weights, of k specific OWA operators, and that the Sugeno integral w.r.t. a symmetric le-order maxitive fuzzy measure is characterized as a weighted maximum of k order statistics. In this paper, these characterizations are extended to the general, non-symmetric case, thereby providing additional insight in the symmetric case. More specifically, a new general decomposition of the Choquet integral w.r.t. a k-order additive fuzzy measure and of the Sugeno integral w.r.t. a k-order maxitive fuzzy measure are established.
decomposition sugeno integral choquet integral k-order additivity fuzzy measure k-order maxitivity aggregation operator (possibilistic) mobius transform