A nonlinear integral which generalizes both the Choquet and the Sugeno integral

Abstract

The Choquet and the Sugeno integral provide a useful tool in many problems in engineering and social choice where the aggregation of data is required. However, their applicability is somehow restricted because of the special operations used in the construction of these integrals. This survey presents the main ideas and results concerning the construction of a universal integral generalizing both the Choquet and the Sugeno case. For functions with values in the nonnegative real numbers, universal integrals can be defined on arbitrary measurable spaces and for arbitrary monotone measures. A more detailed exposition and the proofs of the propositions can be found in [38]. © 2010 Springer-Verlag Berlin Heidelberg.