May. 17 2010 1:30PM

May. 17 2010 3:00PM

Lebesgue integral generalizes Riemann integral, allowing to deal with any abstract measurable space equipped with a sigma-additive measure. Note that on the other hand, Lebesgue integral can be computed by means of Riemann integral (similarly, as the expected value of a random variable), in which approach the sigma-additivity of the underlying measure is not important, but it can be relaxed to the monotonicity, thus yielding Choquet integral. A general framework for integrals a la Choquet will be presented. The name "universal integral" mean that it acts on any measurable space and is well defined for any monotone measure. Extremal universal integrals will be discussed, with special cases as Sugeno and Shilkret integrals. Also a copula-based approach to universal integrals will be presented.

Pravidelný seminář Inteligentní systémy (Contact person: Tomáš Kroupa)