Do we know how to integrate?

Authors:
Radko Mesiar
Affiliations:
Slovak University of Technology, Bratislava, Slovakia,Institute of Theory of Information and Automation Czech Academy of Sciences, Prague, Czech Republic
Venue:
MDAI'12 Proceedings of the 9th international conference on Modeling Decisions for Artificial Intelligence
Year:
2012

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Abstract

After a short history of integration on real line, some examples of optimization tasks are given to illustrate the philosophy behind some types of integrals with respect to monotone measures and related to the standard arithmetics on real line. Basic integrals are then described both in discrete case and general case. A general approach to integration known as universal integrals is recalled, and introduced types of integrals as universal integrals are discussed. A special stress is given to copula---based universal integrals. Several types of integrals based on arithmetics different from the standard one are given, too. Finally, some concluding remarks are added.