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Do We Know How to Integrate?

  • Conference paper
Modeling Decisions for Artificial Intelligence (MDAI 2012)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 7647))

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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.

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Author information

Authors and Affiliations

  1. Slovak University of Technology, Bratislava, Slovakia

    Radko Mesiar

  2. Institute of Theory of Information and Automation Czech Academy of Sciences, Prague, Czech Republic

    Radko Mesiar

Authors
  1. Radko Mesiar
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Editor information

Editors and Affiliations

  1. IIIA-CSIC, Campus UAB s/n, 08193, Bellaterra, Catalonia, Spain

    Vicenç Torra

  2. Toho Gakuen, 3-1-10, Naka, 186-0004, Kunitachi, Tokyo, Japan

    Yasuo Narukawa

  3. Universitat de Girona, Campus Montilivi, building EPS-4, 17071, Girona, Spain

    Beatriz López  & Mateu Villaret  & 

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Mesiar, R. (2012). Do We Know How to Integrate?. In: Torra, V., Narukawa, Y., López, B., Villaret, M. (eds) Modeling Decisions for Artificial Intelligence. MDAI 2012. Lecture Notes in Computer Science(), vol 7647. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34620-0_3

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  • DOI: https://doi.org/10.1007/978-3-642-34620-0_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-34619-4

  • Online ISBN: 978-3-642-34620-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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