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Probabilistic Measures and Integrals: How to Aggregate Imprecise Data

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Modeling Decisions for Artificial Intelligence (MDAI 2020)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 12256))

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Abstract

This paper develops the theory of probabilistic-valued measures and integrals as a suitable aggregation tool for dealing with certain types of imprecise information. The motivation comes from Moore’s interval mathematics, where the use of intervals in data processing is due to measurement inaccuracy errors. In case of rounding, the intervals can be considered in distribution function form linked to random variables uniformly distributed over the relevant intervals. We demonstrate how the convolution of distribution functions is taken into account, and integration with respect to probabilistic-valued measures is converted into convolving certain distribution functions. We also improve some existing features of the integral and investigate its convergence properties.

This work was supported by the Slovak Research and Development Agency under the contract No. APVV-16-0337 and also cofinanced by bilateral call Slovak-Poland grant scheme No. SK-PL-18-0032 with the Polish National Agency for Academic Exchange PPN/BIL/2018/1/00049/U/00001.

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Author information

Authors and Affiliations

  1. Institute of Mathematics, Lodz University of Technology, ul. Wólczańska 215, 90-924, Lodz, Poland

    Michał Boczek & Marek Kaluszka

  2. Institute of Mathematics, Faculty of Science, Pavol Jozef Šafárik University in Košice, Jesenná 5, 040 01, Košice, Slovakia

    Lenka Halčinová & Ondrej Hutník

Authors
  1. Michał Boczek
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  2. Lenka Halčinová
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  3. Ondrej Hutník
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  4. Marek Kaluszka
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Corresponding author

Correspondence to Lenka Halčinová .

Editor information

Editors and Affiliations

  1. Department of Computing Science, Umeå University, Umeå, Sweden

    Vicenç Torra

  2. Department of Management Science, Tamagawa University, Tokyo, Japan

    Yasuo Narukawa

  3. Department of Operations, Innovation and Data Sciences, ESADE, Sant Cugat, Spain

    Jordi Nin

  4. Department of Operations, Innovation and Data Sciences, ESADE, Sant Cugat, Spain

    Núria Agell

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Boczek, M., Halčinová, L., Hutník, O., Kaluszka, M. (2020). Probabilistic Measures and Integrals: How to Aggregate Imprecise Data. In: Torra, V., Narukawa, Y., Nin, J., Agell, N. (eds) Modeling Decisions for Artificial Intelligence. MDAI 2020. Lecture Notes in Computer Science(), vol 12256. Springer, Cham. https://doi.org/10.1007/978-3-030-57524-3_7

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  • DOI: https://doi.org/10.1007/978-3-030-57524-3_7

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-57523-6

  • Online ISBN: 978-3-030-57524-3

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