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Normalization-Invariant Fuzzy Logic Operations Explain Empirical Success of Student Distributions in Describing Measurement Uncertainty

  • Hamza AlkhatibEmail author
  • Boris Kargoll
  • Ingo Neumann
  • Vladik Kreinovich
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 648)

Abstract

In engineering practice, usually measurement errors are described by normal distributions. However, in some cases, the distribution is heavy-tailed and thus, not normal. In such situations, empirical evidence shows that the Student distributions are most adequate. The corresponding recommendation – based on empirical evidence – is included in the International Organization for Standardization guide. In this paper, we explain this empirical fact by showing that a natural fuzzy-logic-based formalization of commonsense requirements leads exactly to the Student’s distributions.

Notes

Acknowledgments

This work was performed when Vladik was a visiting researcher with the Geodetic Institute of the Leibniz University of Hannover, a visit supported by the German Science Foundation. This work was also supported in part by NSF grant HRD-1242122.

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Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  • Hamza Alkhatib
    • 1
    Email author
  • Boris Kargoll
    • 1
  • Ingo Neumann
    • 1
  • Vladik Kreinovich
    • 2
  1. 1.Geodätisches InstitutLeibniz Universität HannoverHannoverGermany
  2. 2.Department of Computer ScienceUniversity of Texas at El PasoEl PasoUSA

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