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

Authored by

Hamza Alkhatib, Boris Kargoll, Ingo Neumann, Vladik Kreinovich

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.

Details

Organisation(s): Geodetic Institute
External Organisation(s): University of Texas at El Paso
Type: Contribution to book/anthology
Volume: 648
Pages: 300-306
No. of pages: 7
Publication date: 2018
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Control and Systems Engineering, General Computer Science
Electronic version(s): https://doi.org/10.1007/978-3-319-67137-6_34 (Access: Closed )
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