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

Authors

Hamza Alkhatib, Leibniz University HannoverFollow
Boris Kargoll, Leibniz University HannoverFollow
Ingo Neumann, Leibniz University HannoverFollow
Vladik Kreinovich, The University of Texas at El PasoFollow

Publication Date

6-2017

Comments

Technical Report: UTEP-CS-17-55

To appear in: Proceedings of the 2017 Annual Conference of the North American Fuzzy Information Processing Society NAFIPS'2017, Cancun, Mexico, October 16-18, 2017

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.