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

摘要

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\u27s distributions.