Santiago, RegivanBergamaschi, FlaullesBustince Sola, HumbertoPereira Dimuro, GraçalizDa Cruz Asmus, TiagoSanz Delgado, José Antonio2021-06-252021-06-2520202227-739010.3390/math8112092https://academica-e.unavarra.es/handle/2454/40056The impreciseness of numeric input data can be expressed by intervals. On the other hand, the normalization of numeric data is a usual process in many applications. How do we match the normalization with impreciseness on numeric data? A straightforward answer is that it is enough to apply a correct interval arithmetic, since the normalized exact value will be enclosed in the resulting 'normalized' interval. This paper shows that this approach is not enough since the resulting 'normalized' interval can be even wider than the input intervals. So, we propose a pair of axioms that must be satisfied by an interval arithmetic in order to be applied in the normalization of intervals. We show how some known interval arithmetics behave with respect to these axioms. The paper ends with a discussion about the current paradigm of interval computations.18 p.application/pdfeng© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license.Interval arithmeticsIntervalsNormalizationNormalization of interval dataPartition principle and interval division structuresinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccess