Standard Article

Fuzzy Numbers and Nonprecise Data

Statistical Theory and Methods

  1. Reinhard Viertl

Published Online: 15 SEP 2006

DOI: 10.1002/9780470057339.vaf019

Encyclopedia of Environmetrics

Encyclopedia of Environmetrics

How to Cite

Viertl, R. 2006. Fuzzy Numbers and Nonprecise Data. Encyclopedia of Environmetrics. 2.

Author Information

  1. Technische Universität Wien, Austria

Publication History

  1. Published Online: 15 SEP 2006

Abstract

Real data obtained from measurements of continuous quantities are not precise numbers or vectors but more or less nonprecise. This uncertainty is different from measurement errors and has to be described formally in order to obtain realistic results of data analysis. Real-life examples are poisons in different environmental media at a fixed time. These are typically not a precise multiple of the scale unit for the measurements. Such data are called nonprecise. In the past, this kind of uncertainty was neglected in statistical analysis. The reason behind this was the philosophical idea of the existence of a ‘true’ value which is identified with a real number times the measurement unit; but this is not realistic. The formal description of such nonprecise measurements can be given using so-called fuzzy numbers.