1.1 One-dimensional fuzzy data
Measurement results of one-dimensional continuous quantities are frequently idealized to be numbers times a measurement unit. However, real measurement results of continuous quantities are never precise numbers but always connected with uncertainty. Usually this uncertainty is considered to be statistical in nature, but this is not suitable since statistical models are suitable to describe variability. For a single measurement result there is no variability, therefore another method to model the measurement uncertainty of individual measurement results is necessary. The best up-to-date mathematical model for that are so-called fuzzy numbers which are described in Section 2.1 [cf. Viertl (2002)].
Examples of one-dimensional fuzzy data are lifetimes of biological units, length measurements, volume measurements, height of a tree, water levels in lakes and rivers, speed measurements, mass measurements, concentrations of dangerous substances in environmental media, and so on.
A special kind of one-dimensional fuzzy data are data in the form of intervals [a;b]⊆. Such data are generated by digital measurement equipment, because they have only a finite number of digits.