# Statistics with Fuzzy Data

• R. Viertl
Conference paper
Part of the International Centre for Mechanical Sciences book series (CISM, volume 363)

## Abstract

Besides stochastic variation of real data there is another kind of uncertainty in observations called imprecision and the corresponding measurement results are called non-precise data. Usually this kind of uncertainty is not described in statistics. Especially in environment statistics, where also very small quantities are measured, this imprecision cannot be neglected. Otherwise by extrapolations the precision of results is very misleading. Therefore statistical methods have to be generalized for non-precise data. The mathematical concept to describe non-precise data are so-called non-precise numbers and non-precise vectors. Situations are explained, where the characterizing functions of non-precise numbers can be given explicitly. Using the mathematical concept of non-precise numbers and vectors statistical procedures can be generalized to non-precise data. These generalizations are explained in the contribution.

## Keywords

Fuzzy Data Extension Principle Observation Space Predictive Density Stochastic Quantity
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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