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Statistical Methods for Fuzzy Data by Reinhard Viertl

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1.3 Fuzziness and variability

In statistics frequently so-called stochastic quantities (also called random variables) are observed, where the observed results are fuzzy. In this situation two kinds of uncertainty are present: Variability, which can be modeled by probability distributions, also called stochastic models, and fuzziness, which can be modeled by fuzzy numbers and fuzzy vectors, respectively. It is important to note that these are two different kinds of uncertainty. Moreover it is necessary to describe fuzziness of data in order to obtain realistic results from statistical analysis. In Figure 1.1 the situation is graphically outlined.

Figure 1.1 Variability and fuzziness.

c01f001.eps

Real data are also subject to a third kind of uncertainty: errors. These are the subject of Section 1.4.

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