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Statistical Methods for Fuzzy Data by Reinhard Viertl

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1.4 Fuzziness and errors

In standard statistics errors are modeled in the following way. The observation y of a stochastic quantity is not its true value x, but superimposed by a quantity e, called error, i.e.

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The error is considered as the realization of another stochastic quantity. These kinds of errors are denoted as random errors.

For one-dimensional quantities, all three quantities x, y, and e are, after the experiment, real numbers. But this is not suitable for continuous variables because the observed values y are fuzzy.

It is important to note that all three kinds of uncertainty are present in real data. Therefore it is necessary to generalize the mathematical operations for real numbers to the situation of fuzzy numbers.

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