Application of Interval, Statistical, and Fuzzy Methods to the Evaluation of Measurements

In mathematics the uncertainties of numerical results can be represented by intervals, by dispersion characterisitcs, or by fuzzy numbers. By considering the measurement result not as a point but as a set, interval calculus may be introduced into the evaluation of measurements. With interval representation an analogy to the correlation of statistical data is to be considered. The use of statistical methods for the evaluation of measurements is justified if the state of statistical control is checked, usually by means of control charts. A pulse-density distribution within the interval is used for the combination of interval and statistical methods. Intervals can be transformed to fuzzy numbers which allow the uncertainty of uncertainty to be considered.

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