The generation of fuzzy sets and the~construction of~characterizing functions of fuzzy data

Measurement results contain different kinds of uncertainty. Besides systematic errors and random errors individual measurement results are also subject to another type of uncertainty, so-called emph{fuzziness}. It turns out that special fuzzy subsets of the set of real numbers $RR$ are useful to model fuzziness of measurement results. These fuzzy subsets $x^*$ are called emph{fuzzy numbers}. The membership functions of fuzzy numbers have to be determined. In the paper first a characterization of membership function is given, and after that methods to obtain special membership functions of fuzzy numbers, so-called emph{characterizing functions} describing measurement results are treated.