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

Measurement results contain different kinds of uncertainty. Besides systematic errors andrandom 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 RRare 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 firsta characterization of membership function is given, and after that methods to obtainspecial membership functions of fuzzy numbers, so-called emph{characterizing functions} describingmeasurement results are treated.

Keywords:

Characterizing function , fuzzy data , Generating families , Measurement results , Vector-characterizing function