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

Abstract

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 fuzziness.

It turns out that special fuzzy subsets of the set of real numbers R are useful to model fuzziness of measurement results. These fuzzy subsets x* are called 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 characterizing functions describing measurement results are treated.

Keywords

• Characterizing function
• Fuzzy data
• Generating families
• Measurement results
• Vector-characterizing function