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

Document Type : Research Paper


1 Faculty of Mathematics and Physics, Charles Univer- sity in Prague, Czech Republic

2 Faculty of Mathematics and Geoinformation, Vienna University of Tech- nology, Austria


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.


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