Measurements are basic for all quantitative science and for many human activities. By the limited accuracy of every measurement equipment the result of one measurement of a continuous quantity is not a precise number but more or less nonprecise containing different kinds of uncertainty. Besides systematic errors and random errors individual measurement results are also subject to another type of uncertainty, socalled fuzziness. This unavoidable imprecision has to be analyzed in order to obtain realistic results. It turns out that special fuzzy subsets x* of the set of real numbers R, called fuzzy numbers, are useful to model fuzziness of measurement results. Using the concept of fuzzy numbers a more realistic description of measurement results is possible. In the thesis fuzzy numbers, fuzzy vectors and vectors of fuzzy numbers are defined. ^I have proposed and proved a characterization of membership functions of fuzzy sets, and especially a characterization of characterizing functions of fuzzy numbers. I have proposed and proved a generalization of the extension principle for fuzzy vectors, and given a graphical visualization. I have proposed different methods of how to construct the characterizing function of a fuzzy number and the vectorcharacterizing function of a fuzzy vector, explained all the methods by examples. I have explained a method for computing with fuzzy numbers, and compared the resulting characterizing functions depending on the used tnorm. Fuzzy valued functions are introduced and I have proved a statement about its integral. At the end of the thesis, I have demonstrated how to apply fuzzy concepts to measurement theory. The dissertation thesis is written in a formally mathematical way using definitions, theorems, proofs and examples. ^I have explained in detail various approaches how to use fuzzy numbers through their representation via characterizing functions. I have shown the presented methods on examples including detailed figures to enable better understanding. A significant part of the work was published as a requested paper in the impact journal "Iranian Journal of Fuzzy Systems". The dissertation thesis can serve as theoretical background for experts engaging with measurement in practice.
