Fuzzy arithmetical methods for possibilistic uncertainty analysis

In the development process, the engineer is always facing the issue that there are uncertainties about particular aspects of the respective system. These uncertainties may, for instance, be stemming from variability of the modeling parameters or from a lack of knowledge about the true configuration of the system. The latter type of uncertainties associated with incomplete knowledge is properly described by a possibilistic uncertainty model. The well-known fuzzy sets provide a mathematical formulation of such a possibilistic model, so that fuzzy arithmetical concepts can be applied for the corresponding uncertainty analysis. This thesis shall provide new aspects and a different point of view on possibilistic uncertainty analysis by, first, reviewing and recapitulating existing concepts in a concise and suitable way in order to present them in a new perspective, and, second, developing new methods for the different aspects of uncertainty analysis on that basis. Therefore, an overview of the fundamental concepts of possibility theory and its application to uncertainty analysis is presented in the first part, including its proper description and quantification by fuzzy set theory. The second part of the thesis is devoted to the development of strategies for the numerical solution of possibilistic systems, namely the direct problem, which is given by the calculation of the uncertainties of the output of an uncertain system, the sensitivity problem, where the influence of each individual model parameter on the overall output uncertainty is to be determined, and the inverse problem, where the goal is to identify the model parameters including the implied uncertainty on the reliability of the identification result.