Non Deterministic Approaches

Historically, the introduction of the non-probabilistic approaches for non-deterministic analysis has initiated a profound discussion in literature. On one side, some claim that the probabilistic approach is only a subcategory of a more universal non-probabilistic approach. Therefore, the latter would represent a more unified approach for non-deterministic analysis. On the other side, some argue that probabilistic methods are able to model anything the non-probabilistic approach can. The goal of this section is not to choose either side in this discussion, but merely to review the applicability of the non-probabilistic concepts from an objective point of view. Therefore, for each concept, its compatibility with the definitions of uncertainty and variability in the previous section is discussed. This discussion focusses on the ability to objectively represent the available information. In order to enable a critical review of the capabilities of the non-probabilistic concepts, this section first starts with a brief discussion on the main features of the probabilistic concept in the framework of uncertainty and variability modelling.

Evidence Theory [31] can be regarded as a generalisation that covers both the probabilistic as well as the non-probabilistic approaches for non-deterministic analysis, although the operations and inference rules in these theories are completely different. Evidence theory is regarded as a universal approach that can handle combinations of both probabilistic and non-probabilistic information in a single analysis. Its practical application is based on the availability of information in the form of basic belief assignments. The practical value of this approach therefore depends by large on the availability of the information in this form. While this theory is gaining interest in recent literature, its practical application in real-life engineering has yet to be proven. Therefore, it is left out of the current discussion. The following paragraphs briefly discuss the probabilistic concept, the interval concept and the fuzzy concept as stand-alone tools for the representation of non-deterministic parameters in engineering analysis. Finally, some hybrid non-deterministic numerical modelling concepts are briefly discussed.