Dempster-Shafer theory offers an alternative to traditional probabilistic theory for the mathematical representation of uncertainty. The significant innovation of this framework is that it allows for the allocation of a probability mass to sets or intervals. DempsterShafer theory does not require an assumption regarding the probability of the individual constituents of the set or interval. This is a potentially valuable tool for the evaluation of risk and reliability in engineering applications when it is not possible to obtain a precise measurement from experiments, or when knowledge is obtained from expert elicitation. An important aspect of this theory is the combination of evidence obtained from multiple sources and the modeling of conflict between them. This report surveys a number of possible combination rules for Dempster-Shafer structures and provides examples of the implementation of these rules for discrete and interval-valued data. 4 ACKNOWLEDGEMENTS

This report summarizes a variety of the most useful and commonly applied methods for obtaining Dempster-Shafer structures, and their mathematical kin probability boxes, from empirical information or theoretical knowledge. The report includes a review of the aggregation methods for handling agreement and conflict when multiple such objects are obtained from different sources.

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Probabilistic uncertainty and imprecision in structural parameters and in environmental conditions and loads are challenging phenomena in engineering analyses. They require appropriate mathematical modeling and quantication to obtain realistic results when predicting the behavior and reliability of engineering structures and systems. But the modeling and quantication is complicated by the characteristics of the available information, which involves, for example, sparse data, poor measurements and subjective information. This raises the question whether the available information is sucient for probabilistic modeling or rather suggests a set-theoretical approach. The framework of imprecise probabilities provides a mathematical basis to deal with these problems which involve both probabilistic and non-probabilistic information. A common feature of the various concepts of imprecise probabilities is the consideration of an entire set of probabilistic models in one analysis. The theoretical dierences between the concepts mainly concern the mathematical description of the set of probabilistic models and the connection to the probabilistic models involved.This paper provides an overview on developments which involve imprecise probabilities for the solution of engineering problems. Evidence theory, probability bounds analysis with p-boxes, and fuzzy probabilities are discussed with emphasis on their key features and on their relationships to one another.