This paper deals with evidential networks to manage imprecise probabilities. Evidential networks are directed acyclic graphs that handle random, and epistemic uncertainties thanks to Dempster-Shafer structures. After we recall useful bases of the Dempster-Shafer theory, and the relation with probability intervals, we explain how to handle imprecision. Evidential networks are extended with imprecise utility functions to deal with system performance evaluation problems. We explain the application of evidential networks to system reliability evaluation problems. Then, applications to multi-state performance evaluation are proposed. The last section of the paper is devoted to study case systems.
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