Uncertainty Expression and Propagation in the Risk Assessment of Uncertain Random System

Expressions and propagations of uncertainties have been the core topics in the development of risk science in last decades, whose purpose is to provide decision-makers with clear information about the uncertainty of system's risk. Uncertainty theory is an emerging theory that has great advantages in the expression of epistemic uncertainty, compared to the theories such as subjective probability, evidence theory, and possibility theory. A new framework of uncertainty expression is proposed in this article to properly express different uncertainty sources that exist in the system, where the uncertainty theory is used to express epistemic uncertainties and frequentist probability is used to express aleatory uncertainties. A general propagation method is further developed to address the joint calculations of proposed uncertainty expressions, which can be degenerated into pure probabilistic approach and pure uncertainty-based approach. A case study is conducted to show the effectiveness of proposed method, whose results indicate that the application of proposed method will lead to a result which is easier to be understood than results of theories such as evidence theory and possibility theory, and is more robust than results of Bayesian approach.