Risk Index and Expected Loss for Complex Systems with Incomplete Information: An Approach of U-S Chance Measurement

Classical risk analysis based on probability theory fails to be effective in situations with incomplete information, where either sufficient historical data is lacking or the real prob- ability cannot be distinguished within a set of probabilities [Formula: see text]. These two types of incomplete information can be characterized by uncertainty theory and sub-linear ex- pectation theory, respectively. In this paper, we conduct risk analysis for systems with incomplete information using a novel framework called U-S chance theory, derived from sub-linear expectation theory and uncertainty theory. Within this framework, the cal- culation formulas for upper and lower chance distributions are obtained. Furthermore, we define the risk index and expected loss, and derive their formulas. Finally, the main results on risk index and expected loss are applied to various incomplete information systems, such as series systems, parallel systems, and so on.