Abstract
Real-life decisions are usually made in the state of uncertainty or risk. In this article we present two types of risk metrics of loss function for uncertain system. Firstly, the concept of value at risk (VaR) of loss function is introduced based on uncertainty theory and its fundamental properties are examined. Then the tail value at risk (TVaR) concept of loss function is evolved and some fundamental properties of the proposed TVaR are investigated. Both the VaR and TVaR are harmonious risk metrics. The suggested VaR or TVaR methodology can be widely used as tools of risk analysis in uncertain environments.
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