Distortion risk measures of uncertain systems

Decision making in real world is usually under uncertainty and subject to various risks. In this paper we present the distortion risk measure of an uncertain system. First, we introduce the concept of distortion risk measure and harmonious measure of risk based on uncertainty theory. Then, some fundamental properties of the proposed distortion risk measure are investigated. It is proved that the proposed distortion measure of risk is a harmonious measure of risk. Finally, some numerical examples are illustrated.