Uncertain random programming models in the framework of U-S chance theory and their applications

In order to handle some problems in which human uncertainties coexist with stochasticities characterized by non-additive probabilities, we develop uncertain random programming models based on four different types of expectations in the framework of U-S chance theory. In this paper, firstly, the operational law for uncertain random variables is proved in this framework. Then, based on sub-linear expectations and Choquet integrals, four types of expectations of uncertain random variables are defined. Finally, four uncertain random programming models are proposed and applied to optimal investment in incomplete financial market and system reliability design.