Analysis of order statistics of uncertain variables

Optimal Control of a Multifactor Uncertain System

Along with the development of the modern science and technology, people face a lot of data in different areas of production and life. In dealing with these data which include many indeterminant factors, we can use the multifactor uncertain system to describe a dynamical system with uncertain noises. Optimal control problem is an important research topic which aims at finding the optimal strategy in a dynamical system. In this paper, we consider the optimal control problem for the multifactor uncertain system with two evaluation criterions. Then a two person zero sum differential game model in a multifactor uncertain system is discussed. Finally, as an application, our result is used to solve an uncertain portfolio game model.

Uncertainty Distribution of Some Composite Uncertain Variables

In this paper, we named the composition by a real-valued measurable function and an uncertain variable as a composite uncertain variable. We focused on the uncertainty distribution for two kinds of composite uncertain variables. The conclusions show: (1) it exists a lower bound when the composed function is continuous and strictly monotonically decreasing at first and then strictly monotonically increasing (e.g. convex downward functions); (2) it exists an upper bound when the composed function is continuous and strictly monotonically increasing at first and then strictly monotonically decreasing (e.g. convex upward functions).