在模糊集理论的一般讨论中,大多以交、并算子作为演算算子,但在一些实际问题中,有时需要用到别的演算算子.首先以最大乘积算子作为模糊集的演算算子,证明了最大乘积算子满足分配率.然后引入了模糊概率随机变量的独立性,给出了离散型模糊概率随机变量的数学期望性质的证明.最后根据离散型模糊概率随机变量的数学期望是一个模糊集,对离散型模糊概率随机变量的方差作出了一种新的定义,并对方差的性质进行了证明.Mathematical expectation and variance
According to the risk management process of financial markets,a financial risk dynamic system is constructed in this paper.Through analyzing the basic dynamic properties,we obtain the conditions for stability and bifurcation of the system based on Hopf bifurcation theory of nonlinear dynamic systems.In order to make the system's chaos disappear,we select the feedback gain matrix to design a class of chaotic controller.Numerical simulations are performed to reveal the change process of financial market risk.It is shown that,when the parameter of risk transmission rate changes,the system gradually comes into chaos from the asymptotically stable state through bifurcation.The controller can then control the chaos effectively.
