Random variables and uncertain variables are respectively used to model randomness and uncertainty. While randomness and uncertainty always coexist in a same complex system. As an evolution of random variables and unc...Random variables and uncertain variables are respectively used to model randomness and uncertainty. While randomness and uncertainty always coexist in a same complex system. As an evolution of random variables and uncertain variables, uncertain random variable is introduced as a tool to deal with complex phenomena including randomness and uncertainty simultaneously. For uncertain random variables, a basic and important topic is to discuss the convergence of its sequence.Specifically, this paper focuses on studying the convergence in distribution for a sequence of uncertain random sequences with different chance distributions where random variables are not independent.And the result of this paper is a generalization of the existing literature. Relations among convergence theorems are studied. Furthermore, the theorems are explained by several examples.展开更多
Stochastic optimization offers a means of considering the objectives and constrains with stochastic parameters. However, it is generally difficult to solve the stochastic optimization problem by employing conventional...Stochastic optimization offers a means of considering the objectives and constrains with stochastic parameters. However, it is generally difficult to solve the stochastic optimization problem by employing conventional methods for nonlinear programming when the number of random variables involved is very large. Neural network models and algorithms were applied to solve the stochastic optimization problem on the basis of the stability theory. Stability for stochastic programs was discussed. If random vector sequence converges to the random vector in the original problem in distribution, the optimal value of the corresponding approximation problems converges to the optimal value of the original stochastic optimization problem.展开更多
基金the Natural Science Foundation of Hebei Province under Grant No.F2020202056Key Project of Hebei Education Department under Grant No. ZD2020125。
文摘Random variables and uncertain variables are respectively used to model randomness and uncertainty. While randomness and uncertainty always coexist in a same complex system. As an evolution of random variables and uncertain variables, uncertain random variable is introduced as a tool to deal with complex phenomena including randomness and uncertainty simultaneously. For uncertain random variables, a basic and important topic is to discuss the convergence of its sequence.Specifically, this paper focuses on studying the convergence in distribution for a sequence of uncertain random sequences with different chance distributions where random variables are not independent.And the result of this paper is a generalization of the existing literature. Relations among convergence theorems are studied. Furthermore, the theorems are explained by several examples.
基金The National Natural Science Foundation of China(No70271039)
文摘Stochastic optimization offers a means of considering the objectives and constrains with stochastic parameters. However, it is generally difficult to solve the stochastic optimization problem by employing conventional methods for nonlinear programming when the number of random variables involved is very large. Neural network models and algorithms were applied to solve the stochastic optimization problem on the basis of the stability theory. Stability for stochastic programs was discussed. If random vector sequence converges to the random vector in the original problem in distribution, the optimal value of the corresponding approximation problems converges to the optimal value of the original stochastic optimization problem.
