多步决策过程中有效解的平稳性

ON THE STATIONARINESS OF EFFICIENT SOLUTION SEQUENCE IN THE MULTISTEP DECISION PROCESS

本文首先论述多步决策过程及其性能指标,引进有关信息集、半收敛和强收敛等概念,给出多步决策的含时有效解和定态有效解及其平稳性的定义。然后探讨了集值映射序列在拓扑意义下的收敛和以Pompeiu-Hausdauff距离意义的收敛之间的关系,证明了几个对应关系定理。最后,文章系统地考察了决策过程中有效解的平稳性质。

In this paper, the notions and concepts about information set, semi-cenvergence, strong convergence, etc. are introduced and the definitions of transient efficient solution as well as its stationariness in multi-step decision process are given. Then the paper studies the relation between the conergence in the sense of topology and the strong convergence in the sense of pompeiu-Hausdauff Matrix, and proves the corresponding theorems under weak conditions. Finally the paper systematically investigates the stafionariness of efficient solution sequence.