Study on Construction of Optimal Decision-making Processes under Fuzzy Environment and/or under Uncertainty and its Applications

本文运用数学方法分析了模糊环境下多阶段决策过程的最优结构，并将其应用于经济和工程领域。我们已经提出了一些在运筹学和数学金融学中都适用的方法。作为方法论，我们给出了动态优化的理论基础，其中动态规划是核心部分。具体地说，三种方法--(1)总历史方法，(2)报酬-参数方法，(3)多阶段随机/模糊决策表方法--给出了共同的最优解。与此同时，这些方法培育了一个新的大领域的悬而未决的问题1。1997学年，我们通过不变量嵌入给出了模糊环境下多阶段决策过程的最优结构。推导了后验条件过程、先验过程和原始(无条件)过程的最优解，明确了三个过程之间的区别。1998年，我们分析了不确定条件下的多阶段决策过程。从政策空间的角度，阐明了累加性奖励制度与非累加性奖励制度的区别。提出了简单奖励制和复合奖励制。在过去的一年里，我们主要关注相关方法在经济和工程领域的应用。我们举例说明了一些最优解的图形表示和可视化显示。

In this study, we have analyzed optimal structure of multi-stage decision-making processes in fuzzy environment through mathematical approaches and have applied it to economic and engineering fields. We have proposed a few applicable methods both in operations research and in mathematical finance. As methodology, we give a theoretical basis of dynamic optimization, where dynamic programming takes a central part. Specifically, three methods - (1) total history methods, (2) reward-parametric method, (3) multi-stage stochastic/fuzzy decision-table method - gives a common optimal solution. As the same time, these methods cultivates a new large fields of unsolved problems.1. In academic year 1997, we gave as optimal structure of multi-stage decision-making processes in fuzzy environment through invariant imbedding. Deriving optimal solution to the a posteriori conditional process, the a priori and the original (unconditional) process, we have clarified differences among the three processes.2. In 1998, we analyzed the multi-stage decision-making processes under uncertainty. From the viewpoint of policy-space, we clarified the difference between additive reward system and nonadditive one. We proposed both simple reward system and compound one.3. In the last year, we were mainly concerned with applications of the related approaches to both economic and engineering fields. We illustrated some graphical presentations and visual shows of optimal solutions.