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

本文通过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。我们在运筹学和数学金融学中都提出了一些适用的方法。在方法上，给出了以动态规划为核心的动态优化的理论基础。具体而言，三种方法(1)总历史法，(2)奖励参数法，(3)多阶段随机/模糊决策表法给出了一个共同的最优解。与此同时，这些方法也为尚未解决的问题开辟了广阔的新领域。在1997学年度，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，阐明了三种过程之间的区别。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，阐明了加性奖励制度与非加性奖励制度的区别。我们提出了简单的奖励系统和复合的奖励系统。在过去的一年里，我们主要关注的是相关方法在经济和工程领域的应用。我们举例说明了一些图形表示和最优解的可视化展示。

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.