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

模糊环境和/或不确定性下最优决策过程的构建及其应用研究

基本信息

批准号：
09480080
负责人：
IWAMOTO Seiichi
金额：
$ 5.82万
依托单位：
KYUSHU UNIVERSITY
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (B)
财政年份：
1997
资助国家：
日本
起止时间：
1997 至 1999
项目状态：
已结题

项目摘要

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.

本研究利用数学方法分析模糊环境下多阶段决策过程的最优结构，并将其应用于经济与工程领域。我们提出了一些在运筹学和数理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，其中动态规划占据了核心部分。具体而言，三种方法-（1）全历史方法，（2）奖励参数方法，（3）多阶段随机/模糊决策表方法-给出了一个共同的最优解。同时，这些方法也为未解决的问题开辟了新的广阔领域.在1997学年，我们通过不变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，明确了三种过程的区别. 1998年，我们分析了不确定性下的多阶段决策过程。从政策空间的角度，阐明了可加报酬系统与非可加报酬系统的区别。我们提出了简单奖励制度和复合奖励制度。3.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最优解的图形演示和可视化显示。