| Co-Investigator(Kenkyū-buntansha) |
FURUKAWA Tetsuya Kyushu University, Faculty of Economics, Associate Professor, 経済学部, 助教授 (00209165)
NAKAI Toru Kyushu University, Faculty of Economics, Professor, 経済学部, 教授 (20145808)
TOKINAGA Shozo Kyushu University, Faculty of Economics, Professor, 経済学部, 教授 (30124134)
KAWASAKI Hidefumi Kyushu University, Mathematics, Associate Professor, 数理学研究科, 助教授 (90161306)
YASUDA Masami Chiba University, Math. & Info., Professor, 理学部, 教授 (00041244)
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| Research Abstract |
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.
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