Grant-in-Aid for Scientific Research (B)
|Allocation Type||Single-year Grants |
|Research Institution||Chiba University |
NAKAGAMI Jun-ichi Chiba University, Faculty of Science, Professor, 理学部, 教授 (30092076)
KURANO Masami Chiba University, Faculty of Science, Professor, 教育学部, 教授 (70029487)
YASUDA Masami Chiba University, Faculty of Science, Professor, 理学部, 教授 (00041244)
YOSHIDA Yuji The University of Kita-Kyushu, Faculty of Economics, Professor, 理学部, 教授 (90192426)
TAGURI Masaaki Chiba University, Faculty of Science, Professor, 理学部, 教授 (10009607)
TANEMURA Hideki Chiba University, Faculty of Science, Associate Professor, 理学部, 助教授 (40217162)
辻 尚史 千葉大学, 理学部, 教授 (70016666)
|Project Period (FY)
2001 – 2004
Completed (Fiscal Year 2004)
|Budget Amount *help
¥8,700,000 (Direct Cost: ¥8,700,000)
Fiscal Year 2004: ¥2,000,000 (Direct Cost: ¥2,000,000)
Fiscal Year 2003: ¥2,100,000 (Direct Cost: ¥2,100,000)
Fiscal Year 2002: ¥2,100,000 (Direct Cost: ¥2,100,000)
Fiscal Year 2001: ¥2,500,000 (Direct Cost: ¥2,500,000)
|Keywords||Markov decision process / fuzzy relation / optimal stopping problem / perception / optimality equation / robustness / fuzzy preference / American option / マルコフ決定過 / ファジー推移 / 区間解析と凸解析 / 区間ゲーム / 多段決定過程 / ファジー数の順序|
A fuzzy treatment of Markov decision processes is a main research subject to a research group of the mathematical programming in Chiba University since 1991, its members are Masami Kurano, Masami Yasuda, Jun-ichi Nakagami and Yuji Yoshida.
This research project, grant-in-aid for scientific research ‘Research on theories and applications of the robust structure of fuzzy decision processes' is widely applicable to many actual problems in the real life and would be a fundamental technique in the study of the sequential decision theory.
In four years term of our project, our focal point is to analyze the fundamental structure of the fuzzy decision processes and to try to consider a perceptive analysis of the fuzzy decision processes which is introduced by Zadeh in 2002 as a new interpretation of fuzzy numbers.
The main results given in the references are summarized as follows :
(1)Concerning with the topics of a fuzzy max order, we consider its extension as a pseudo order on a class of fuzzy s
ets on R^n. This order is developed by using a non-empty closed convex cone and characterized by the projection into its dual cone. Especially a structure of the lattice can be illustrated with the class of rectangle-type fuzzy sets.
(2)Interval methods for uncertain Markov decision processes are considered. That is, a controlled Markov set-chain model with a finite state is developed by an interval arithmetic analysis, and we will find Pareto optimal policies which maximize the discounted or average expected rewards over all stationary policies under some partial order. The optimal policies are characterized by a maximal solution of an optimal equation including efficient function.
(3)In a continuous-time fuzzy stochastic system, a stopping model with fuzzy stopping times is presented. The optimal fuzzy stopping times are given under an assumption of regularity for stopping rules. Also, the optimal fuzzy reward is characterized as a unique solution of an optimality equation under a differentiability condition.
(4)Stimulated by Zadeh's paper (J.Statistical Planning and Inference, 2002,105,233-264), we try to consider a perceptive analysis of the optimal stopping problem. The fuzzy perception value of the expectation of the optimal stopped reward is characterized and calculated by a new recursive equation.
Finally, we express our appreciation of Grant-in-Aid for Scientific Research to our research project. Less