Grant-in-Aid for Scientific Research (C)
|Allocation Type||Single-year Grants |
General mathematics (including Probability theory/Statistical mathematics)
|Research Institution||CHIBA UNIVERSITY |
KURANO Masami Chiba Univ., Faculty of Education, Professor, 教育学部, 教授 (70029487)
NAKAGAMI Jun-ichi Chiba Univ., Faculty of Education, Professor, 理学部, 教授 (30092076)
YASUDA Masami Chiba Univ., Faculty of Science, Professor, 理学部, 教授 (00041244)
KENMOCHI Nobuyuki Chiba Univ., Faculty of Education, Professor, 教育学部, 教授 (00033887)
YOSHIDA Yuji University of Kitakyusyu, Faculty of Economics and Business Administration, Professor, 経済学部, 教授 (90192426)
KADOTA Yoshinobu Wakayama Univ., Faculty of Education, Professor, 教育学部, 教授 (90116294)
|Project Period (FY)
2000 – 2001
Completed(Fiscal Year 2001)
|Budget Amount *help
¥3,500,000 (Direct Cost : ¥3,500,000)
Fiscal Year 2001 : ¥1,700,000 (Direct Cost : ¥1,700,000)
Fiscal Year 2000 : ¥1,800,000 (Direct Cost : ¥1,800,000)
|Keywords||Dynamic programming / Markov decision processes / Fuzzy dynamic programming / Fuzzy reward / Fuzzy clustering / Fuzzy max order / Fuzzy stopping / Interval matrix game / ファジイ動的計画法 / ファジイ利得 / ファジイクラスターリング / ファジイマックス順序 / ファジイストッピング / カァジィクラスターリング / ファジイストツプイング / 区間行列ゲーム|
In this project, our objective is to establish the mathematical theory on Dynamic Programming (DP in short) with more flexible structure, applicable to soft or rough mathematical models. To this end, we have done theoretical studies on flexibility and using intervals and fuzzy sets tried to develop analytical studies on various flexible DP models. The main research results are as follows:
(1) Theoretical studies on flexibility
We have succeeded in extending the concept of one-dimensional fuzzy max order to multi-dimensional fuzzy sets. Moreover, we develop limit theorems and potential theory for a sequence of multi dimensional fuzzy sets. Also, we derived a saddle point theorem for constrained Markov decision processes (MDPs in short) under average criteria.
(2) Uncertain MDPs
Applying interval analysis and fuzzy theory, we proposed some approximation model for uncertain MDPs, called controlled Markov set-chains or fuzzy treatment models, in which the validity of DP methods was proved.
(3) Fuzzy stopping models
Introducing fuzzy stopping time, dynamic fuzzy systems have been analyzed by optimal DP equations, which enlarge the application of DP methods.
(4) Fuzzy clustering models
Applying DP methods we solved the optimal clustering problem in which the metric between any two elements is given by a fuzzy metric.
(5) Sequential Markov game models
We considered interval matrix games with interval valued payoffs, for which the concept of saddle points is introduced and characterized as equilibrium points of corresponding non-zero sum parametric games. These results are extended to fuzzy sequential games.