1999 Fiscal Year Final Research Report Summary
Analysis of fuzzy-valued stopping problem
| Project/Area Number |
10640104
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Chiba University |
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Principal Investigator |
NAKAGAMI Jun-ichi Chiba University, Faculty of Science, Professor, 理学部, 教授 (30092076)
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| Co-Investigator(Kenkyū-buntansha) |
YOSHIDA Yuji Kita-kushu University, Faculty of Economics, Professor, 経済学部, 教授 (90192426)
YASUDA Masami Chiba University, Faculty of Science, Professor, 理学部, 教授 (00041244)
KURANO Masmi Chiba University, Faculty of Education, Professor, 教育学部, 教授 (70029487)
TANEMURA Hideki Chiba University, Faculty of Science, Associate Professor, 理学部, 助教授 (40217162)
TAGURI Masaki Chiba University, Faculty of Science, Professor, 理学部, 教授 (10009607)
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| Project Period (FY) |
1998 – 1999
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| Keywords | multi-stage decision process / fuzzy transition / fuzzy relation / optimal stopping problem / fuzzy optimization / order of fuzzy numbers / fuzzy stopping rule |
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| Research Abstract |
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 "Analysis of fuzzy-valued stopping problem" is widely applicable to many acutual problems in the real life and would be a fundamental technique in the study of the sequential decision theory.
In two years term of our project, Our focal point is to analyze the fundamental structure of the fuzzy (optimal) stopping problem and to introduce a new definition to the set of n-dimensional fuzzy numbers. The main results given in the references are summarized as follows :
(1) A dynamic fuzzy system is considered under a monotone property of the fuzzy relation. We study the limit of a sequence of fuzzy sets and obtain a convergenece theorem. The limit is charecterized as a solution of a fuzzy relational
… More
equaton.
(2) For a dynamic fuzzy system, the fundamental method is to analyze its recursive reration of fuzzy states. It is similar in that the Bellman equation is a important tool in the dynamic programming. We derive the existence and the uniqueness of the solution of a fuzzy relational equation.
(3) We consider a game variant of an asset selling problem. We formulate the actual situation as a stopping problem of a two-person noncooperative game and prove the existece theorem of an equilibrium point.
(4) A new class of fuzzy stopping times which is called as a monotone fuzzy stopping time is introduced for a dynamic fuzzy system. Since the fuzzy stopping time is constructed using by α-cuts of fuzzy sets, the explicit derivation of an optimal one is obtained.
(5) Concerning with the topics of a fuzzy max order, we consider its extension as a pseudo order on a class of fuzzy sets on RィイD1nィエD1(n【greater than or equal】1). This order is developed by using a non-empty closed convex cone and charcterized by the projection into its dual cone. Especially a structure of the lattice can be illustrated with the class of rectangle-type fuzzy sets.
Finally, we express our appreciation of Grant-in-Aid for Scientific Research to our research project. Less
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