Grant-in-Aid for Scientific Research (C)
|Allocation Type||Single-year Grants|
General mathematics (including Probability theory/Statistical mathematics)
|Research Institution||KOCHI UNIVERSITY|
NIIZEKI Shozo(1999) Faculty of Science, KOCHI UNIVERSITY, Professor, 理学部, 教授 (60036572)
大坪 義夫 高知大, 理学部, 助教授 (20136360)
IWAMOTO Seiiti Kyushu University Faculty of Economics, Professor, 経済学部, 教授 (90037284)
FURUKAWA Nagata Soka University Faculty of Engineering, Professor, 工学部, 教授 (50037165)
NOMAKUCHI Kentaro Faculty of Science, KOCHI UNIVERSITY, Professor, 理学部, 教授 (60124806)
KATO Kazuhisa Faculty of Science, KOCHI UNIVERSITY, Professor, 理学部, 教授 (20036578)
YASUDA Masami Chiba University Faculty of Science, Professor, 理学部, 教授 (00041244)
新関 章三 高知大学, 理学部, 教授 (60036572)
|Project Period (FY)
1998 – 1999
Completed(Fiscal Year 1999)
|Budget Amount *help
¥3,300,000 (Direct Cost : ¥3,300,000)
Fiscal Year 1999 : ¥1,100,000 (Direct Cost : ¥1,100,000)
Fiscal Year 1998 : ¥2,200,000 (Direct Cost : ¥2,200,000)
|Keywords||uncertain model / optimization theory / optimal stopping / Fuzzy decision process / dynamic programming / Lebesgue measure / statistical inference / Hausdorff dimension / ハウスドルフ次元|
The summary of research results is as follows.
1. We gave two approximation methods for the value of the problem without a finite constraint in the zero-sum Dynkin problem and introduced several new constraints and established the relationship between their values.
2. We proved the following result by means of elementary Lebesgue measure and integral theory in RィイD1NィエD1 : let f be a locally integrable function over RィイD1NィエD1. If an integral of a product of f and a continuous function with any compact support is O,, then f = O a.e..
3. Childs conjectured and Moran proved that a generating function of an orthoscheme probability equals tan Z + sin Z. We gave their generalization.
4. We proved that the Hausdorff dimension of a CィイD11+γィエD1 generalized cookie-cutter Cantor set is less than 1.
5. As a typical optimization problem, we chose a mathematical partition problem in the scheme of three-body ; discrete, continuous and continuum and proved that Euler Partition Rule holds through three bodies.
6. We introduced a new class of fuzzy stopping times which called as a monotone fuzzy stopping time and gave an explicit derivation of an optimal stopping under appropriate assumptions.
7. In a book "Mathematics of Fuzzy Optimization" , we mathematically and systematically developed fuzzy theory and fuzzy optimization.