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Multi-valued optimization problems on uncertain models

Research Project

Project/Area Number 10640124
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionKOCHI UNIVERSITY

Principal Investigator

NIIZEKI Shozo (1999)  Faculty of Science, KOCHI UNIVERSITY, Professor, 理学部, 教授 (60036572)

大坪 義夫 (1998)  高知大学, 理学部, 助教授 (20136360)

Co-Investigator(Kenkyū-buntansha) 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
Project Status 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)
Keywordsuncertain model / optimization theory / optimal stopping / Fuzzy decision process / dynamic programming / Lebesgue measure / statistical inference / Hausdorff dimension / ハウスドルフ次元
Research Abstract

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.

Report

(3 results)
  • 1999 Annual Research Report   Final Research Report Summary
  • 1998 Annual Research Report
  • Research Products

    (27 results)

All Other

All Publications (27 results)

  • [Publications] Y.Ohtsubo: "The values in Dynkin stopping problem with th Some constraints"Mathematica Japonica. 51・1. 75-81 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] S.Niizeki: "On some properties of the locally integrable function over R^N"Men.Fac.Sci.Kochi Univ.(Math.). 21. 103-108 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] K.Nomakuchi: "A Generalization of the Childs-Moran Result for Orthoscheme Probability"Australian & New Zealand Journal of Statistics. 40. 103-109 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] K.Kato: "Hausdorff dimensions of generalized cookie-cutter Cantor sets"Far East J.Appl.Math.. 2・3. 191-202 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] S.Iwamoto: "Euler partition rule"Proc.Int.Conf.on "Nonlinear Analysis and Convex Analysis", World Scientific, by Ed.T.Tanaka and W.Takahashi. 173-180 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Y.Yoshida: "A Monotone Fuzzy Stopping Time in Dynamic Fuzzy Systems,with M.Yasuda,J.Nakagami,M.Kurano"Bulletin lnformatics & Cybenetics. 31. 91-99 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] 古川長太: "ファジィ最適化の数理"森北出版. 179 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Y. Ohtsubo: "The values in Dynkin stopping problem with th some constraints"Mathematica Japonica. Vol. 51. 75-81 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] S. Niizeki: "On some properties of the locally integrable function over RィイD1NィエD1"Mem. Fac. Sci. Kochi Univ. (Math). Vol. 21. 103-108 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] K. Nomakuchi: "A Generalization of the Childs-Moran Result for Orthoscheme Probability"Australian & New Zealand Journal of Statistics. Vol. 40. 103-109 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] K. Kato: "Hausdorff dimensions of generalized cookie-cutter Cantor sets"Far East J. Appl. Math.. Vol. 2, No. 3. 191-202 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] S. Iwamoto: "Euler partition rule"Proc. Int. Conf. on 'Nonlinear Analysis and Convex Analysis', World Scientific, by Ed. T. Tanaka and W. Takahashi. 173-180 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Y. Yoshida, M. Yasuda, J. Nakagami, M. Kurano, A. Monotone: "Fuzzy Stopping Time in Dynamic Fuzzy Systems"Bulletin Informatics & Cybenetics. Vol. 31. 91-99 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] N. Furukawa: "Mathematics of Fuzzy Optimization"Morikita Shupan(in Japanese). 179 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] S.Niizeki: "On some properties of the locally integrable function over R^N"Mem.Fac.Sci.Kochi Univ.(Math.). 21. 103-108 (2000)

    • Related Report
      1999 Annual Research Report
  • [Publications] S.Niizeki: "Remarks on the Lusin's theorem for the Lebesgue measurable functions on R^n"Mem.Fac.Sci.Kochi Univ.(Math.). 20. 127-134 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] S.Iwamoto: "Euler partition rule"Proc.Int.Conf.on "Nonlinear Analysis and Convex Analysis",World Scientific,by Ed.T.Tanaka and W.Takahashi. 173-180 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] Y.Yoshida: "A Monotone Fuzzy Stopping Time in Dynamic Fuzzy Systems,with M.Yasuda,J.Nakagami,M.Kurano"Bulletin Informatics & Cybenetics. 31. 91-99 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] 古川長太: "ファジイ最適化の数理"森北出版. 179 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] Y.Ohtsubo: "The values in Dynkin stopping problem with th some constraints" Mathematica Japonica. 51・1 印刷中. 印刷中 (2000)

    • Related Report
      1998 Annual Research Report
  • [Publications] Y.Ohtsubo: "Optimality in multi-person stopping problem with general rewards" Proc.Int.Conf.on Nonlinear Analysis and Convex Analysis,World Scientific. 印刷中. 印刷中 (1999)

    • Related Report
      1998 Annual Research Report
  • [Publications] S.Niizeki: "Remarks on the Lusin's theorem for the Lebesgue measurable functions on R^n" Mem.Fac.Sci.Kochi Univ.(Math.). 20. 127-134 (1999)

    • Related Report
      1998 Annual Research Report
  • [Publications] K.Nomakuchi: "A Generalization of the Childs-Moran Result for Orthoscheme Probability" Australian & New Zealand Journal of Statistics. 40. 103-109 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] N.Furukawa: "First-order necessary optimality conditions in fuzzy nonlinear pogramming problems" 数理解析研究所講究録. 1068. 134-141 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] S.Iwamoto: "On expected values of Markov statistics" Bull.Informatics Cybernetics. 20・1. 1-24 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] Y.Yoshida: "ファジィシステムにおける意思決定の展開(Decision-Making in Dynamic Fuzzy Systems)(in Japanese),with M.Yasuda" Journal of Japan Society for Fuzzy Theory and Systems. 10・6. 1053-1062 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] K.Kato: "Hausdorff dimensions of generalized cookie-cutter Cantor sets" Far East J.Appl.Math.2・3. 191-202 (1998)

    • Related Report
      1998 Annual Research Report

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Published: 1998-04-01   Modified: 2016-04-21  

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