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Analysis of fuzzy-valued stopping problem

Research Project

Project/Area Number 10640104
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 InstitutionChiba University

Principal Investigator

NAKAGAMI Jun-ichi  Chiba University, Faculty of Science, Professor, 理学部, 教授 (30092076)

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)
Project Period (FY) 1998 – 1999
Project Status Completed (Fiscal Year 1999)
Budget Amount *help
¥1,100,000 (Direct Cost: ¥1,100,000)
Fiscal Year 1999: ¥1,100,000 (Direct Cost: ¥1,100,000)
Keywordsmulti-stage decision process / fuzzy transition / fuzzy relation / optimal stopping problem / fuzzy optimization / order of fuzzy numbers / fuzzy stopping rule
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

Report

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

    (26 results)

All Other

All Publications (26 results)

  • [Publications] M.Kurano他2名: "Controlled Markov set-chains with set-valued rewards"Nonlinear Analysis and Cconvex Analysis (World Scientific). 205-212 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] M.Kurano他3名: "The time average reward for some dynamic fuzzy systems"International J. of Comp. & Math. with Applications. 37. 77-86 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] J.Nakagami: "A two-person noncooperative game for assets selling problem : Independent..."International J. of Comp. & Math. with Applications. 37. 207-212 (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他3名: "A monotone fuzzy stopping time in dynamic fuzzy systems"Bulletin of Informatics and Cybernetics. 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] M.Kurano他3名: "Fuzzy decision processes with an average reward criterion"Mathematical and Computing Modelling. 30. 7-29 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] M.Kurano他3名: "Ordering of Fuzzy sets - A brief survey and new results"J. of Operations Research Society of Japan. 43. 138-148 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Y. Yoshida, M. Yasuda, J. Nakagami, M. Kurano: "A limit theorem, in dynamic fuzzy systems with a monotone proprety"Fuzzy Sets and Systems. Vol.94 No.1. 109-119 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] M. Kurano, M. Yasuda, J. Nakagami, Y. Yoshida: "A fuzzy relational equation in dynamic fuzzy systems"Fuzzy Sets and Systems. Vol.101, No.3. 439-443 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] M. Kurano, M. Yasuda, J. Nakagami, Y. Yoshida: "The time average reward for some dynamic fuzzy systems"An International J. Computers & mathematics with Applications. Vol.37, No.11/12. 77-86 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] J Nakagami: "A two-person noncoperative game for assets selling preblem : Independent case"An International J. Computers & mathematics with Applications. Vol.37,No.11/12. 207-212 (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 of Informatics and Cybernetics. Vol.31, No.1. 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] M. Kurano, J Nakagami, M. Horiguchi: "Controlled Markov set-chains with set-valued rewards"Proceedings of the International Conference on Nonlinear Analysis and Convex Analysis, Editors W. Takahashi and T. Tanaka. 205-212 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] M. Kurano, M. Yasuda, J. Nakagami, Y. Yoshida: "Fuzzy decision processes with an average reward criterion"Mathematical and Computing Modelling. Vol.30. 7-20 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] M. Kurano, M. Yasuda, J. Nakagami, Y. Yoshida: "Ordering of convex fuzzy sets - A brief survey and new results"Journal of Operations Research Society of Japan. No.1, Vol.43. 138-148 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] M. Kurano 他2名: "Controlled Markov set-chains with set-valued rewards"Nonlinear Analysis and Cconvex Analysis (World Scientific). 205-212 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] M. Kurano 他3名: "The time average reward for some dynamic fuzzy systems"International J. of Comp. & Math. with Applications. 37. 77-86 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] J. Nakagami: "A two-person noncooperative game for assets selling problem: Independent..."International J. of Comp. & Math. with Applications. 37. 207-212 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] Y. Yoshida 他3名: "A monotone fuzzy stpping time in dynamic fuzzy systems"Bulletin of Informatics and Cybernetics. 31. 91-99 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] M. Kurano 他3名: "Fuzzy decision processes with an average reward criterion"Mathematical and Computing Modelling. 30. 7-29 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] M. Kurano 他3名: "Ordering of convex fuzzy sets - A brief survey and new results"J. of Operations Research Society of Japan. 43. 138-148 (2000)

    • Related Report
      1999 Annual Research Report
  • [Publications] M. Kurano 他2名: "Constrained Markov decision processes with compact state and action spaces" 数理解析研究所講究録. 1048. 1-13 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] Y. Yoshida 他3名: "A limit theorem in dynamic fuzzy systems with a monotone property" Fuzzy Sets and Systems. 94. 109-119 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] M. Kurano 他3名: "Fuzzy stopping of a dynamic fuzzy system" Proceedings KES'98 Adelaide. Vol.3. 547-552 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] M. Kurano 他3名: "Some pseudo-order of fuzzy sets on R^n" 数理解析研究所講究録. 1068. 142-149 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] M. Kurano 他3名: "A fuzzy relational equation in dynamic fussy systems" Fuzzy Sets and Systems. 101. 439-443 (1999)

    • Related Report
      1998 Annual Research Report
  • [Publications] M. Kurano 他2名: "Controlled Markov set-chains with set-valued rewards" To appear in Proceedings NACA98 Niigata. (1999)

    • Related Report
      1998 Annual Research Report

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Published: 1999-04-01   Modified: 2016-04-21  

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