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Research on theories and applications of the robust structure of fuzzy decision processes

Research Project

Project/Area Number 13480110
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field 社会システム工学
Research InstitutionChiba University

Principal Investigator

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

Co-Investigator(Kenkyū-buntansha) KURANO Masami  Chiba University, Faculty of Science, Professor, 教育学部, 教授 (70029487)
YASUDA Masami  Chiba University, Faculty of Science, Professor, 理学部, 教授 (00041244)
YOSHIDA Yuji  The University of Kita-Kyushu, Faculty of Economics, Professor, 理学部, 教授 (90192426)
TAGURI Masaaki  Chiba University, Faculty of Science, Professor, 理学部, 教授 (10009607)
TANEMURA Hideki  Chiba University, Faculty of Science, Associate Professor, 理学部, 助教授 (40217162)
辻 尚史  千葉大学, 理学部, 教授 (70016666)
Project Period (FY) 2001 – 2004
Project Status Completed (Fiscal Year 2004)
Budget Amount *help
¥8,700,000 (Direct Cost: ¥8,700,000)
Fiscal Year 2004: ¥2,000,000 (Direct Cost: ¥2,000,000)
Fiscal Year 2003: ¥2,100,000 (Direct Cost: ¥2,100,000)
Fiscal Year 2002: ¥2,100,000 (Direct Cost: ¥2,100,000)
Fiscal Year 2001: ¥2,500,000 (Direct Cost: ¥2,500,000)
KeywordsMarkov decision process / fuzzy relation / optimal stopping problem / perception / optimality equation / robustness / fuzzy preference / American option / マルコフ決定過 / ファジー推移 / 区間解析と凸解析 / 区間ゲーム / 多段決定過程 / ファジー数の順序
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 ‘Research on theories and applications of the robust structure of fuzzy decision processes' is widely applicable to many actual problems in the real life and would be a fundamental technique in the study of the sequential decision theory.
In four years term of our project, our focal point is to analyze the fundamental structure of the fuzzy decision processes and to try to consider a perceptive analysis of the fuzzy decision processes which is introduced by Zadeh in 2002 as a new interpretation of fuzzy numbers.
The main results given in the references are summarized as follows :
(1)Concerning with the topics of a fuzzy max order, we consider its extension as a pseudo order on a class of fuzzy s … More ets on R^n. This order is developed by using a non-empty closed convex cone and characterized by the projection into its dual cone. Especially a structure of the lattice can be illustrated with the class of rectangle-type fuzzy sets.
(2)Interval methods for uncertain Markov decision processes are considered. That is, a controlled Markov set-chain model with a finite state is developed by an interval arithmetic analysis, and we will find Pareto optimal policies which maximize the discounted or average expected rewards over all stationary policies under some partial order. The optimal policies are characterized by a maximal solution of an optimal equation including efficient function.
(3)In a continuous-time fuzzy stochastic system, a stopping model with fuzzy stopping times is presented. The optimal fuzzy stopping times are given under an assumption of regularity for stopping rules. Also, the optimal fuzzy reward is characterized as a unique solution of an optimality equation under a differentiability condition.
(4)Stimulated by Zadeh's paper (J.Statistical Planning and Inference, 2002,105,233-264), we try to consider a perceptive analysis of the optimal stopping problem. The fuzzy perception value of the expectation of the optimal stopped reward is characterized and calculated by a new recursive equation.
Finally, we express our appreciation of Grant-in-Aid for Scientific Research to our research project. Less

Report

(5 results)
  • 2004 Annual Research Report   Final Research Report Summary
  • 2003 Annual Research Report
  • 2002 Annual Research Report
  • 2001 Annual Research Report
  • Research Products

    (38 results)

All 2005 2004 2003 2002 Other

All Journal Article (19 results) Publications (19 results)

  • [Journal Article] A Discrete-Time American Put Option Model with Fuzziness of Stock Prices2005

    • Author(s)
      Y.Yoshida, M.Yasuda, J.Nakagami, M.Kurano
    • Journal Title

      Fuzzy Optimization and Decision Making Vol.4 No.3(in press)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Annual Research Report 2004 Final Research Report Summary
  • [Journal Article] A Discrete-Time American Put Option Model with Fuzziness of Stock Prices2005

    • Author(s)
      Yoshida, Y., Yasuda, M., Nakagami, J., Kurano, M.
    • Journal Title

      Fuzzy Optimization and Decision Making Vol.4(in press)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] An Objective Function based on Fuzzy Preferences in Dynamic Decision Making2004

    • Author(s)
      Y.Yoshida, M.Yasuda, M.Kurano, J.Nakagami, S.Kumamoto
    • Journal Title

      Lecture Notes in Artificial Intelligence 3214 Knowledge-Based Intelligent Information and Engineering Systems(edited by M.Ch.Negoita, R.J.Howlett and L.C.Jain)(Springer)

      Pages: 1230-1236

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] A fuzzy stopping problem with the concept of perception2004

    • Author(s)
      M.Kurano, M.Yasuda, J.Nakagami, Y.Yoshida
    • Journal Title

      Fuzzy Optimization and Decision Making Vol.3,No.2

      Pages: 367-374

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Annual Research Report 2004 Final Research Report Summary
  • [Journal Article] An Objective Function based on Fuzzy Preferences in Dynamic Decision Making.2004

    • Author(s)
      Yoshida, Y., Yasuda, M., Kurano, M., Nakagami, J., Kumamoto, S.
    • Journal Title

      Lecture Notes in Artificial Intelligence 3214,Knowledge-Based Intelligent Information and Engineering Systems, Part II(M.Ch.Negoita, R.J.Howlett, L.C.Jain(Ed))(Springer)

      Pages: 1230-1236

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] A fuzzy stopping problem with the concept of perception.2004

    • Author(s)
      Kurano, M., Yasuda, M., Nakagami, J., Yoshida, Y.
    • Journal Title

      Fuzzy Optimization and Decision Making Vol.3

      Pages: 367-374

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] An Objective Function based on Fuzzy Preferences in Dynamic Decision Making2004

    • Author(s)
      Y.Yoshida, M.Yasuda, M.Kurano, J.Nakagami, S.Kumamoto
    • Journal Title

      Lecture Notes in Artificial Intelligence 3214

      Pages: 1230-1236

    • Related Report
      2004 Annual Research Report
  • [Journal Article] A fuzzy stopping problem with the concept of perception : the finite and infinite horizon cases2004

    • Author(s)
      M.Kurano, M.Yasuda, J.Nakagami, Y.Yoshida
    • Journal Title

      Proceedings of the Third International Conference on NACA

      Pages: 233-243

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Lusin's Theorem on Fuzzy Measure Spaces2004

    • Author(s)
      Li Jun, M.Yasuda
    • Journal Title

      Fuzzy Sets and Systems Vol.146

      Pages: 121-133

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Egoroff's Theorem on Monotone Non-additive Measure Spaces2004

    • Author(s)
      Li Jun, M.Yasuda
    • Journal Title

      International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems Vol.12

      Pages: 61-68

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Markov decision processes with fuzzy rewards.2003

    • Author(s)
      Kurano, M., Yasuda, M., Nakagami, J., Yoshida, Y.
    • Journal Title

      Journal on Nonlinear Analysis and Convex Analysis Vol.4

      Pages: 105-115

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Fuzzy Stopping Problems in Continuous-Time Fuzzy Stochastic Systems.2003

    • Author(s)
      Yoshida, Y., Yasuda, M., Nakagami, J., M.Kurano, M.
    • Journal Title

      Fuzzy Sets and Systems Vol.139

      Pages: 349-362

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] A Multi-Objective Fuzzy Stopping in a Stochastic and Fuzzy Enviroment.2003

    • Author(s)
      Yoshida, Y., Yasuda, M., Nakagami, J., M.Kurano, M.
    • Journal Title

      Computers and Mathematics with Applications Vol.46

      Pages: 1165-1172

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] A Discrete-Time Portfolio Selection with Uncertainty of Stock Prices.2003

    • Author(s)
      Y.Yoshida, M.Yasuda, M.Kurano, J.Nakagami, S.Kumamoto
    • Journal Title

      Lecture Notes in Artificial Intelligence 2715,‘Fuzzy Sets and Systems - IFSA2003(edited by T.Bilgic, B.De Baets and O.Kaynac)(Springer)

      Pages: 245-252

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Fuzzy Stopping Problems in Continuous-Time Fuzzy Stochastic Systems.2003

    • Author(s)
      Yoshida, Y., Yasuda, M., Nakagami, J., Kurano, M.
    • Journal Title

      Fuzzy Sets and Systems Vol.139

      Pages: 349-362

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] A Multi-Objective Fuzzy Stopping in a Stochastic and Fuzzy Environment.2003

    • Author(s)
      Yoshida, Y., Yasuda, M., Nakagami, J., Kurano, M.
    • Journal Title

      Computers and Mathematics with Applications Vol.46

      Pages: 1165-1172

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] A Discrete-Time Portfolio Selection with Uncertainty of Stock Prices.2003

    • Author(s)
      Yoshida, Y., Yasuda, M., Nakagami, J., Kurano, M.
    • Journal Title

      Lecture Notes in Artificial Intelligence 2715,Fuzzy Sets and Systems-IFSA 2003,(T.Bilgic, B.De Baets, O.Kaynac(Eds))(Springer)

      Pages: 245-252

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Interval methods for uncertain Markov decision processes.2002

    • Author(s)
      Kurano, M., Yasuda, M., Nakagami, J.
    • Journal Title

      Markov Processes and Controlled Markov Chains},(Zhenting Hou, Jerzy A.Filar and Anyue Chen(Eds.))(Kluwer Academic Publisher)

      Pages: 223-232

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Interval methods for uncertain Markov decision processes.2002

    • Author(s)
      Kurano, M., Yasuda, M., Nakagami, J.
    • Journal Title

      Markov Processes and Controlled Markov Chains(Zhenting Hou, Jerzy A.Filar and Anyue Chen(Eds.))(Kluwer Academic Publisher)

      Pages: 223-232

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Publications] M.Kurano, M.Yasuda, J.Nakagami, Y.Yoshida: "Markov decision processes with fuzzy rewards"Journal on Nonlinear Analysis and Convex Analysis. Vol.4. 105-115 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] Y.Yoshida, M.Yasuda, J.Nakagami, M.Kurano: "Fuzzy Stopping Problems in Continuous-Time Fuzzy Stochastic Systems"Fuzzy Sets and Systems. Vol.139. 349-362 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] Y.Yoshida, M.Yasuda, J.Nakagami, M.Kurano: "A Multi-Objective Fuzzy Stopping in a Stochastic and Fuzzy Environment"Computers and Mathematics with Applications. Vol.46. 1165-1172 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] Y.Yoshida, M.Yasuda, J.Nakagami, M.Kurano: "A Discrete-Time Portfolio Selection with Uncertainty of Stock Prices"Lecture Notes in Artificial Intelligence 2715 'Fuzzy Sets and Systems - IFSA2003', Springer. 245-252 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] Y.Yoshida: "The Valuation of European Options in Uncertain Environment"European Journal of Operational Research. Vol.145. 221-229 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] Y.Yoshida: "Continuous-Time Fuzzy Decision Processes with Discounted Rewards"Fuzzy Sets and Systems. Vol.139. 333-348 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] M.Hosaka, J.Nakagami, M.Kurano: "Controlled Markov set-chains with set-valued rewards the average case"International Transactions in Operational Research. Vol.9. 113-123 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] Y.Yoshida, M.Yasuda, J.Nakagami, M.Kurano: "Decision Making for American Options with Uncertainty of Stock Prices in Financial Engineering"The 9th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems. Vol.1. 463-469 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] M.Kurano, M.Yasuda, J.Nakagami, Y.Yoshida: "Markov decision processes with fuzzy rewards"Proceedings of the Second International Conference on NACA. 221-232 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] Y.Yoshida, M.Yasuda, J.Nakagami, M.Kurano: "Discrete-Time American Options Evaluated by Weighting Functions"Proceedings of KES 2002 (Knowledge-Based Intelligent Engineering Systems and Allied Technologies). Vol.1. 255-259 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] Y.Yoshida, M.Yasuda, J.Nakagami, M.Kurano: "An approach to stopping problems of a dynamic fuzzy system"Fuzzy Sets and Systems. Vol.131/2. 225-233 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] M.Kurano, M.Yasuda, J.Nakagami: "Interval methods for uncertain Markov decision processes"Zhenting Hou, Jerzy A.Filar and Anyue Chen(Eds.) : Markov Processes and Controlled Markov Chains, Kluwer Academic. 223-232 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] Y.Yoshida, M.Yasuda, J.Nakagami, M.Kurano: "On a fuzzy extension of stopping times"数理解析研究所講究録 1207「不確実なモデルによる動的計画論の課題とその展望」. 1207. 157-164 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] M.Kurano, M.Yasuda, J.Nakagami, Y.Yoshida: "Markov decision processes with fuzzy rewards"数理解析研究所講究録 1207「不確実なモデルによる動的計画論の課題とその展望」. 1207. 165-176 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] M.Kurano, M.Yasuda, J.Nakagami, Y.Yoshida: "A note on interval games and their saddle points"数理解析研究所講究録 1241「数理最適化の理論とアルゴリズム」. 1241. 171-178 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] M.Kurano, M.Yasuda, J.Nakagami, Y.Yoshida: "A Fuzzy treatment of Markov decision processes under uncertain transition probabilities"17th Fuzzy System Symposium(Chiba,Japan). 197-200 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] M.Kurano, M.Yasuda, J.Nakagami, Y.Yoshida: "Order relations and monotone convergence theorem in the class of fuzzy sets on R^n"Dynamical Aspects in Fuzzy Decision Making.Editor:Yuji Yoshida,Physica-Verlang,Heiderberg. 187-211 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] M.Hosaka, J.Nakagami, M.Kurano: "Controlled Markov set-chains with set-valued rewards-the average case"International Transactions in Operational Research. Vol.9. 113-123 (2002)

    • Related Report
      2001 Annual Research Report
  • [Publications] Yuji Yoshida(editor): "Dynamical Aspects in Fuzzy Decision Making"Physica-Verlang,Heiderberg. 240 (2001)

    • Related Report
      2001 Annual Research Report

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Published: 2001-04-01   Modified: 2016-04-21  

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