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STUDIES OF FUZZY DECISION PROCESSES AND THEIR APPLICATIONS

Research Project

Project/Area Number 10640131
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 InstitutionKITAKYUSHU UNIVERSITY

Principal Investigator

YOSHIDA Yuji  KITAKYUSHU UNIVERSITY, ECONOMICS, PROFESSOR, 経済学部, 教授 (90192426)

Co-Investigator(Kenkyū-buntansha) NAKAGAMI Jun-ihi  CHIBA UNIVERSITY, MATHEMATICS,PROFESSOR, 理学部, 教授 (30092076)
YASUDA Masami  CHIBA UNIVERSITY, MATHEMATICS,PROFESSOR, 理学部, 教授 (00041244)
KURANO Masami  CHIBA UNIVERSITY, EDUCATION, PROFESSOR, 教育学部, 教授 (70029487)
IWAMOTO Seiichi  KYUSHU UNIVERSITY, ECONOMICS, PROFESSOR, 経済学部, 教授 (90037284)
Project Period (FY) 1998 – 1999
Project Status Completed (Fiscal Year 1999)
Budget Amount *help
¥3,000,000 (Direct Cost: ¥3,000,000)
Fiscal Year 1999: ¥1,700,000 (Direct Cost: ¥1,700,000)
Fiscal Year 1998: ¥1,300,000 (Direct Cost: ¥1,300,000)
KeywordsDynamic fuzzy systems / Decision Making / Dynamic programming / Optimality equation / Fuzzy relational equation / Limit theorem / Optimal stopping / Zero-sum game / 双対性 / 周期性
Research Abstract

The aim of this research is analysis of the mathematical structure of dynamic fuzzy systems and its application to decision making. The main results are as follows.
(i) Limit theorems of sequences of fuzzy states in dynamic fuzzy systems are studied when fuzzy relations are monotone/transitive.
(ii) The space of the solutions of fuzzy relational equations is characterized.
(iii) The recurrence and the cyclic behavior of the dynamic fuzzy systems are analyzed.
(iv) The optimal stopping problems in dynamic fuzzy systems are studied by introducing fuzzy reward, and the optimal rewards are characterized by unique solutions of fuzzy relational equation. The fuzzy rewards are estimated by a fuzzy expectation induced from fuzzy goals, and an optimal stopping times is also given.
(v) In the two-person zero-sum stopping games in dynamic fuzzy systems with fuzzy rewards, a minimax theorem is proved and optimal stopping points and the value of the game are also given.
(vi) The duality of the dynamic fuzzy systems is discussed for a stopping problem, and the solutions are characterized by the recurrence set.
(vii) fuzzy decision processes, under the criteria of time-average rewards, are discussed from a viewpoint of a dynamic fuzzy system and fuzzy dynamic programming. The time-average reward is characterized, by introducing a relative value function, as a unique solution of the associated equation.
These results are published by the international journals, Fuzzy Sets and Systems, Information Sciences, Computers and Mathematics with Applications, Mathematical and Computer Modelling, Journal of Math. Analy. Appl. and so on. We have also presented some results at international conferences a d workshops, KES '98, EUFIT '98, IIZUKA '98, IFSA '99 and so on.
In this research, we have analyzed the mathematical structure of dynamic fuzzy systems and we have obtained its application to decision making.

Report

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

    (54 results)

All Other

All Publications (54 results)

  • [Publications] 蔵野 正美(共著): "A Fuzzy Relational Equation in Dynamic Fuzzy Systems"Fuzzy Sets and Systems. Vol 101 No.3. 439-443 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] 吉田 祐治: "A Minimax Theorem for Zero-Sum Stopping Games in Dynamic Fuzzy Systems"Mathematical and Computer Modelling. Vol. 29 No.1. 19-33 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] 蔵野 正美(共著): "The Time Average Reward for Some Dynamic Fuzzy Systems"Computers & Mathematics with Applications. Vol. 37 No.11-12. 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] 吉田 祐治: "Superharmonic Fuzzy Sets on Recurrent Sets in Dynamic Fuzzy Systems"Computers & Mathematics with Applications. Vol. 37 No.11-12. 87-93 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] 岩本 誠一: "Conditional Decision Processes with Recussive Function"J. Math. Anal. Appl.. Vol. 230 No.1. 193-210 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] 吉田 祐治: "A Limit Theorem in Dynamic Fuzzy Systems with Transitive Fuzzy Relations"Fuzzy Sets and Systems. Vol. 109 No.3. 371-378 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Yuji Yoshida, Masami Yasuda, Jun-ichi Nakagami and Masami Kurano: "A limit Theorem in Dynamic Fuzzy Systems with a Monotone Property"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] Yuji Yoshida: "Duality in Dynamic Fuzzy Systems"Fuzzy Sets and Systems. Vol.98, No.1. 53-65 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Yuji Yoshida: "Cyclic Classes and an Ergodic Theorem in Dynamic Fuzzy Systems"Fuzzy Sets and Systems. Vol.95, No.2. 189-199 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Yuji Yoshida: "The Recurrence of Dynamic Fuzzy Systems"Fuzzy Sets and Systems. Vol.95, No.3. 319-332 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Yuji Yoshida: "A Time-Average Fuzzy Reward Criterion in Fuzzy Decision Processes"Information Sciences. Vol.110, No.1-2. 103-112 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Yuji Yoshida: "An Optimal Stopping Zero-sum Game in Discrete-Time Multi-Armed Bandit Processes"J. Infor. Optimi. Sci. Vol.19, No.3. 385-402 (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, J. Song, M. Hosaka and Y. Huang: "Controlled Markov Set-Chains with Discounting"J. Appl. Prob.. Vol.35. 293-302 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Y. Kadota, M. Kurano and M. Yoshida: "On the General Utility of Discounted Markov Decision Processes"Inter. Trans. in Oper. Res. Vol.5, No.1. 27-34 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Seiichi Iwamoto: "On Expected Values of Markov Statistics"Bull. Infor. Cyber. Res. Ass. Stat. Sci., Kyushu University. Vol.30, No.1. 1-24 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Seiichi Iwamoto and Moshe Sniedovich: "Sequential Decision Making in Fuzzy Environment"J. Math. Anal. Appl. Vol.222, No.1. 208-224 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Seiichi Iwamoto: "Decision-making in Fuzzy Environment : A Survey from Stochastic Decision Process"Proceedings of the 2nd International Conference on Knowledge-based Intelligent Electronics Systems (KES '98). Vol.3. 542-546 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Yuji Yoshida, Masami Yasuda, Jun-ichi Nakagami and Masami Kurano: "Fuzzy Stopping of a Dynamic Fuzzy System"Proceedings of the 2nd International Conference on Knowledge-based Intelligent Electronics Systems (KES '98). Vol.3. 547-552 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Yuji Yoshida: "Optimal Stopping of a Continuous-Time Dynamic Fuzzy System under Possibility Theory"Proceedings of the 2nd International Conference on Knowledge-based Intelligent Electronics Systems (KES '98). Vol.3. 553-558 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Yuji Yoshida: "Fuzzy Stopping of a Dynamic Fuzzy System"Proceedings of the 6th European Congress on Intelligent Techniques and Soft Computing (EUFIT '98). Vol.1. 150-153 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Yuji Yoshida: "On Fuzzy Stopping of Fuzzy Random Sequences"Proceedings of the 5th International Conference on Soft computing (IIZUKA '98). Vol.1. 507-510 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Masami Kurano, Masami Yasuda, Jun-ichi Nakagami and Yuji Yoshida: "A Fuzzy Relational Equation in Dynamic Fuzzy Systems"Fuzzy Sets and Systems. VOL.101, No.3. 439-443 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Yuji Yoshida: "A Minimax Theorem for Zero-Sum Stopping Games in Dynamic Fuzzy Systems"Mathematical and Computer Modelling. Vil.29, No.11-12. 19-33 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Masami Kurano, Masami Yasuda, Jun-ichi Nakagami and Yuji Yoshida: "The Time Average Reward for Some Dynamic Fuzzy Systems"Computer & 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] Yuji Yoshida: "Superharmonic Fuzzy Sets on Recurrent Sets in Dynamic Fuzzy Systems"Computer & Mathematics with Applications. ol.37, No.11-12. 87-93 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Yuji Yoshida, Masami Yasuda, Jun-ichi Nakagami and Masami Kurano: "A Monotone Fuzzy stopping Time for Dynamic Fuzzy Systems"Bull. Infor. Cyber. Res. Ass. Stat. Sci., Kyushu University. 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] Masami Kurano, Masami Yasuda, Jun-ichi Nakagami and Yuji Yoshida: "Fuzzy Decision Processes with an Average Reward Criterion"Mathematical and Computer Modelling. Vol.31. 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. Hosaka and M. Kurano: "Non-Discounted Optimal Policies in Controlled Markov Set-Chains"J. of Oper. Research Society of Japan. Vol.42-3. 256-267 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Seiichi Iwamoto: "Conditional Decision Processes with Recursive Function"J. Math. Anal. Appl. Vol.230, No.1. 193-210 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] S. Iwamoto, K. Tsurusaki and T. Fujita: "Conditional Decision-Making in a Fuzzy Environment"J. Operations Res. Soc. Japan. Vol.42, No.2. 198-218 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] S. Iwamoto and T. Ueno: "Inverse Partition Problems"Bull. Infor. Cyber. Res. Ass. Stat. Sci., Kyushu University. Vol.31, No.1. 67-90 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Yuji Yoshida: "Stopping Game of a Sequence with Randomness and Fuzziness"Proceedings of the 8th World Congress of International Fuzzy System Association (IFSA '99). Vol.1. 326-366 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Masami Kurano, Masami Yasuda and Jun-ichi Nakagami: "Interval Methods for Uncertain Markov Decision Processes"Proceedings of the International Workshop on Markov Processes and Controlled Markov Chains, Changsha, Husam, China. 22-28 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Yuji Yoshida: "A Stopping Game in a Stochastic and Fuzzy Environment"Mathematical and Computer Modelling. Vol.30. 147-158 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Yuji Yoshida: "A Limit Theorem in Dynamic Fuzzy systems with transitive Fuzzy Relations"Fuzzy Sets and Systems. Vol.109, No.3. 371-378 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Yuji Yoshida: "A Continuous-Time Dynamic Fuzzy System.(I). A Limit Theorem"Fuzzy Sets and Systems. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Yuji Yoshida: "A Continuous-Time Dynamic Fuzzy System.(II). Fuzzy Potentials"Fuzzy Sets and Systems. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] H. Kamimura and M. Kurano: "Clustering by a Fuzzy Metric"Fuzzy Sets and Systems. (to appear).

    • 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 and Y. Huang: "Constrained Markov Decision Processes with Compact State and Action Spaces : The Average Case"Optimization. to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Masami Kurano, Masami Yasuda, Jun-ichi Nakagami and Yuji Yoshida: "Ordering of Convex Fuzzy Sets - A Brief Survey and New Results"J. Operations Research Soc. Japan. to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Masami Kurano, Masami Yasuda and Jun-ichi Nakagami: "A Fuzzy Treatment of Uncertain Markov Decision Processes"Proceeding s of the International Conference on Applied Stochastic System Modeling (ASSM '2000), Kyoto. to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Yuji Yoshida, Masami Yasuda, Jun-ichi Nakagami and Masami Kurano: "A Multi-Objective Optimal Stopping Problem in a Stochastic and Fuzzy Environment"Proceeding s of the International Conference on Applied Stochastic System Modeling (ASSM '2000), Kyoto. to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] 蔵野 正美(共著): "A Fuzzy Relational Equation in Dynamics Fuzzy Systems"Fuzzy Sets and Systems. Vol.101.No3. 439-443 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] 吉田 祐治: "A Minimax Theorem for Zero-Sum Stopping Games in Dynamics Fuzzy Systems"Mathematical and Computer Modelling. Vol.29 No.1. 19-33 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] 蔵野 正美(共著): "The Time Average Reward for Some Dynamics Fuzzy Systems"Computers & Mathematics with Applications. Vol.37 No.11-12. 77-86 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] 吉田 祐治: "Superharmonic Fuzzy Sets on Recurrent Sets in Dynamic Fuzzy Systems"Computers & Mathematics with Applications. Vol.37 No.11-12. 87-93 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] 岩本誠一: "Conditional Decision Processes with Recussive Function"J.Math.Anal.Appl.. Vol.230 No.1. 193-210 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] 吉田 祐治: "A Limit Theorem in Dynamic Fuzzy Systems with Transitive Fuzzy Relations"Fuzzy Sets and Systems. Vol.109 No.3. 371-378 (2000)

    • Related Report
      1999 Annual Research Report
  • [Publications] 吉田祐治(共著): "A Limit Theorem in Dynamic Fuzzy Systems with a Monotone Property" Fuzzy Sets and Systems,. Vol.94,No.1. 109-119 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] 吉田祐治: "Duality in Dynamic Fuzzy Systems," Fuzzy Sets and Systems. Vol.95,No.1. 53-55 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] 吉田祐治: "Cyclic classes and an Ergodic Theorem in Dynamic Fuzzy Systems" Fuzzy Sets and Systems. Vol.95,No.2. 189-199 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] 吉田祐治: "The Recurrence of Dynamic Fuzzy Systems" Fuzzy Sets and Systems. Vol.95,No.3. 319-332 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] 吉田祐治: "A Time-Average Fuzzy Reward Criterion in Fuzzy Decision Processes" Information Sciences. Vol.110,No.1-2. 103-112 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] 岩本誠一(共著): "Sequential decision making in fuzzy environment," J.Math.Analy.Appl.Vol.221,No.1. 208-222 (1998)

    • Related Report
      1998 Annual Research Report

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

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