Analysis of fuzzy-valued stopping problem

模糊值停止问题分析

• 批准号: 10640104
• 负责人: NAKAGAMI Jun-ichi
• 金额: $ 0.7万
• 依托单位: Chiba University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 1998
• 资助国家: 日本
• 起止时间: 1998 至 1999
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-10640104/
• 关键词: multi-stage decision process; fuzzy transition; fuzzy relation; optimal stopping problem; fuzzy optimization; order of fuzzy numbers; fuzzy stopping rule

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

马尔可夫决策过程的模糊处理是千叶大学数学规划研究小组自1991年以来的主要研究课题，其成员为Masami Kurano、Masami Yasuda、Jun-ichi Nakagami和Yuji Yoshida。该研究项目获得资助。科学研究援助 《模糊值停止问题分析》广泛适用于现实生活中的许多实际问题，将成为顺序决策理论研究的一项基本技术。 为期两年在我们的项目中，我们的重点是分析模糊（最优）停止问题的基本结构，并对 n 维模糊数集引入新的定义。参考文献中给出的主要结果总结如下：（ 1）在模糊关系的单调性质下考虑动态模糊系统，我们研究模糊集序列的极限，并得到收敛定理，该极限被表征为模糊关系的解。 (2) 对于动态模糊系统，其基本方法是分析其模糊状态的递推关系。 相似之处在于贝尔曼方程是动态规划中的一个重要工具。 (3)我们考虑资产出售问题的博弈变体，将实际情况表述为两人非合作博弈的停止问题，并证明均衡的存在定理。 (4) 为动态模糊系统引入了一类新的模糊停止时间，称为单调模糊停止时间，因为模糊停止时间是通过模糊集的α-割构造的，因此可以显式推导。 (5)对于模糊最大阶的主题，我们将其扩展视为一类模糊集上的伪阶等于】1）。这个阶是用非空闭凸锥展开的，并通过投影到它的对偶锥上来表征。特别是，格子的结构可以用矩形模糊集的类来表示。表达我们对科学研究补助金对我们研究项目的赞赏。

项目成果

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)

M. Kurano、M. Yasuda、J. Nakagami、Y. Yoshida：“某些动态模糊系统的时间平均奖励”An International J. Computers

J.Nakagami: "A two-person noncooperative game for assets selling problem : Independent..."International J. of Comp. & Math. with Applications. 37. 207-212 (1999)

J.Nakagami：“资产出售问题的两人非合作博弈：独立......”International J. of Comp.

Y.Yoshida他3名: "A monotone fuzzy stopping time in dynamic fuzzy systems"Bulletin of Informatics and Cybernetics. 31. 91-99 (1999)

Y. Yoshida 和其他 3 人：“动态模糊系统中的单调模糊停止时间”信息学和控制论通报 31. 91-99 (1999)。

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)

M. Kurano 和其他 3 人：“某些动态模糊系统的时间平均奖励”International J. of Comp & Math. 37. 77-86 (1999)

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)

M.Kurano 和其他 3 人：“某些动态模糊系统的时间平均奖励”International J. of Comp & Math. 37. 77-86 (1999)