STUDIES OF FUZZY DECISION PROCESSES AND THEIR APPLICATIONS

本研究的目的是分析动态模糊系统的数学结构及其在决策中的应用。主要结果如下：(1)研究了模糊关系单调/传递时动态模糊系统中模糊状态序列的极限定理；(2)刻画了模糊关系方程的解空间；(3)分析了动态模糊系统的常返性和循环行为；(4)通过引入模糊报酬，研究了动态模糊系统的最优停止问题，并用模糊关系方程的唯一解刻画了最优报酬。利用模糊目标诱导出的模糊期望来估计模糊报酬，并给出了最优停止次数。(V)在具有模糊报酬的动态模糊系统中的二人零和停止对策中，证明了一个极小极大定理，给出了最优停止点和对策的值。(Vi)讨论了一个停止问题的动态模糊系统的对偶问题，并用递归集刻画了它的解。(Vii)从动态模糊系统和模糊动态规划的角度讨论了时间平均报酬准则下的模糊决策过程。时间平均奖励的特征是引入一个相对价值函数，作为相关方程的唯一解。这些结果发表在国际期刊《模糊集与系统》、《信息科学》、《计算机与应用数学》、《数学与计算机建模》、《数学杂志》上。阿纳利。APPL诸若此类。我们还在KES‘98、EUFIT’98、Iizuka‘98、IFSA’99等国际会议和研讨会上介绍了一些结果。在这项研究中，我们分析了动态模糊系统的数学结构，并得到了它在决策中的应用。

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.