Studies on Flexibly Structured Models of Decision Making

在这个项目中，我们的目标是应用合成和集成的思想，建立具有更灵活的砂软结构的决策过程的数学理论。为此，我们处理了各种柔性结构的模型。主要研究成果如下：1。基于感知信息的不确定马尔可夫决策过程(MDP)建立了MDP的模糊感知模型，其中转移矩阵的感知用模糊集来描述，我们成功地导出了模糊最优关系来估计最优模糊报酬，从而使得软计算算法成为可能。自适应马尔可夫决策模型针对多链MDP的通信情况，提出了一种奖罚型学习算法，并利用该算法构造了一种自适应最优策略。并成功地进行了数值实验。模糊停止模型及其在群决策过程中的应用建立了停止问题的感知模糊模型，得到了最优停止时模糊感知报酬的计算方法。这些思想被用来发展一个基于感知的理论来解决具有单调规则的多变量停车问题。并在一定程度上成功地将我们的分析结果应用于金融工程(美式看跌期权等)。4.用广义后悔效用函数建立决策模型考虑了具有吸收集的可数状态半MDP的广义后悔效用情形的最优化问题，成功地导出了确定最优后悔策略的最优性方程。这些结果已推广到多约束的情况

In this project, our objective is to establish the mathematical theory on decision making processes with more flexible sand soft structure, applying the ideas of symthesis and integration. To this end, we have dealt with various flexibly structured models.The main research results are as follows.1. Uncertain Markov decision processes (MDPs) with perception-based informationFormulating a fuzzy perceptive model for MDPs in which the perception for transition matrices is described by fuzzy sets, we have succeeds in deriving a fuzzy optimality relation to estimate the optimal fuzzy reward by which a soft computing algorithm becomes to be possible.2. Adaptive Markov decision modelsWe have developed a learning algorithm of the reward-penalty type for the communicating case of multichain MDPs by which an adaptively optimal policy is constructed. Also, a numerical experiment has been done successfully.3. Fuzzy stopping models and their applications to group decision processesThe perceptive fuzzy model for stopping problems has been formulated and the method of computing the fuzzy perceptive reward when stopped optimally has been obtained. These ideas are applied to develop a perception-based theory for a multivariate stopping problem with a monotone rule. Moreover, to some extent, it succeeds in applying our analytic results to finance engineering (American put option and so on).4.Decision making models with general regret utility functionsThe optimization problem of general regret utility case for countable sate semi-MDPs with an absorbing set is considered., We have succeeded in deriving the optimality equations which determine the optimal regret policy. These results has been extended to the case of multiple constraints