Studies on Flexibly Structured Models of Decision Making

本课题的目标是应用综合集成的思想，建立具有更柔性和更软结构的决策过程的数学理论。为此，我们研究了多种柔性结构模型，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，其中对转移矩阵的感知由模糊集描述，我们成功地导出了一个模糊最优性关系来估计最优模糊报酬，从而使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通信问题，提出了一种奖惩型学习算法，并由此构造了自适应最优策略。并成功地进行了数值试验.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，并给出了最优停止时模糊感知报酬的计算方法。这些想法被应用到发展一个基于感知的理论，一个多变量停止问题的单调规则。此外，本文还在一定程度上成功地将分析结果应用于金融工程（美国看跌期权等）中。4.具有一般后悔效用函数的决策模型考虑了具有吸收集的可数状态半MDP的一般后悔效用情形的优化问题。我们成功地推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