Focused on the technique , interaction and result of visualization , the system for transitional state visualization is put forward , which effectively promotes the transfer , analysis and synthesis course of transitional information with better visualizability , figurativeness and maneuverability . the main work of this dissertation is as follows : the main characteristics of transitional state , such as fuzziness , randomness , fractal and chaos , are concluded . based on the combination of the fuzzy mathematics , stochastic process , fractal and chaotic theory , the feature description model of transitional state is put forward to make itself the foundation of following visualization methods and applications 论文的主要工作包括：系统地提出了过渡状态的特征刻画模型，概括了过渡状态的模糊性、随机性以及分形性与混沌性等主要特性，结合模糊数学理论、随机过程理论以及分形理论与混沌理论等，以过渡率、过渡集合等作为特征刻画模型的主要内容，以过渡映射作为特征刻画的形成过程，有效地描述了过渡特征的渐变过程，为可视化方法与应用的具体实现奠定了理论基础。
