The automation of scientific discovery has been an active research topic for many years. The promise of a formalized approach to developing and testing scientific hypotheses has attracted researchers from the sciences, machine learning, and philosophy alike. Leveraging the concept of dynamical symmetries a new paradigm is proposed for the collection of scientific knowledge, and algorithms are presented for the development of EUGENE – an automated scientific discovery tool-set. These algorithms have direct applications in model validation, time series analysis, and system identification. Further, the EUGENE tool-set provides a novel metric of dynamical similarity that would allow a system to be clustered into its dynamical regimes. This dynamical distance is sensitive to the presence of chaos, effective order, and nonlinearity. I discuss the history and background of these algorithms, provide examples of their behavior, and present their use for exploring system dynamics. / Master of Science / Determining why a system exhibits a particular behavior can be a difficult task. Some turn to causal analysis to show what particular variables lead to what outcomes, but this can be time-consuming, requires precise knowledge of the system’s internals, and often abstracts poorly to salient behaviors. Others attempt to build models from the principles of the system, or try to learn models from observations of the system, but these models can miss important interactions between variables, and often have difficulty recreating high-level behaviors. To help scientists understand systems better, an algorithm has been developed that estimates how similar the causes of one system’s behaviors are to the causes of another. This similarity between two systems is called their ”dynamical distance” from each other, and can be used to validate models, detect anomalies in a system, and explore how complex systems work.

本文將模糊理論的觀念，應用到時間數列分析上。研究重點包括模糊自相似度的定義與度量，模糊自迴歸係數的分析，模糊相似度辨識與自迴歸階次認定、模糊時間數列模式建構與預測等。我們首先給定模糊時間數列模式的概念與一些重要性質。接著提出模糊相似度的定義與度量，以及模式建構的流程。經由系統性的模擬與分析，我們建立階次認定的演算法則與認定程序。藉著詳細的演算比較這些類型的模糊時間數列。並以模糊關係方程式推導，提出合適的模糊時間數列模式建構方法。並利用提出的方法對台灣的景氣對策信號，及台灣結婚率建立模糊時間數列模式。最後，使用所建構的模糊時間數列模式對未來進行預測，以驗證所建構模糊時間數列模式的效率性與實用性。 / In modeling a time series the accuracy of various model constructions and forecasting techniques, certain rules and models are adhered to. Traditional methods on the model construction for a time series are based on the researchers' experience by choosing a "good" model, which will satisfactorily explain its dynamic behavior, from a model-base. But a fundamental question that often arises is: does the data exhibit the real case honestly? In this research we show how fuzzy time series construction be applied for this purpose. An order detection process for fuzzy time series is presented. Simulation has been used extensively to explore general properties of statistical procedures, and the approach is particularly useful in fuzzy time series construction. Statistical strategies typically consist of sequences of rules used repeatedly on the same data set. This paper is organized as follows: In Chapter 2 we will discuss about the definition of fuzzy time series as well as certain important properties. In Chapter 3, We use the similarity comparison process to decide the order of a fuzzy time series. Simulations and analysis with the results about various types of autocorrelation are experienced in Chapter 4. Finally, we apply our methods to three empirical examples, Taiwan business cycle index, marriage rate and numbers of students enrollment in Chapter 5. Chapter 6 is the conclusion and the discussion of future researches.