時間數列的模式識別在近年來逐漸受到注意。因為根據時間數列所產生的走勢型態可以作為判斷事件發生與預測未來的基礎。雙線性模式是由ARMA模式所延伸，所以不易與ARMA做一區別。本文就針對這類的問題，提出解決的方法。 在本文中，我們應用統計檢定結合模糊理論，建構一個整合式的識別過程。由特徵擷取，找出各種模式之間的差異，再藉由其中的異同建立模糊規則庫。接下來計算出時間數列相對應的特徵屬性，最後由模糊規則庫做出判斷。我們以台積電與聯電的每日收盤價格與成交張數為例，識別的結果與一般的認知相同。 / Identification of time series model gets more and more attention, because we can analyze the events happened and forecast what will occur in the future based on the accurate model. Bilinear time is extended by ARMA model, so it is hard to distinguish bilinear model and ARMA model. This paper focuses on this type of subject and proposes some possible way to solve. In this paper, we combine statistical tests and fuzzy methods to build a "composite" identification process. First, we try to find out differences between each model by featuring and building the fuzzy rule bases by the differences. Then, we calculate the membership of feature according the time series data. Finally, we make our decision according to the fuzzy rule bases.

群體運動在現今的電玩、動畫或電影中，有十分重要的應用；透過群體性的運動，可以表現出故事背景設定的張力。在群體運動的模擬中，除了個體本身的運動行為模擬外，重要的是如何呈現出群體運動的整體效果。過去文獻中多數的群體運動模擬系統，要能在群體運動中呈現出特定形狀的效果，多需花費大量的時間反覆調整個體的模擬結果；個體本身的運動行為模型，則多採用虛擬力場的方式，被動的影響個體的運動，較缺乏直觀設定行為模型的方式。本論文的目標是建立一套人群模擬系統，此系統包括兩個部份：第一個部份是使用者可根據個人偏好設定群體運動理想中的外觀形狀，使此系統在模擬前能根據所輸入的環境資訊，利用運動計畫的方式，自動產生形體形變的路徑，以做為維持群體外形的參考目標。第二部份則是改進人群模擬時個體與群體的行為模型。我們利用模糊數學的特性，來表示行為模型以語意表達時的不確定性，使個體的行為能表現出貼近使用者所需求的結果。我們提出了三種類型的模糊行為模型與對應的原生動作，用以表現個體與群體的運動行為。根據我們實做出來的系統及實驗顯示，透過這樣的系統，我們可以利用程序化的方式為電腦動畫師產生具有特定群體外觀的群體模擬，減少其在製作相關動畫所需要的時間與技術成本，同時也提供了直觀的方式建立人群的行為模型，增加行為的豐富性。 / The effects of crowd behavior are becoming indispensable in computer games and computer animation. In crowd simulation, beside the issue of simulating the motion for individual agents, the more important one is how to simulate a specific behavior of a crowd based on the motion of individuals. In order for a crowd to conform to a specific shape, most simulation systems reported in the literature require the users to spend a great amount of time in tuning the behavior parameters of each individual, governed by virtual forces computed according to inter-agent relations. In this thesis, we aim to build a system of crowd simulation consisting two parts: a path planner for a flexible shape and a motion controller with fuzzy logic. The path planner can search for a feasible path for a region of flexible shape allowing the user to set his preference on the shape of the crowd. The local motion controller for each agent is based on fuzzy logic rules that can be used to present the uncertainty of linguistic behavior models. We have proposed three types of fuzzy behavior models and their corresponding primitive actions. Our experiments show that, with this simulation system, we allow a computer animator to use an intuitive way to create specific appearance and richer.

投資的獲利多寡並不單單基於預測的準確性，信心度的大小亦攸關獲利的結果。因為信心度愈大，則投資人將會提高投資的金額，而獲得更多的利潤。反之，雖然預測的結果是準確的，但若信心度很小，則投資人將不敢投入較多的金額，如此一來所獲得的利潤就有限了。本文嘗試著應用信心度函數來輔助說明多變量模糊時間數列預測結果，亦即預測模式對預測結果的屬性所具有的信心程度。最後利用多變量模糊時間數列模式，結合加權股價指數的收盤價及成交量兩個變量，針對台灣加權股價指數進行預測及衡量預測屬性的信心度。相信這對於風險控管及提高投資報酬深具意義。

本文嘗試以模糊理論的觀念，應用到時間數列分析上。研究重點包括模糊關係、模糊規則庫和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。接著提出模糊規則庫的定義，以及模式建構的流程，並以模糊關係方程式的推導，提出模糊時間數列模式建構方法。最後，利用提出的方法，對台灣地區加權股票指數建立模糊時間數列模式，並對未來進行預測，且考慮以平均預測準確度來做預測效果之比較。這對於財務金融的未來走勢分析將深具意義。 / The paper has attempted to apply the concept of fuzzy method on the analysis of time series. This reserch is also to include fuzzy relation, fuzzy rule base, fuzzy time series model constructed and forecasting. First, we'll define the concept of fuzzy time series model and some important properties. Next, the definition of fuzzy rule base will also be put forward, along with procedure of model constructed, the formation of fuzzy relation polynomial, and the methods to construct fuzzy time series model. At last, with the above methods, we'll build up fuzzy time series model on Taiwan Weighted Index and predict future trend while examine the predictive results with average forecasting accuracy. This shall carry profund signifigornce on the analysis of future trend in terms of financialism.

近年來，隨著科技的進步與工商業的發展，預測技術的創新與改進愈來愈受到重視，同樣地，對於預測準確度的要求也愈來愈高。尤其在經濟建設、人口政策、經營規畫、管理控制等問題上，預測更是決策過程中不可或缺的重要資訊。有鑑於此，本論文嘗試應用模糊關係方程式，提出多變量模糊時間數列建構過程及轉折區間檢測模式理論架構。另一方面，多變量模糊時間數列模式建構過程，研究者曾提出很多轉折點之偵測與檢定方法，然而在實際的例子中，時間數列之結構改變所呈現出來的是一種緩慢的改變過程，即轉折點本身就是模糊不確定。這個概念在建構不同模式分析各國經濟活動數據時更顯重要。本論文針對轉折區間之檢測提出一個完整的認定程序。多變量時間數列系統中的隸屬度函數等於在計算成果指標群時的群集中心。應用本論文提出的方法，我們以德國、法國及希臘之總體經濟指標GDP為例，考慮通貨膨脹率、GDP成長率及投資率來進行轉折區間的檢測。 / In recent years, along with the technological advancement and commercial development, the creation and improvement of forecasting techniques have more and more attention. Especially at the economic developments, population policy, management planning and control, forecasting gives necessary and important information in the decision-making process. Regarding stock market as the example, these numerals of closing price are uncertain and indistinct. Again, the factors of influence on quantity are numerous, such as turnover, exchange rate etc. Therefore, if we consider merely the closing price of front day to build and forecast, we will not only misestimate the future trend, but also will cause unnecessary damage. Owing to this reason, we propose the procedure of multivariate fuzzy time series model constructed and theory structure by fuzzy relation equation. Combining closing price with turnover, we apply our methods to build up multivariate fuzzy time series model on Taiwan Weighted Index and predict future trend while examine the predictive results with average forecasting accuracy. A fuzzy time series is defined on averages of cumulative fuzzy entropies of the tree time series. Finally, an empirical study about change periods identification for Germany, France and Greece major macroeconomic indicators are demonstrated.