模糊集合論是由L. A. Zadeh教授在1965年首先提出，到目前為止，模糊集合論已被應用到許多領域上，如決策分析(Decision Analysis)、系統理論(System Theory)、人工智慧(Artificial Intelligence)、經濟學(Economics)及控制理論(Control Theory)等，不過，直到1993年，才由Song及Chissom提出模糊時間序列方法來提供新的方法以因應一些特殊的動態過程。
本篇論文提出兩種方法去分別預測長期趨勢及季節變動時間序列問題，修改的模糊時間序列方法使用Song及Chissom的一階時間獨立模型來預測歷史資料是語意值的問題，我們使用阿拉巴馬大學的升學人數例子來說明我們的預測過程，這個方法可以獲得較佳的平均誤差；而使用模糊迴歸觀念的方法則解決了模糊時間序列方法無法解決季節性時間序列問題的缺點，這個方法也提供決策者彈性地在不同信心水準下選擇不一樣的預測區間。

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Fuzzy Sets Theory was introduced by L. A. Zadeh in 1965. Up to now, fuzzy sets have been applied to many fields such as Decision Analysis, System Theory, Artificial Intelligence, Economics and Control Theory. However, until 1993, Q. Song and B.S Chissom proposed a fuzzy time series method which provides an alternative approach for some special dynamic process.
This paper presents two methods to forecast secular trend and seasonal variation time series problems respectively. The revised fuzzy time series method uses Song and Chissom’s first-order time-invariant model to predict such linguistic historical data problems and we illustrate the forecasting process by the enrollments of the University of Alabama. This method obtains a better average error than the error in Song and Chissom’s method. The method using fuzzy regression theory solves the shortcoming that fuzzy time series method could not work in dealing with seasonal variation time series problems. Under different confidence level the resultant forecasting interval would provide more flexibility for a decision maker in making decisions.

ABSTRACT ii

ACKNOWLEDGEMENTS iii

CONTENTS iv

TABLE CAPTIONS iv

FIGURE CAPTIONS iv

LIST OF NOTATIONS iv

Chapter 1 INTRODUCTION 1

Chapter 2 LITERATURE REVIEW 3

2.1 Fuzzy Time Series 3

2.2 Fuzzy Regression 8

2.3 Conclusions 11

Chapter 3 A FUZZY TIME SERIES MODEL FOR SECULAR DATA 12

3.1 S&C Fuzzy Time Series Method 13

3.2 A Revised Fuzzy Time Series Method 20

3.3 Evaluation and Discussion 25

Chapter 4 FUZZY REGRESSION METHOD FOR SEASONAL TREND 30

4.1 Fuzzy Regression Model 31

4.2 Conclusion and Discussion 36

Chapter 5 SUMMARY AND CONCLUSION 38

REFERENCE 40

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