臺灣博碩士論文加值系統

人類社會中存在許多不確定性的問題，如經濟成長率、財務危機的預測等，自從Song 與Chissom 兩位學者在1993 年提出所謂的模糊時間序列(Fuzzy Time Series)的觀念後，許多學者先後提出不同的模式來處理這些問題，然而先前的研究通常未考慮相關變數選取以及在模糊化過程中僅依據主觀意見進行模糊語意的離散化，因此不能夠客觀地反應資料集的特性，此外在進行預測時往往將模糊規則視為同等重要，未能考慮每一條模糊規則的重要性。基於上述原因，本研究透過自組織映射圖網路(Self-Organizing Map, SOM)進行變數選取(Factor Selection)並提出多變量高階加權模糊時間序列模式基於模糊神經網路(Fuzzy-BPN)，且採用循序加權平均運算子(Ordered Weighted Averaging operator, OWA)進行加權預測。因此，為了驗證提出的方法，採用台灣證券交易所(Taiwan Stock Exchange Corporation)提供的台灣股價加權指數(Taiwan Stock Exchange Capitalization Weighted Stock Index, TAIEX)為實驗預測目標，以此篩選適當相關變數，在實驗最後納入近年其他的研究模式與本研究一併比較，結果顯示本研究之預測能力有進一步的改善。

There are many uncertainty problems in the Human society, such as the forecasting of economic growth rate, financial crisis, etc. Since Song and Chissom proposed the concept of fuzzy time series in 1993, many scholars have proposed different models to deal with these problems. However, previous studies usually do not consider the factor selection and transfer original data to the fuzzy linguistic value by the subjective opinions in fuzzy process, which cannot objectively show the characteristics of the data. In addition, the fuzzy rules usually assign equal weight in the forecasting process, and it failed to consider the importance of each fuzzy rule. Based on above concepts, this study adopt the self-organizing map network (SOM) for the purpose of factor selection and proposed a multivariate high-order weighted fuzzy time series model based on fuzzy neural network (Fuzzy-BPN) and ordered weighted averaging operator (OWA) to make forecasts. In order to verify the proposed method, the Taiwan Stock Exchange Capitalization Weighted Stock Index (TAIEX) from the Taiwan Stock Exchange Corporation are used in the experiment and filter the appropriate factors, and the experiment results are compared with other methods in with this study. The forecasting performance shows that the proposed method has better forecasting ability.

目錄
第一章 緒論 1
1. 1 研究背景 1
1. 2 研究動機 2
1. 3 研究目的 4
1. 4 研究範圍與限制 5
1. 5 研究流程 6
第二章 文獻探討 7
2. 1 模糊集合論(Fuzzy Set Theory) 7
2.1.1 傳統集合與模糊集合 7
2.1.2 歸屬函數與基本運算 8
2.1.3 語意變數 12
2.1.4 模糊關係 13
2. 2 模糊時間序列(Fuzzy Time Series) 14
2. 3 模糊時間序列相關研究 16
2. 4 離散化方法 18
2.4.1 累積機率分配方法(CPDA) 19
2.4.2 最小化熵原理方法(MEPA) 21
2.4.3 均等之梯形模糊化方法(TFA) 23
2. 5 類神經網路(Artificial Neural Networks) 24
2.5.1 自組織映射圖網路(SOM) 25
2.5.2 倒傳遞類神經網路(Back-Propagation Neural Network ) 26
2.5.3 輸入數據預處理 27
2. 6 循序加權平均運算子(OWA) 28
第三章 新的模糊時間序列預測模式 30
3. 1 模糊時間序列模式基礎流程 30
3. 2 多變量高階加權模糊時間序列基於模糊神經網路 30
3. 3 不同離散化方法實驗與比較 36
3.3.1 修正後的累積機率分配方法(MCPDA) 37
3.3.2 修正後的最小化熵原理方法(MMEPA) 39
3. 4 本研究之模糊神經網路模式 41
第四章 實驗數據與分析 43
4. 1 資料來源與說明 43
4. 2 本研究模型驗證 48
4.2.1 變數選取過程與績效比較 48
4.2.2 不同離散化方法的績效比較 51
4.2.3 多變量高階加權模糊時間序列基於模糊神經網路驗證 57
4. 3 實驗結果與分析 69
第五章 結論與建議 78
5. 1 討論與結論 78
5. 2 未來研究方向與建議 80
參考文獻 82

圖目錄
圖2.1 離散型歸屬函數表示法 9
圖2.2 連續型歸屬函數表示法 10
圖2.3 三角形歸屬函數表示圖 11
圖2.4 梯形歸屬函數表示圖 11
圖2.5 五等尺度之語意變數表示圖 12
圖2.6自組織映射圖網路拓樸圖(SOM) 25
圖2.7 前饋式倒傳遞神經網路架構(BPN) 27
圖3.1 本研究模式之流程 31
圖3.2 高階模糊神經網路架構(Fuzzy-BPN) 41
圖3.3 多層並聯式模糊神經網路（MF-BPN） 42
圖4.1 TAIEX之收盤價歷史數據走勢圖[49] 46
圖4.2 Dow Jones之收盤價歷史數據走勢圖[48] 46
圖4.3 NASDAQ之收盤價歷史數據走勢圖[48] 47
圖4.4 S&P 500之收盤價歷史數據走勢圖[48] 47
圖4.5 TAIEX之收盤價訓練資料定義域U 52
圖4.6 各變數訓練集預測績效之RMSE 64
圖4.7 不同α值下之OWA運算子權重分佈 65
圖4.8 MF-BPN與OWA運算子整合架構示意圖 66
圖4.9 訓練集－MF-BPN在不同α下之訓練誤差(RMSE) 67
圖4.10 測試集－MF-BPN預測值與實際值之比較(OWA) 68
圖4.11 訓練集－不同α下之訓練誤差(2000~2003) 71
圖4.12 訓練集－不同α下之訓練誤差(2004 & 2009~2011) 72
圖4.13 直條圖：各年份實驗數據之訓練集標準差 76
圖4.14 直條圖：各年份實驗數據之測試集標準差 76
圖4.15 直條圖：與其他方法之預測績效比較 77

表目錄
表2.1 五等尺度之語意變數與三角模糊數對照表 13
表3.1 不同其數(k)之倍數遞減加權分配於模糊規則 34
表3.2 MCPDA方法之模糊語意三角歸屬函數說明 39
表4.1 相關變數代號與說明 44
表4.2 TAIEX、Dow Jones、NASDAQ與S&P之收盤價歷史數據 45
表4.3 第一次於不同族群數之分群結果 49
表4.4 第二次於不同族群數之分群結果 50
表4.5 採用SOM網路進行變數選取下之預測績效改變 51
表4.6 CPDA離散化方法之訓練集預測結果 53
表4.7 MEPA離散化方法之訓練集預測結果 53
表4.8 TFA離散化方法之訓練集預測結果 54
表4.9 MCPDA離散化方法之訓練集預測結果 54
表4.10 MMEPA離散化方法之訓練集預測結果 54
表4.11 2000年TAIEX之不同離散化方法績效比較 55
表4.12 2000~2002年TAIEX之不同離散化方法績效綜合比較 56
表4.13 歷史數據：TAIEX、Dow Jones與S&P 500之漲跌幅比例 58
表4.14 訓練資料：TAIEX採用MCPDA方法所建立之模糊語意值 58
表4.15 訓練資料：Dow Jones採用MCPDA方法所建立之模糊語意值 59
表4.16 訓練資料：S&P 500採用MCPDA方法所建立之模糊語意值 59
表4.17 訓練資料：TAIEX採用MCPDA方法之三階模糊關係式 60
表4.18 訓練資料：Dow Jones採用MCPDA方法之三階模糊關係式 60
表4.19 訓練資料：S&P 500採用MCPDA方法之三階模糊關係式 60
表4.20 Fuzzy-BPN之網路參數設定 61
表4.21 主要因子TAIEX之訓練集預測結果 62
表4.22 主要因子Dow Jones之訓練集預測結果 63
表4.23 主要因子S&P 500之訓練集預測結果 63
表4.24 不同α值下OWA運算子權重值 65
表4.25 訓練集：MF-BPN網路之訓練結果(RMSE) 70
表4.26 測試集：MF-BPN網路之預測績效(RMSE) 70
表4.27 測試集：MF-BPN網路之預測績效(MAPE) 73
表4.28 測試集：MF-BPN網路之預測績效(DA) 73
表4.29 2000~2004年MF-BPN與其他類神經網路方法之比較(RMSE) 73
表4.30 2000~2004年MF-BPN與其他非類神經網路之方法比較(RMSE) 74
表4.31 2009~2011年MF-BPN與其他方法之比較(RMSE) 75

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