時間序列預測在各種預測問題中扮演著重要的角色，然傳統的統計時間序列預測模式無法處理語意不清與不完全的資料。Song and Chissom於1993年提出了模糊時間序列預測架構，其運用模糊邏輯推理有效地處理模糊及不確定環境下的語意資料。此架構主要有七個步驟，許多後續的研究皆依此架構提出各種改良的預測模式。然目前文獻中的各種高階預測模式尚不能適當地選擇預測模式的階數及無法有效地控制資料中的不確定性，且預測準確度與區間長度也無法達到一致性。本研究擬針對以上階數問題、不確定性、及一致性等相關議題提出改善之法，以有效解決這些限制且能提升預測的準確度，進而擴展為多因子模式，以符合實務上的需求，接著以FCM探討不同區間分割法對預測準確度的影響。
首先，本研究藉由確定狀態(certain state)的定義以及回溯演算法的設計，提出了一新的預測模式，除了能有效地降低預測的不確定性、分割論域及滿足預測準確度與區間長度一致的性質；並推演出一項重要的定理，即由此模式所建立的確定狀態集合中，可以得到模糊關係群組的最大階數，即部份序列的最大長度。實驗結果驗證了此模式能提升預測的準確度、穩定性及可靠性；另一方面，在實務問題上，影響預測的因子往往多而複雜，因此，本研究將根據所提出的預測模式擴展至多因子模式，使其更能符合實際需求，並藉由不需建立所有模糊關係群組的方法以降低計算複雜度。
本研究接著擬以不同的論域分割法探討分割法對預測模式的影響，在本文中提出FCM-based多因子決定性預測模式，以模糊c均值聚群法(Fuzzy c-means, FCM)為論域分割法，分割出不等長度的區間，並與等長區間分割法、基因演算法及k均值聚群法(k-means)進行比較。因為以FCM分割論域會因初始值的不同而得到不同的區間，所以本研究以Monte Carlo模擬實驗結果，並以箱型圖說明FCM對預測結果的影響及預測資料的分佈情形。此外，在文獻中，大部份的模糊時間序列預測模式的績效評估皆忽略了概化(generalization)的重要議題，而以同一樣本集(in-sample)進行訓練及預測，本研究也將以多因子決定性預測模式及FCM-based多因子決定性預測模式探討此重要議題。最後本研究將和文獻中已提出的各項預測模式進行深入且完整的效能與效率之比較，以驗證所提出的模式之效能。

The forecasting problem of time series plays an important role in various contexts. The tradition statistical paradigm of time series analysis cannot handle the vagueness and incompleteness in data. In 1993, Song and Chissom incorporated fuzzy logic to tackle these problems and proposed a new paradigm of forecasting time series, fuzzy time series, which is capable of dealing with vague and incomplete data represented as linguistic values under uncertain circumstances. This model and related modifications are based on the seven major steps they introduced. Many subsequent researches follow this framework and propose various enhanced forecast models. However, the issues of choosing order, controlling uncertainty in forecasting and consistently achieving forecasting accuracy with different interval lengths remain unsolved; there is still no work in the literature in the fuzzy time series to carry on the discussion to the issues. In this study, we will focus on the aforementioned issues and will attempt to propose novel models to tackle them.
First, we propose a novel effective forecasting model to tackle with the issues of controlling uncertainty in forecasting, effectively partitioning intervals, and consistently achieving forecasting accuracy with different interval lengths. In addition, an important parameter, the maximum length of subsequence in a fuzzy time series resulting in a certain state, is deterministically quantified. Experimental results demonstrate that the proposed forecasting model outperforms the existing models in terms of accuracy, robustness, and reliability. Moreover, the forecasting model adheres to the consistency principle that a shorter interval length leads to more accurate results. Next, we plan to extend our previous work to handle the multi-factor forecasting problem since, in real-world cases, one event may be caused by more than one factors. We intend to reduce the computation complexity without deriving all fuzzy logical relationships in advance.
In addition, this model applies fuzzy c-means (FCM) clustering to deal with interval partitioning, which takes the nature of data points into account and produces unequal-sized intervals. Furthermore, in order to cope with the randomness of initially assigned membership degrees of FCM clustering, Monte Carlo simulations are used to justify the reliability of the proposed model. The superior accuracy of the proposed model is demonstrated by experiments comparing it to other existing models using real world empirical data. Moreover, all forecasting models of fuzzy time series proposed in the literature fail to account for the generalization performance of the forecasting model; they only deal with in-sample data forecasting. This important issue will be handled in this study by the multifactor and FCM-based models. Comprehensive experiments will be conducted to justify the effectiveness and efficiency of the proposed forecasting model.

摘要 I
Abstract III
致謝 V
目錄 VI
圖目錄 VIII
表目錄 IX
第一章 緒論 1
1.1 研究背景 2
1.2 研究動機 5
1.3 研究目的 6
1.4 研究架構 7
第二章 文獻探討 10
2.1 定義語彙論域及分割論域 10
2.2 模糊時間序列 12
2.3 預測模式 16
2.3.1 模糊關係 18
2.3.2 時變性模糊時間序列預測模式 21
2.3.3 非時變性模糊時間序列預測模式 24
2.4 小結 31
第三章 研究方法 33
3.1 單因子決定性預測模式 33
3.2 多因子決定性預測模式 46
3.3 FCM-based多因子決定性預測模式 52
3.4 小結 55
第四章 實驗分析與結果 56
4.1 單因子決定性預測模式 56
4.2 多因子決定性預測模式 63
4.3 FCM-based多因子決定性預測模式 75
4.4 小結 85
第五章 結論與未來研究方向 86
5.1 結論 86
5.2 研究限制 88
5.3 未來研究方向 89
參考文獻 91

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