轉折型時間序列在現實生活中常常可見，例如因戰爭、政策改變、罷工或自然界的條件劇變等，而使時間序列的走勢發生明顯的轉變。傳統上，對這種轉折型時間序列資料進行轉折點的偵測時，大部分均從事後的觀點，主觀上先行認定結構轉變發生的時點，而後再以檢定加以確認。但此種方法過於主觀，而且轉型並非一蹴可幾，若以單一的轉折點來解釋轉型的現象，似乎不太恰當。 　　有鑑於此，本文利用模糊轉折區間統計認定法，以事前的觀點，對具有平均數或變異數改變的轉折型時間序列進行轉折區間的認定。並以匯率及貿易餘額的實際例子，利用我們所提出的方法進行單變數及雙變數的模糊分類，進而求出個別及聯合的轉折區間。 / Structure-changing time series are often seen in daily life. For example, war, change of policy, labor strike, or change of natural phenomena result in obvious change of time series. Most of detection of change points for structure-changing time series take place afterwards. In this paper, we pre-sent a change periods detection method for trend time series using the concept of fuzzy logic. Empirical example about exchange rate and balance of international trade is illustrated with detailed analysis.

模糊理論開始於 1960 年代中期,關於這方面的研究與發展均已獲得相當不錯的成果.其中尤以在群落分析應用上的專題研究更是廣泛.Bezdek 提出的模糊分類演算法,乃根據 Dunn 的C平均法所作的一改良方法.但仍有其缺點,例如,未考慮權重且以靜態資料為主. 有鑑於此,本研究對 Bezdek 之方法加以改進推廣,提出加權模糊分類法.對於評價因素為多變量時,應加入模糊權重的考量.此外更結合時間因素,使準則函數成為動態的模式,將傳統的模糊分類法由靜態資料轉為動態資料形式,以反映真實 的情況. / Research on the theory of fuzzy sets has been growing steadily since itsinception during the mid-1960s. The literature especially dealing with fuzzycluster analysis is quite extensive. But the research on FCM still has somedisadvantages. For instance, the

對於一個具有結構性改變性質的非線性時間數列，通常很難判斷何處為轉 捩點，或者何處為所謂的轉型期。雖然長久以來已有不少偵查轉捩點的方 法被提出，但是對於轉捩區間以及對於一些語言性的時間數列資料問題（ 例如：景氣指標的紅綠燈時間數列），都很少被提出來。本論文中，我們 首先引用Zadeh於1965年提出來的模糊理論的觀念來介紹糢糊時間數列（ FTS）。進而定義出在□水準下的模糊點（FP）和模糊轉捩區間（FCP）， 並且證明了一些有用的性質。最後再以台灣地區出生率資料為例，說明□ 水準的模糊轉捩區間的判定方法，並列出了詳細的執行步驟。實驗結果更 證明出我們的模糊檢驗法非常具有實用性及有效性。 / As far as structural change of a non-linear time series is concerned, it is hard to tell when the change point or the fuzzy change period occurs. Though many methods are used for the task of detecting, most of them primarily deal with the case of change point, and few examine the problem of fuzzy change period and linguistic time series ( for example, the index of prosperity represented by red or green light ). In this article, we adopt the theory of fuzzy which is proposed by Zedeh ( 1965 ) to introduce the concept of fuzzy time series ( FTS ). Furthermore, we define the □level of fuzzy point (FP) as well as fuzzy change period (FCP), and prove some useful properties. Finally we explain the method we proposed in detecting the □level of fuzzy change period in terms of the data of Taiwan birth rate and provide step-by-step procedures. Experimental results show that the proposed method of fuzzy detecting is available and practical in detecting the □level of fuzzy change period.