動態資料往往隨著時間區間取法或測量工具的不同而有差異,此種不確定的特質我們稱為模糊性。但是傳統的時間數列仍是以確定的觀察值來記錄具有模糊性的動態資料。為了更完整的表示一個動態過程,我們考慮模糊時間數列(fuzzy time series)以具有不確定性的模糊集合來取代明確的數值,保持原來的模糊性。 本文探討模糊時間數列中模糊自我迴歸模式(fuzzy autoregressive model簡寫為 FAR 模式)的建構過程,並分別利用此模式來預測中央政府總預算和匯率。FAR 模式乃根據Box-Jenkins(1970)所提出的 ARMA 三階段模式建立的流程並推廣Zadeh(1965)所提出的模糊集合理論而來。在這過程中 ,我們考慮人類思維方法,使FAR 模式更具有彈性且適合未來預測時的需要。而對於所討論的動態過程,也不需要任何模式上的假設(例如:線性或穩定 ),因此 FAR 模式的適用範圍極為廣泛,更不會因為模式的誤判而導致預測時的嚴重錯誤。最後,我們將 FAR 模式的預測結果與傳統 ARMA 模式做比較。 文中關於模糊時間數列的一些性質,例如:模糊趨勢(fuzzy trend)和模糊穩定(fuzzy stationary),由於傳統文獻中沒有加以討論,本文亦提出定義和新的看法。 / Representations of dynamic data are always different as the time interval or measuring tool change. We call these characteristics of uncertainty fuzziness. But traditional time series use crisp observations to record a fuzzy dynamic process. To completely represent, we consider fuzzy time series replacing the crisp numbers with fuzzy sets and preserve original fuzziness. In this paper, the fuzzy autoregressive model (FAR model) of fuzzy time series is studied and used to forecast the Central government expenditure and exchange rates, respectively. The modeling process is according to Box- Jenkins' (1970) method of ARMA model and merged with the fuzzy set theory proposed by Zadeh (1965). Reasonable human judgements and ways of thinking are taken into consideration throughout the modeling process to make the FAR model more elastic and appropriate for forecasting. Unlike certain incorrectly identified models which lead to inaccurate forecasts, the FAR model can be widely applied due to its not having any assumptions on the original time series (e.g., linearity and stationarity). Finally, the performances of the FAR model to Central government expenditure and exchange rates are compared with that of the traditional ARMA model. Additionally, some properties about fuzzy time series, e.g., fuzzy trend and fuzzy stationary, have not been studied in the literature, and we propose definitions and new opinions.

近年來，由於人類對自然現象、社會現象或經濟現象的認知意識逐漸產生多元化的研判與詮釋，也因此致使人類思維數據化的概念已逐漸廣泛的被應用，對數據分析已從傳統以單一數值或平均值的分析作法，演變為考量多元化數值的分析作為。有鑑於此，在數據資料具備「模糊性」特質的現今，藉由模糊區間的演算方法，進一步探討之間的關係。 傳統的統計分析，對於兩變數間線性關係的強度判斷，一般是藉由皮爾森相關係數（Pearson’s Correlation Coefficient）的方法予以衡量，同時也可以經由係數的正、負符號判斷變數間的關係方向。然而，在現實生活中無論是環境資料或社會經濟資料等，均可能以模糊的資料型態被蒐集，如果當資料型態係屬於模糊性質時，將無法透過皮爾森相關係數的方法計算。 因此，本研究欲研擬一個較簡而易懂的方法，計算模糊區間資料的相關係數，據以呈現兩組模糊區間資料的相互影響程度。此外，若時間性之模糊區間資料被蒐集之際，我們亦提出利用中心點與長度之模糊自相關係數（ACF with the Fuzzy Data of Center and Length；簡稱CLACF）及模糊區間資料之自相關函數(ACF with Fuzzy Interval Data；簡稱FIACF)的方法，探討時間性模糊資料的自相關係數予以衡量。 / The classical Pearson’s correlation coefficient has been widely adopted in various fields of application. However, when the data are composed of fuzzy interval values, it is not feasible to use such a traditional approach to evaluate the correlation coefficient. In this study, we propose the specific calculation of fuzzy interval correlation coefficient with fuzzy interval data to measure the relationship between various stocks. In addition, in time series analysis, the auto-correlation function (ACF) can evaluate the effect of stationary for time series data. However, as the fuzzy interval data could be occurred, then the classical time series analysis will be not applied. In this paper, we proposed two approaches, ACF with the fuzzy data of center and length (CLACF) and ACF with fuzzy interval data (FIACF), to calculate the auto-correlation coefficient for fuzzy interval data, and use the scheme of Mote Carlo simulation to illustrate the effect of evaluation methods. Finally, we offer empirical study to indentify the performance of CLACF and FIACF which may measure the effect of lagged period of fuzzy interval data for daily price (low, high) of the Centralized Securities Trading Market and the result show that the effect of evaluation lagged period via CLACF and FIACF may response the effect more easily than classical evaluation of ACF for the close price of Centralized Securities Trading Market.

十二年國教及中小學教師評鑑即將上路，教學方向的調整與教師能力的提升在不久的將來將列為重要的教師績效指標之一。教師應如何轉型，及如何提升學生的上課狀況，都可透過教學問卷的回饋來作參考；教學問卷可直接且快速的反應學生想法並成為師生溝通的交流管道，使教師反省自我教學方式及技巧，進而改善；因此，在使用問卷時，若利用傳統的統計分析方式來研究結果，強迫學生採用二元邏輯的方式思考與解釋問卷結果，將可能會導致偏差或錯誤的結論。本論文應用模糊理論的概念，以模糊問卷為工具，利用模糊德菲法探討學生喜歡的數學老師類型，再提出新反模糊化值，並藉由模糊威克生等級和檢定及變異數檢定方法，分析學生滿意度是否會因性別、年紀、成績、背景而有所不同，最後討論學校老師及校外老師間的滿意度是否有差別。由實證例子分析結果顯示，我們提出的檢定方法，能有效分析模糊樣本的問題，進而期望能對教學問卷的分析和決策有所貢獻，並將此方法運用於其它模糊性議題之研究。 / The twelve-year compulsory education and the evaluation of the primary and secondary school teachers are brought into practice. The way teachers organizing their teaching strategies and improving their capability will be the key indicators of teachers’ performance review in the coming future. How will teachers fine-tune their instructional skill to attract students’ focus and then to boost students’ learning motivation and academic performance, is binding to the result of a practical Teaching Assessment System. The satisfaction questionnaires designed to students as teachers’ Teaching Assessment is a good evaluation tool to have student’s feedback on teachers’ performance. The questionnaires can quickly and directly reflect the thoughts of the students and serve as a communication channel between the teachers and the students, which can help teachers examine and ameliorate how and what they teach. The result could be used as reference for teachers to enhance the quality and effectiveness of teaching. In those varies of statistical methods used as analysis, if conventional statistical analysis is adapted to analyze the questionnaires and force the students to think and to explain through binary logic, it may result in deviations or erroneous consequences. Furthermore, it may drive to the exaggerated interpretation and detrimental decision. The study, based on Fuzzy Delphi Methods, aims to apply the concept of fuzzy theory and uses fuzzy questionnaires as a tool to analyze what kinds of mathematics teachers the students like. We propose the counter-fuzzy transformation, by using the Fuzzy Wilcoxon Rank-Sum Test and variance test to assay whether the students’ satisfaction differ owing to gender, age, grade, or their family background. Lastly, we will discuss whether the satisfaction is different between the school teachers and the teachers in other schools. The result demonstrates that assaying method, as using fuzzy statistics analysis, is a functional and competent way to analyze fuzzy sampling data through its aims and objectives. We believe it could sustain to support related analysis and decision making on Teaching Assessment, and also could be used to other fuzzy test study.

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.

在具有多變性、不確定性與訊息不完整的資訊網路時代，過去使用單一數值樣本來計算統計參數的方法，似乎已漸不符合現今多變與複雜的環境的需求。尤其在財金領域的資料採礦(data mining)研究中，利用模糊統計分析與軟計算方法，將會是一種更為接近實務需要的測度與估計工具。本研究提出模糊期望值的定義及一些相關性質，希望能配合隸屬度函數之觀念，將多元思維取代傳統二元邏輯的思考模式。並對複雜的財金問題，提出更符合人類社會行為及思考模式之實務探討。

傳統的迴歸是假設觀測值的不確定性來自於隨機，模糊迴歸則是假設不確定性來自多重隸屬現象。一般的模糊迴歸採用樣本模糊數 來對模糊迴歸參數進行估計，其中 為觀測模糊數， 依舊為實數值。我們認為 的假設不能真實地表達出樣本所蘊含的資訊，本研究將假設 也為模糊數，如此一來對樣本的解釋方式將更為貼近現實，且估計的過程則採用通用的最小平方估計，保留迴歸原始精神但是在模糊數上則有更深入的探究。迴歸常用來建構經濟和財務的模型，而此種模型經常帶有模糊的特質，例如景氣循環、不規則趨勢等。在本文中也會舉出例子來輔助說明此研究的實用性。 關鍵字：模糊迴歸參數區間估計、最小平方法、區間模糊數距離

在房地產生命週期中，建設公司扮演了土地取得、資金籌措、個案企畫、規劃興建、銷售與管理維護等角色，可說是房地產相關行業中最主要之關鍵；因此包括購屋者、股票購買者、公司管理階層、金融機構、證券管理機構等，皆必須以不同的角度來關切個別建設公司的經營績效，以供其行為決策的參考。 基於此，本研究第一部份先運用模糊理論衍生之模糊綜合評估法對上市建設公司的財務績效等相關指標進行各種綜合評估，並以劃分為「劣」、「普」、「良」、「優」四個級距的方式對公司進行評等。第二部份則搭配定性描述的產品績效予以交叉探討，以進一步了解不同類型建設公司的經營特質，共獲致以下結論。 在公司財務績效評等方面，相較於傳統簡單加權法，模糊綜合評估法因搭配權重的不同而在測試考驗上有較大落差；不過就評估結果而言，幾種評估權重的一致程度皆相當高，其中以同時考量到建築投資業產業特質（如高負債比率、低周轉率、經營規模成長快等）與員工生產力的評等模式穫得了最佳的測試成績。在該評估模式下，八十三年第四季至八十六年第三季各公司的評等結果分別為：「劣」等級包括宏福、宏總等兩家；「普」等級包括潤建、龍邦、長谷、緯城、仁翔等五家；「良」等級包括國揚、太設、太子、長億、寶祥、宏璟、皇普、昱成、春池等九家；「優」等級包括國建、寶建、冠德、華建、三采、尖美、宏盛、宏普、基泰等九家。 而在上市建設公司財務績效與產品績效交叉探討的部份：本研究從公司上市時間、成立時間、資本額，存貨內涵、政府認證等幾個角度做為產品績效的測試基準，有以下三點重要發現： 1.財務表現優良的上市建設公司亦有不錯的股價表現，至於財務表現不良的公司股價表現相對較差。 2.財務表現優良的公司平均上市時問較短，財務表現不良的公司平均上市時間則較長。 3.財務表現優良的公司帳面上的養地比率較高，財務表現不良的公司帳面上養地比率則較低。

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.

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。

在知識經濟之社會，多元思維逐漸取代傳統二元邏輯的思考與分析方法。過去使用單一數值的樣本來計算中位數的方法，已漸不符現今複雜多變的智慧科技時代之需求。尤其是在具有多變性、不確定性、與訊息不完整性的財金與經濟環境下，過分強調對於數值之運算及數學假設的前提，反而更容易造成與現實環境及條件的背離、甚至是脫節。故在進行財金與經濟方面問題的研究時，利用隸屬度函數與模糊統計的分析將會是一種較為進步的測度方法。本文在此提出模糊中位數的分析理論，並將其應用於財務金融的分析測度上，期望能對複雜的財金經濟現狀提供一套更有效且精確合理的分析方法。 / In the society of economic knowledge, Multi-valued logic goes to replace binary logic gradually. In the traditional way, we usually ask the task-taker to response the answer according to the thinking of binary logic. But such kind of response is improper since the human thinking is fuzzy and uncertain. So it should be an improved measurement using membership functions and fuzzy statistics. 　　In this paper, we will propose the definition of fuzzy median, and present some of its application. According to the above theoretical contents, we give some examples, which is used frequently in financial and economic assessment. From the explanation and discussion of fuzzy median in these examples, we can recognize that fuzzy statistics is more meaningful and proper for research of finance and economics. At last, based upon the findings of this study, certain recommendations for further research are suggested.