ARCH在財務分析近來頗受重視，然而實務在建構ARCH模式時參數估計值很難有效估計，而且參數數字本身亦常存在不確定性，其原因可能來自時間數列資料的模糊的性質。利用此一假性的數值來建構模式影響預測，也可能擴大預測結果和實際狀況的誤差，很難讓一般投資者使用並判斷。本文在建構ARCH模式中，加入模糊邏輯概念，以符合實際情況在建構ARCH模式時參數動態的不確定性。嘗試以模糊數的來建構股價加權指數FUZZY ARCH模式，進一步預測，並與ARCH模式作比較分析。 / ARCH is more emphasized in financial analysis recently. However, it is difficult to estimate the parameters of ARCH model in practice. Because of the fuzzy property in time series , there exists the uncertainty in the parameters. Use the fictitious value to construct model and forecast the model will make the errors largely between the forecasts and the practical ones. In this thesis, we add the concept of the fuzzy logic to construct the ARCH model in order to conform the real situation. Also, an analysis of the stock data is provided.

本研究主要是探討兩個區間型模糊數之間的直線對應關係。主要的方式是以最小平方估計法(least squares estimation)分別求出區間型模糊數上、下界所對應的迴歸方程式，以該迴歸方程式所求得的上、下界，做為所估計區間型模糊數的上、下界。 單就所蒐集到的上界或下界資料而言，它們是一組明確的資料，並不模糊。研究中所探討的區間型模糊數是由一組明確的上、下界值所構成的。考慮所估計的上、下界值需具有較小的誤差才能增加所構成區間型模糊數的代表性，使用最小平方估計法並以傳統的迴歸方式來求得上、下界迴歸直線，應該是減少估計的上、下界值誤差較佳的方式。 然而以最小平方估計法所估計的上、下界值是相對於資料算術平均數誤差最小。如果所蒐集到的數據愈分散，則算術平均數的代表性將愈低，連帶影響所估計區間型模糊數的準確性。這是使用最小平方估計法做為研究工具的隱憂。 解釋係數是最常被用來判別迴歸模型優劣的參考數值。有鑑於區間型模糊數的模糊特性，傳統迴歸分析的解釋係數並不適用於模糊線性迴歸關係。本研究提出模糊覆蓋率的概念，來判別兩個區間型模糊數之間線型迴歸關係的優劣。最後以中華民國80年到96年間製造業平均月工時對應平均月薪資為例，說明模糊覆蓋率在實務上的應用。 / The aim of this paper is to discuss the linear correspondance between two interval fuzzy random variables. We construct the regression equations of the upper and lower bounds of some interval fuzzy random variables, respectively, by the least squares. The upper and lower bounds of the estimated interval fuzzy random variables are derived by the regression equations of upper and lower bounds, respectively. The collected upper and lower bounds are all crisp data, not fuzzy ones. In this paper, the interval fuzzy random variables discussed are constructed by crisp upper and lower bounds. In order to increase the reprsentative of the interval fuzzy random variables, we need to minimize the errors of the estimated upper and lower bounds. Applying the least squares along with the conventional regression analysis to construct regression lines of upper and lower bounds, respectively, should be the better way to minimize the errors of the estimated upper and lower bounds. However, the errors of the upper and lower bounds estimated by the least squares are the least according to the arithmetic mean value. The more discrete the data we collected , the less representative of the arithmetic mean value is. That will also affect the accuracy of the estimated interval fuzzy random variables. This is what we are worried while we take the least squares as an tool to analyse the interval fuzzy random variables. The coefficient of determination is a reference value which is mostly often used to distinguish the accuracy of the conventional regression model. In the view of the characteristics of fuzzy regression model, the conventional coefficient of determination cannot properly explain the fuzzy linear regression model. In this paper, we propose the fuzzy coverage rate to distinguish the accuracy of the fuzzy linear regression model between two interval fuzzy random variables. Finally, we give an example about the mean monthly working-hour and the mean monthly salary of the manufacturing industry in Taiwan from 1991 to 2007, demonstrating the application of the fuzzy coverage rate in reality.

台灣上市公司不預警地宣布重整，跳票、全額交割或下市，造成投資大眾的損失，因此，必須建立企業信用模型來偵測其經營狀況。本研究發現財務比率自企業危機前五年起逐漸惡化，表示財務比率在危機發生前有惡化現象，另外危機發生後幾年財務比率仍有影響，故本研究視企業危機為一逐年遞增或遞減的變數，使用模糊數轉化，加入危機發生前後的總體變數，並且結合統計多變量分析和資料探勘中的乏析理論建立模型，使用窮舉法找出解釋力最佳之企業信用模型，結果顯示，採用模糊數轉化之應變數相當顯著。 / The listed companies in Taiwan suddenly announced restructuring, bankruptcy or out of stock, and their investors lost a lot. Therefore, we must set up the enterprise credit model to detect and examine their management states. We discover that the financial ratios decrease gradually since the past five years of enterprise's crisis. Besides, financial ratios still diminish after the crisis take place. Therefore, this research regards enterprise's crisis as one parameter, and we transform the parameter by fuzzy numbers. In addition, we use the macro economical parameters and combine multivariate analysis and fuzzy logic theory to find out a higher significant model. The result shows it is high significant to adopt the fuzzy number dependent variable.

本研究之目的在於釐清幼兒園教育品質之概念與內涵，並建構「幼兒園教育品質指標體系」，做為幼兒園人員、家長、主管機關等利害關係人評估幼兒園效能效率表現之參考，並為提升幼兒園教育品質提供涵意。 研究者經由文獻分析，形成「幼兒園教育品質指標適切性問卷」與「幼兒園教育品質構面相對重要性問卷」，以幼兒園、托兒所之園所長、教職員共計151名為對象，以瞭解幼兒園內部人員對於指標適切性與構面相對重要性之觀點。研究者運用三角模糊數整合專家意見、以常模參照方式篩選指標，另透過AHP層級分析法建立構面相對權重，續以三角模糊數歸一化的方式，將構面權重分配予各項指標，以完成「幼兒園教育品質指標體系」。 本研究獲致之研究結果如下： 一、 幼兒園教育品質為一以幼教歷程為核心、逐漸向外拓展的概念，幼兒園教育品質的探究範圍包含幼兒經歷之幼教歷程、教室層級之環境與組織層級之管理。 （一） 幼教文獻中，幼兒園教育品質係以幼兒發展為本位，關注教室層級以內，主要就歷程、結構、教師之相關因素做深入探討，於幼兒園組織管理層面探討較少。 （二） 本研究中，幼兒園教育品質係以幼兒園為本位，探究範圍較廣，關注幼兒園組織層級，並主張以全面品質充實幼兒園教育品質之概念與內涵。 二、 本研究以全面品質觀點建構幼兒園教育品質指標，參考包德理治教育指標之架構，包含幼教歷程、教職員管理、家長關係、園所長領導、幼兒園策略規劃、資訊分析與知識管理、幼兒園經營策略等七構面，指標內涵整合了幼兒環境量表（ECERS-R）、NAEYC認證標準與包德理治教育指標，初擬70項指標，經由幼兒園內部觀點篩選，保留66項指標。 三、 以AHP層級分析法求得幼兒園教育品質構面之相對權重，依權重值排序，幼兒園教育品質構面依序為：幼教歷程（15.8%）、園所長領導（15.6%）、幼兒園策略規劃（15.2%）、教職員管理（14.2%）、幼兒園經營策略（14.2%）、資訊分析與知識管理（12.6%）、家長關係（12.5%）。續透過三角模糊數歸一化之方式，將構面權重分配予各項指標，完成「幼兒園教育品質指標體系」與「幼兒園教育品質自我評估表」。 研究者針對指標篩選結果與權重建構結果進行相關討論，文末並根據研究結果與發現，就實務面與未來研究方向提出具體建議。 / The purpose of this study aims to clarify the concept and contents of educational quality in ECE schools providing 4-6 year-old children early childhood education, and also to establish a system of educational quality indicators in ECE schools. Through literature review and analysis, two questionnaires “the properness of the educational quality indicators in ECE schools” and “the relative importance of the educational quality dimensions in ECE schools” --- were constructed. Total of 151 subjects consisting of leaders, teachers and staffs in ECE schools were invited to complete these two questionnaires in order to form the internal perspective to the educational quality indicators. The data were analyzed by computing triangular fuzzy sets and using Analytic Hierarchy Process (AHP). The conclusions are as follows: 1. The core concept of the educational quality in ECE schools is ECE process, and the concept extends outward gradually. The ECE process, the environment and the management of the organization all should be included when the educational quality in ECE schools is discussed. (i) In the literature, the concept of the educational quality in ECE schools is based on the development of children. The concept is more about factors inside the classroom, including factors related to ECE process, structure, and teachers, and factors related to organizational management were less discussed. (ii) In this study, the concept of educational quality in ECE schools is school-based. The concept is more about factors related to organizational management. The author suggested that the concept and contents of educational quality in ECE schools will broaden and be enriched if the concept of total quality is integrated. 2. The educational quality indicators in ECE schools are composed of 66 indicators which can categorized into seven dimensions --- ECE process, management of the staff, relationship with parents, leadership, strategy, information analysis and knowledge management, and results. 3. The weight for each dimension is ECE process(15.8%), leadership(15.6%), strategic planning(15.2%), staff management(14.2%), strategy(14.2%), information analysis and knowledge management(12.6%), relationship with parents(12.5%). The weight for each indicator is allocated, and the system of educational quality indicators in ECE schools is completed as well. In the end, some implications for ECE practice and future research were suggested according to the findings of this study.

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

本文是針對一個古典的經濟批量問題，在儲存空間不確定而為模糊數時，且訂購週期為二次冪的限制條件下，探討如何求得最佳訂購量，且計算出訂購週期，使得總存貨成本減至最低。曲於儲存空間的變動，會影響訂購量大小，所以我們引進模糊的概念，處理儲存空間不確定的情形，藉由模糊非線性規劃(Fuzzy Nonlinear Programming , FNLP)，及模糊幾何規劃(Fuzzy GeometricProgramming, FGP)的技巧，讓目標函數與儲存空間模糊，並討論在二次冪的限制條件下，目標函數值的最大可能誤差。最後，我們舉一個實例，來說明求解的步驟，利用模糊非線性規劃，及模糊幾何規劃的技巧，很容易求得最佳目標函數值。

兩變數之間是否相關，以及相關的程度與方向是統計研究學者所關注的一項課題。傳統上使用皮爾森相關係數(Pearson’s Correlation Coefficient)來表達兩實數變數間線性關係的強度與方向。然而，對於反映人類思維不確定性的模糊資料而言，傳統的相關分析方法卻有不足與不適用之缺失。 　　本論文的主要目的在於尋求一個合理、適用的區間模糊資料相關係數，提供研究者簡單且容易計算的模糊相關係數求法，用以了解區間模糊資料間的相關程度。接著利用轉換離散型模糊數成為區間模糊數的方式，處理離散型模糊資料間的相關係數。最後，以國中數學教學現場所調查的資料做實例應用。 / In statistical studies, the correlation between two variables and its strength and direction are always concerned. Traditionally, the Pearson’s Correlation Coefficient is used to convey the linear relationship between two variables. However, the traditional correlation analysis is not applicable to the fuzzy data which are able to reflect more appropriately the uncertainty of human thinking. 　　The main purpose of the study is to find a reasonable and usable correlation coefficient of interval fuzzy data which provides researchers a simple and easy way to calculate and find the fuzzy correlation coefficient. Meanwhile, it can help us understand the correlation of interval fuzzy data. Moreover, we use the process of transforming discrete fuzzy number into the interval fuzzy number to deal with the correlation coefficient of discrete fuzzy data. Finally, we utilize the data from mathematics teaching in junior high school for application.

本文主要的目的是藉由The Geometer's Sketchpad (GSP)軟體的設計，幫助我們得到一組連續型模糊樣本。另外對於模糊數的無母數檢定我們提供了一個較為一般的方法，可以針對梯型、三角型，區間型的模糊樣本同時進行處理。 藉由利用GSP. 軟體所設計的模糊問卷，可以較清楚地紀錄受訪者的感覺，此外我們所提供之對於模糊數的無母數檢定方法比其他方法較為有效力。 在未來的研究裡，我們仍有一些問題需要解決，呈述如下：當所施測的樣本數很大時，如何有效率的在網路上紀錄受測者所建構的隸屬度函數？ / The purpose of this paper is to develop a methodology for getting a continuous fuzzy data by using the software The Geometer's Sketchpad (GSP). And we propose a general method for nonparametric tests with fuzzy data that can deal with trapezoid, triangular, and interval-valued data simultaneously. Using the fuzzy questionnaire designed by GSP. can help respondents to record their thoughts more precisely. Additionally our method for nonparametric tests with fuzzy data is more powerful than others. Additional research issues for further investigation are expressed by question such as follows: how to record the membership function on line, especially when the sample size is large?

動機與目的：傳統的統計迴歸模式假設觀測值的不確定性來自於隨機現象，而模糊迴歸則考慮不確定性來自於多重隸屬現象。不同的模型建構所得到的估計值也不一致。如何衡量模型的優劣程度，至今仍沒有一套嚴謹的標準。 研究方法：本研究以區間模糊數建構模糊迴歸模式，如此一來對樣本的解釋方式將更為貼近現實，並提出一套區間模糊數距離測度，以衡量估計值與實際值之間的差距。實證分析中（懸浮微粒PM_10濃度預測、台灣加權股價指數預測），我們藉由此距離測度衡量二維模糊迴歸與傳統二項最小平方法對於樣本的配適性。 創新與推廣：提出區間模糊數距離衡量估計值與原樣本之差異程度。在符合傳統統計迴歸精神之下，當距離最小就是差異最小的估計，最能符合所抽取的樣本，也是最佳估計。 重要發現：利用本區間模糊數距離測度，我們發現二維模糊迴歸方法比起傳統二項最小平方法更有效率且廣義殘差（generalized residual）將更小。 結論：過去以來，我們對於模糊迴歸架構一直都沒有完整的衡量標準。文中我們定義區間模糊數區間距離與平均距離，並推導賦距空間等性質。結合實例分析及應用，建構一合適模糊迴歸模式，以利統計決策分析參考。 / Objective: This study concerns how to develop effective fuzzy regression models. In the literature, little is addressed on how to evaluate the effectiveness of fuzzy regression models developed with different regression methods. We consider this issue in this work and present a framework for such evaluation. Method: We consider fuzzy regression models developed with different regression approaches. A method to evaluate the developed models is proposed. We then show that the proposed method possesses desirable mathematical properties and it is applied to compare the two-dimensional regression method and the traditional least square based regression method in our case studies: predicating the concentration of and the volatility of the weighted price index of the Taiwanese stock exchange. Innovation: We propose a new metric to define a distance between two fuzzy numbers. This metric can be used to evaluate the performance of different fuzzy regression models. When a prediction from one model is closest to the sample data measured in terms of the proposed metric, it can be recognized as the optimal predication. Results: Based on the proposed metric, it can be obtained that the two-dimensional fuzzy regression method is better than the traditional least square based regression method. Especially, its resulting generalized residual is smaller. Conclusion: In the literature, no unified framework has been previously proposed in evaluating the effectiveness of developed fuzzy regression models. In this work, we present a metric to achieve this goal. It facilitates the work to determine whether a fuzzy regression model suitably fits obtained samples and whether the model has potential to provide sufficient accuracy for follow-up analysis in a considered problem.

本文將模糊理論的觀念，應用在估計、檢定及時間數列分析上。研究重點包括離散型及連續型模糊樣本的定義與度量，模糊參數的最佳估計，模糊排序方法應用於無母數檢定，模糊相似度的定義、性質，以及如何將其應用於辨識不同時間數列間的落差l期相似程度等。我們首先將常見的模糊資料分為離散型及連續型，並針對不同類型的資料，給定對應的模糊平均數、模糊變異數等模糊參數的概念與一些重要性質。接著我們提出幾種估計方法，針對不同的模糊參數進行最佳估計並提出可行的評判準則。進一步地，我們將模糊排序方法應用於無母數檢定推論。最後我們提出模糊相似度的定義與度量。經由系統性的模擬與分析，我們建立兩時間數列間模糊相似度演算法則。實證分析方面，我們利用提出的方法對台灣的股價加權指數、個股股價進行估計及檢定；同時，針對台灣歷年GDP、民間消費、毛投資間的相似性進行偵測，以驗證我們提出的模糊參數估計、模糊無母數檢定及模糊相似度演算法的效率性與實用性。 / In this paper, we apply fuzzy theory in estimation, nonparametric test, and time series analysis. Our focus is on: How to define and measure the discrete type fuzzy data and continuous one? How to find the optimal estimators for fuzzy parameters? How to apply fuzzy ranking methods in nonparametric test when the data is vague? How to define and find the degree of fuzzy similarity between two time series? First, fuzzy data is classified according to its type, discrete or continuous. Then we give some definitions and properties on fuzzy mean, fuzzy variance for different type of fuzzy data. Next, we proposed some estimating methods and evaluation rules. Moreover we apply fuzzy ranking methods in nonparametric test, such as Sign test, Wilcoxon signed rank test, Wilcoxon rank sum test, and so on. Finally, we suggest the definitions as well as the algorithm for computing the degree of fuzzy similarity between two time series. We also give some simulate and empirical examples to illustrate the techniques and to analyze fuzzy data. Results show that fuzzy statistics with soft computing are more realistic and reasonable for the social science research.