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.

傳統消費者選擇理論通常假設經濟主體為理性且對自身偏好的感受明確，但基於決策者對事物組合間的偏好具有模糊性的現象，使得以明確偏的衡量方式會因分析方法的限制，讓收集而得的資訊被相當程度的扭曲或漏失，因而造成決策的不適當。經濟學家已開始討論有關模糊性的決策行為，而在模糊決策問題中常遭遇需由模糊效用認定事物組合間順序以作選擇的情形，這可經由模糊效用間的直接比較來解決。Ponsard(1986)證明了模糊效用的存在事實；Billot(1992)運用最大轉換算子的處理，將模糊偏好關係以效用來表示。本文利用兩者的概念為基礎，嘗試建立一修正的模糊效用函數，希望對傳統模式的缺失進行改善。而本模式為Billot的轉換算子的延伸，能對無異類集合內的元素進一步地作排序，使合理的偏好幾乎都能被此模式所代表的效用函數刻劃。

預測技術在決策過程中是不可或缺的重要工具。精確的預測可以提供決策者更多的資訊去做出正確的決策。傳統的點預測方法是目前使用最多的預測方式，其預測模式常需要較嚴格的基本假設，這使得預測模式的建構較為困難。而加權模糊時間數列模式並不需要強烈的基本假設，模式架構較傳統更為簡易，也提供決策者更多的選擇。本研究將傳統的加權模糊時間數列推廣為區間加權模糊時間數列。與常用的幾種區間模糊時間數列做比較，以預測每日台幣對美元的匯率的方式來探討幾種預測方法的效率評估與準確性。 / Forecasting technology has played an important role for the decision makers. Accurate forecasts can provide decision makers more information to make the right decisions. Currently, the most use of forecasts is the traditional point forecasting, whose forecasting model often requires strict assumptions, and this makes it more difficult to construct the forecasting model. Weighted fuzzy time series model does not require so strong assumptions, so the model construction is simpler than traditional ones. It also provides the decision makers more options. In this research, we promote the weighted fuzzy time series model to the interval weighted fuzzy time series model. And we compare it with some commonly used interval fuzzy time series models, to discuss their efficiency evaluations and accuracy by forecasting daily exchange rate for US Dollars to NT Dollars.

配合十二年國教的上路，教育部近年來廣推社區高中，目的是希望透過社區高中的發展，學生能夠就讀所在地附近的社區高中。其中部分因素是可以漸少通勤時間的浪費，避免因通勤時間過長而影響學生學習力及學習表現。本論文目的是欲了解通勤時間過長對學生的學習是否有影響？影響層面如何？本論文，應用模糊理論的概念，以模糊問卷為工具，調查某高中高一學生，將模糊問卷調查值反模糊化，透過模糊相關係數的方式，探討分析「通勤時間的長短」對於「學生學習狀態及學習表現」的相關，最後，採用無母數檢定「長通勤時間與短通勤時間的學生」在「學習狀態及學習表現」是否有顯著差異。 研究結果：一、通勤時間長短對於學生第一節上課精神、上課專注度及學生成績表現呈低度相關。二、檢定結果，長通勤時間學生與短通勤時間學生在學習專注度、上課精神狀態及學習成績表現並無顯著差異。

傳統的統計方法檢定都假定資料來自於某個分配，但若假設檢定包含著不確定性時，有關模糊數的假設檢定有其重要性。由此可知，模糊統計推論已逐漸受到重視，這是符合現在複雜的社會現象所自然發展的結果。針對模糊資料，本文嘗試以簡易的計算配合模糊理論，定義出模糊數及模糊區間的排序方法，並將此方法應用在檢定上。即針對傳統無母數檢定方法，在無法解決參數假設為模糊數或是模糊區間值的情形下，為改進此一缺點，本文提出模糊Kruskal-Wallis檢定和Run test檢定。由實証的例子顯示，本文提出的檢定方法能有效解決模糊樣本問題。 再者，傳統的統計迴歸模式，假設觀察值的不確定性來自於隨機現象，但模糊迴歸則考慮不確定性來自於多重隸屬現象。因而以無母數統計方法，配合模糊迴歸理論，進而提出模糊無母數迴歸Theil法，並應用實際的例子，以顯示其存在的實質意義。 / Traditional statistical hypothesis testing is completely assumed that the data are from some statistical distribution. However if the data includes many uncertainties, fuzzy hypothesis testing will be useful in this condition. Thus it can be seen that fuzzy inferential statistics is gradually emphasized in modern world due to the development of complex social phenomenon. In this paper, the ordination technique, based on the fuzzy data, of fuzzy numbers and intervals will be defined by simple computations with fuzzy theories, and this technique will be applied to statistical testing. In another word, traditional nonparametric statistical hypothesis testing could not deal with the data from fuzzy numbers or intervals. To be successful for this, we provide Kruskal-Wallis Test and Run Test in this paper. The testing techniques mentioned by this paper could solve the limitation of fuzzy samples. Some empirical examples will be given to show for this. Furthermore, traditional statistical regression models assume that the uncertainty of the observed values is from random sampling. Nevertheless, fuzzy statistical regression models assume that the uncertainty of the observed data is from the phenomenon of Multiple Membership. Therefore we bring up Theil fuzzy nonparametric regression model considering nonparametric statistical techniques and fuzzy regression models. One practical example is given to show the application for this fuzzy nonparametric regression model in this paper.

股票是許多人採取投資的項目。若能準確預測股價的漲跌，則可以有效地降低投資風險，賺取利潤。然而，有許多因素會影響股票走勢，例如政治因素，匯率變化，天災人禍。因此，股票走勢很難被精確預測。我們嘗試用模糊統計來解決股價預測的問題。本論文藉由模糊相關矩陣來建立多變量模糊時間數列，以便用來預測股票趨勢。實證研究則以台灣加權股價指數為對象，對每日的收盤價進行模糊時間數列分析與預測，還計算誤差與準確率。實證研究顯示，能降低投資者的風險。

「模糊」這個名詞常被用來表示為不確定性，而模糊理論其實就是在探討統計機率中所表達的「隨機性」。而對於區間型的資料時，由於單一的數值(例如：平均數)常會隱藏住資料的真實情況，因此在處理區間型資料時，我們大多會採用相關係數進行計算。 　　以往之模糊區間資料大多為連續型資料，然而仍有許多計數值資料，例如：旅運量、品管中的缺點數、公司出勤人次等，而本文將針對計數值資料之模糊區間加以討論，並藉由計數值模糊區間資料，生成模糊相關係數。另外，我們也將導入針對計數值資料進行轉換的ISRT法，透過此方法，將計數值資料轉為連續型資料，並比較其兩組數據所生成之模糊相關係數。本文利用模擬分析，生成若干種間斷型分配後再模擬計數型模糊區間資料(Attribute Fuzzy Interval Data)；並加入實證分析，利用實際資料來分析驗證。

科學研究中，我們常關注變數間是否存在某種相關，及其相關的程度與方向。但傳統的相關分析方法，並不適用於更能表達真實情況的模糊資料。 在統計學中，討論資料之相關性的統計量有許多，本研究旨在針對討論兩變數間之線性關係的皮爾森相關係數 (Pearson Product-Moment Correlation Coefficient)，以模糊統計方法的角度，提出合理的模糊直線相關係數定義，以協助處理區間模糊資料，瞭解模糊資料間的線性關係。 / In the scientific research, we often pay attention to whether there are some relations between two variables, and the strength and direction of a linear relationship. But the traditional statistics method is not suitable for the fuzzy data. There are a lot of statistics of discussing the relevance between two variables. In this study, a modified method, combining Pearson Product-Moment Correlation Coefficient and fuzzy theory, was applied to deal with the fuzzy data, and find the linear relation among them.

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.