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.

目前網路上為了解決單身男女尋找配偶的問題，設計出一些網路交友平台。藉由速配機制，從茫茫人海中找出適合的另一半。本篇論文想要探討這些機制是否能夠達到最佳速配，使男女雙方找到適合自己的另一半。我們藉由模糊語意與軟計算技術，考慮以區間模糊數來計算兩者最小距離，以期達到最佳的男女速配。最後，我們改良Yahoo奇摩交友平台，並藉由實際資料來做模擬配對。由實證資料顯示，本研究方法，能將男女的速配度以更精確的數字呈現出來。 / So far, for the purpose of solving the problems of unmarried men and women who want to seek for spouses, people have designed some platforms for helping people make friends on internet. And from the “match system”, one can discover the suitable couple from the boundless huge crowd. But can these mechanisms attain the goal to reach the perfect match and find the another half? This paper use the fuzzy meaning and the soft computation technology to compute the minimum distance between two sets by trapezoid fuzzy number to make the suitability between men and women achieve the maximum.In the research designing part of the paper, we improve the Yahoo personals website in Taiwan, and we have the pals making by real data. From the research, we will find out that this way will help people choosing the pals who are close to everyone’s ideal spouse.

「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.

台灣加權股價指數(TAIEX)，可以說是台灣最重要的經濟指數之一。在預測的方法中，時間序列分析一直都是熱門的課題，也是最常被使用來研究股價預測的方法。近年來，模糊理論在生醫、財務、社會、電機等各領域都有不錯的應用與發展 。本研究欲透過模糊區間的預測，主要是以時間序列預測台灣加權股價指數，來作為模糊區間精確度的探討，並針對區間時間序列進行模式的建構診斷和預測。最後我們將以2012年第一季(Q1)，每日交易股價指數的最高價與最低價作為實際研究的例子，同時也比較不同預測方法所得的結果。結果顯示模糊區間預測提供不同於傳統預測方法所得的資訊，希望能提供投資者另一種投資的參考。 關鍵字 : 台灣加權股價指數(TAIEX) 、模糊理論、模糊區間、區間預測 / Taiwan Weighted Stock Index (TAIEX) is one of Taiwan's most important economic indicators. Among the forecasting methods of time series analysis is always a hot issue on the forecasting methods and is also the most commonly used to make the stock price predictions. In recent years , fuzzy theory makes a great of application and development in various fields , such as , biomedical , financial and social …etc.. For this study, through the fuzzy interval forecasting is mainly based on time series forecasting TAIEX as fuzzy interval accuracy of the construction of diagnosis and prediction of the mode and interval time series. Finally, we will take the daily highest / lowest stock index prices data in the first quarter of 2012 (Q1) for actual research example , and will compare different forecasting methods of the results. The results show that the fuzzy interval forecasting differented from the traditional one on the basis of these information. We hope to offer investors an alternative investment advice. Keyword : Taiwan Capitalization Weighted Stock Index (TAIEX) 、 Fuzzy theory 、 Fuzzy interval、Interval forecasting.

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.