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

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.

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.