傳統迴歸分析乃在於說明解釋變數與反應變數的因果關係，進而達到預測的目的。然而，由於在決策過程中人為影響性以及某些資料具有模糊現象的因素，使得傳統的迴歸分析方法難以適用。而自Tanaka等人將傳統迴歸分析拓展至模糊迴歸分析後，便有越來越多的學者紛紛投入於模糊迴歸模式的建立與分析。過去多數文獻將求解出的迴歸係數假設為模糊數值，結果導致代入反應變數的估計式時，估計值的展度隨著解釋變數數值的增加而急遽擴大，使得模式的估計誤差變大。此外，過去文獻鮮少探討非對稱之模糊數，以及存在迴歸係數為負值的模糊迴歸模式；其次，則是多數文獻的求解方法均限制觀察值為三角模糊數。上述種種缺陷均使得模糊迴歸分析的應用性大打折扣。
本研究提出以距離測度下的兩種求解模式來建構模糊迴歸模式，第一種利用數學規劃法求得反應變數估計值與觀察值之間距離絕對值總和最小下的迴歸係數與模糊調整項。而第二種求解方法同樣基於距離測度下利用統計方法中的最小平方法推導出距離平方總和最小下迴歸係數與模糊調整項的一般式。與過去文獻不同的是，本研究所提之兩種求解模式所求解出的迴歸係數均為明確數值，並同時得到一模糊調整項使得估計誤差更為降低。本研究也利用不同的評估準則與過去文獻的多種求解模式進行比較，驗證本研究的求解方法具有較小的估計誤差。此外，本研究亦考慮迴歸係數存在負值時的求解方法及步驟。而本研究方法對觀察值所利用到α-cut方法並不侷限於三角模糊數更可適用於一般型態的模糊數，使得本研究方法的應用性更為廣泛。

Regression analysis has widespread application for the purpose of exploring the relationship between explanatory variables and responses in a fuzzy environment. However, in the real world, human estimation is often influential in decision-making processes, and the data provided will be fuzzy in nature. A traditional regression isn’t suitable to construct the relationship between input and output variables in a fuzzy environment. Since Tanaka et al. first proposed the fuzzy linear regression model, the concept has motivated a number of researchers’ interest in this issue with regard to both applications and methodologies. However, several studies have made regression coefficients into fuzzy numbers and applied these models to estimations in order to make the spread of the estimated responses wider when the magnitude of the independent variables increases. Another common drawback in existing fuzzy regression models is that the development of the fuzzy regression model is limited to fuzzy observations with symmetrical triangular fuzzy numbers. Furthermore, the existing approaches mainly formulate fuzzy regression models with positive regression coefficients. For cases with negative coefficients, the formulations may not be correct based on fuzzy arithmetic.
This approach proposes two methods to construct a fuzzy regression model based on the concept of distance. First, this approach uses a mathematical programming method to determine the fuzzy regression coefficients and fuzzy adjustment term by minimizing the sum of the absolute difference between the observed and estimated responses. Second, this approach applies the traditional least-squares method based on the same concept of distance to determine the fuzzy regression coefficients and fuzzy adjustment term general formulation by minimizing the sum of squared errors between the observed and estimated responses. In contrast to previous studies, this approach has numeric coefficients and a fuzzy adjustment term and also has comparisons with several methods showing that the performance of the proposed model is satisfactory based on two criteria for the total estimation error. In addition, to overcome the fuzzy regression problem with negative coefficient values, a solution procedure is presented to construct a model with a minimum of total estimation error. The proposed approach applying distance in terms of -cuts to the proposed method for the determination of parameter values is simple and intuitive. This approach can also deal with and effectively perform with fuzzy observations with various types of fuzzy numbers.

【中文部份】
王景南：模糊迴歸分析在籃球比賽攻防技術之應用，國家科學委員會研究彙刊：人文及社會科學，10(3)，287-298，民89。

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曹勝雄、曾國雄、江勁毅：傳統計量迴歸、模糊迴歸、GMDH、類神經網路四種方法在預測應用之比較－以國人赴港旅客需求之預測為例，中國統計學報，34(2)，132-161，民85。

曾能芳：模糊隨機變數在線性迴歸模式上的應用，國立政治大學統計研究所博士論文，民91。

張乃斌、陳育成：以模糊目標迴歸法建立垃圾衛生掩埋場沼氣回收設備之建造成本模式，模糊系統月刊，3，23-48，民86。

謝邦昌、林燦隆、呂理添：甘蔗產量之模糊迴歸預測模式，中國農藝，3 (6)，180-189，民 85。

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