模糊迴歸(fuzzy regression)為決策科學的重要工具之一，然而在某些複雜情況下，使用一般模糊數已不足以表達自然界中的模糊情形，此時使用區間模糊數來表示決策過程中的模糊現象將顯得更為適切。近年來已有許多學者應用區間模糊數於各個研究領域中，但目前卻尚未有文獻著眼於區間模糊迴歸模式的建構與分析，因此，本研究將參考過去文獻中模糊迴歸之建構方法來發展區間模糊迴歸模式。
本研究首先以距離測度為誤差衡量指標，使用目標規劃(goal programming)在三種不同目標數下作探討，並建立相對應的目標式，之後提出兩種求解模式來建構區間模糊迴歸式。第一種為利用固定展幅法求得反應變數估計值與觀察值之間距離總和最小下的迴歸係數與區間模糊調整項；第二種為利用彈性展幅法求得反應變數估計值與觀察值之間距離總和最小下的區間模糊數最可能值及區間模糊展幅項之估計迴歸式。此外，本研究亦考量到決策者在不同的情況下可能訂定各種不同的目標組合，因此提出區間模糊迴歸之目標一般式，使決策者可根據自身的決策態度給予每個目標不同的優先順序(priority)或權重(weight)，以找出符合目標規劃下之最佳區間模糊迴歸式。經由不同例題演算與分析後，發現彈性展幅模式的估計準確度高於固定展幅模式，尤其當觀察資料呈現愈不規則或不對稱時，彈性展幅法愈能顯現其估計誤差較小之優勢。而固定展幅法之估計準確度雖不及彈性展幅法，但其限制式與參數個數隨著觀察值筆數及解釋變數個數增加而攀升的幅度小於彈性展幅法，當每筆觀察值之左右展幅皆一致時，建議決策者採用固定展幅法來進行求解將可降低模式之複雜度。

Fuzzy regression is an important tool in the decision-making field. To express complicated phenomena in the natural world, interval-valued fuzzy numbers are more suitable than regular fuzzy numbers for expressing uncertainty in the decision-making process. Although interval-valued fuzzy numbers have been applied to various research areas, the formulation and analysis of interval-valued fuzzy regression models have not been explored. Therefore, the present study uses fuzzy regression methodologies to develop interval-valued fuzzy regression models.
Objective functions for various numbers of goals are established based on the concept of distance and two methods for constructing interval-valued fuzzy regression models are proposed. The first approach uses a fixed-spread method to determine the regression coefficients and the interval-valued fuzzy adjustment term by minimizing the sum of the differences between the observed and estimated responses. The second approach uses a flexible-spread method to determine the estimated regression of the most likely value and the spread term of interval-valued fuzzy numbers by minimizing the sum of the differences between the observed and estimated responses. In addition, a general objective function of interval-valued fuzzy regression that considers various objective combinations under various situations is proposed. Decision makers can assign a priority and weight to each goal according to their preferences to find the optimal interval-valued fuzzy regression model. The two proposed models are demonstrated using several numerical examples. Results show that the flexible-spread model has a higher estimation accuracy than that of the fixed-spread model. The flexible-spread model is especially suitable for irregular or asymmetric observed data. Although the estimation accuracy of the fixed-spread model is lower than that of the flexible-spread model, the increase in the number of its constraints and parameters is lower when the number of observations and independent variables increases. When the left and the right spreads of each observation are identical, the fixed-spread method is suggested to reduce the complexity of interval-valued fuzzy regression models.

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