迴歸分析為重要決策工具之一，提供決策者分析投入因子與產出因子的關聯性。不論是建立在統計學上的傳統迴歸，或是以模糊理論為根基的模糊迴歸，都廣泛應用於各領域。統計迴歸期望在一群遵循機率分配、隨機出現的變數中，找出彼此之間的關係，認為資料的不確定性來自於隨機性；模糊迴歸則處理變數本身具有不明確性質或是變數彼此關聯性無法明確定義的情況，將這類的不確定稱之為模糊性。然而隨著資訊日趨複雜，現實中資料時常是隨機性與模糊性兩種不確定性並存的，但是，在目前文獻中，甚少有研究同時探討隨機性與模糊性概念的迴歸模式。
本研究整合隨機性與模糊性概念，建立一個能夠同時處理隨機性與模糊性的迴歸式。首先以模糊隨機變數表示兼具兩種不確定性的資料，並將模糊數最可能值視為隨機性之表徵，展幅做為模糊性之表徵，接著，提出兩種求解模式。第一種為權重模糊算術法，參考Chang (2001)所提出之權重模糊算術的概念，計算觀察值與預測值之誤差，在迴歸式平方誤差最小的情況下，求得明確值迴歸係數。第二種為目標規劃法，以距離測度做為觀察值與預測值誤差的衡量指標，建立相對應之目標式與限制式，求取明確值迴歸係數。而本研究提出之模糊迴歸式皆加入一模糊調整項，使模式更具一般性並同時達到降低誤差之成效。

Regression analysis is one of the most important decision making tools allowing decision makers to analyze the relationship between input variables and output variables. Statistical regressions are expected to determine the relationships among a group of variables using probability distributions, assuming the uncertainty of data is due to randomness. In contrast, fuzzy regressions deal with imprecise data or indefinite relationships between variables, viewing this kind of uncertainty as fuzziness. Both statistical regressions and fuzzy regressions are widely applied in specific applicable fields. However, in a real world with complicated information, data is often accompanied with randomness and fuzziness simultaneously. Yet, there have been few studies of regression models that have discussed these two types of uncertainty at the same time.
In this research, the concepts of randomness and fuzziness are aggregated and a fuzzy regression model concerning two types of uncertainty is built. First, fuzzy random variables (FRV) are represented as data with twofold uncertainty, viewing the most likely value of FRVs as randomness and the spread of FRVs as fuzziness. Then, two approaches for constructing a regression model are proposed. The first approach uses weighted fuzzy arithmetic to estimate the sum of deviations between predicted values and the observed values. Subsequently, regression coefficients are obtained under the least-squares criterion. The second approach is called the goal programming method. This approach uses distance criterion for error estimation between a predicted value and an observed value and constructs objective function and constraints, respectively. Furthermore, a fuzzy adjustment term is added in the proposed fuzzy regression model in this research in order to increase generalization and to reduce the total estimation error of the model.

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