迴歸分析(regression analysis)為統計上最常使用的決策分析工具之一，能使決策者知曉投入因子與產出因子的關聯性，針對迴歸分析，過往研究所蒐集與探討的資料都是明確值(crisp value)，然而現實生活中，許多獲得的資料並不是精確的，只能表示個大概，又或是本身為語意，充滿個人主觀態度，為處理這類資料，學者提出了模糊集合理論(fuzzy set theory)，將不確定性表達於資料型態上。為了使不確定性資訊的表達更為符合本質上的不確定，學者由模糊集合理論衍生出直覺式模糊集合(intuitionistic fuzzy set)的概念，不再只考慮正向資訊，更加入了負向資訊進行探討，使表達更為完善。
過往的文獻中，鮮少對於直覺式模糊迴歸模型進行探討者，其迴歸的估計式與求解手法的訂定將決定整體研究的走向。本研究採用係數為明確值、投入產出變數為直覺式模糊數的迴歸估計式，原因乃在於係數為明確值而非直覺式模糊數可避免兩直覺式模糊數相乘而導致的直覺式模糊數之展幅(spread)過份放大，展幅所代表的是模糊性，也免去使用模糊化或解模糊化而造程資訊的流失；而求解手法則使用數學規劃法，期望能有不同於傳統最小平方法的求解過程。
在建模過程中，利用分解定理與直覺式模糊截集(cut)來建立數學規劃模型與迴歸估計式，並提出兩種不同的建構方法，最後用舊有的相似度與新提出的距離差異度來檢驗模型的合適性與優劣性。最後本研究以實際數據成功建構出係數為明確值的直覺式模糊迴歸，其表現不亞於舊有文獻所建構之模型。

Regression analysis is one of the most widely used decision making tools. It allows decision makers to determine the relationship between input variables and output variables. In a statistical regression analysis, data is always precise figures, which are called crisp values. However, in the complex real-world environment, data may be uncertain, written in linguistic terms, or based on personal subjective attitudes. Therefore, fuzzy set theory was developed to deal with these data. In order to express the essence of uncertainty better, scholars proposed the concept of intuitionistic fuzzy sets (IFS) as a generalization of the fuzzy set theory. In addition to including positive information, it also includes negative information.
There have been few studies of intuitionistic fuzzy regression (IFR) models. The direction of these studies was decided by three elements: data-type and parameter-type, solution approaches, and computation of the estimation error. In this study, the available data for both input variables and output variables are assumed to be intuitionistic fuzzy numbers (IFN), and the model parameters are crisp numbers. The parameters are crisp values rather than IFN because IFN multiplied with each other will bring about an over-increase in the spread of the IFN. In other words, the fuzziness of numbers will be over-increased. Different from the traditional solution methods such as the least-squares method, this study uses mathematical programming methods. The concept of decomposition rules and IFN-cuts are also used to build models. Two different approaches are proposed in this study. The predictive ability of the obtained models is evaluated by using similarity and distance measures. The results indicate that the models proposed in this study are better than their counterparts.

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