模糊線性迴歸模式（FLRMs）常用於描述模糊解釋變數與反應變數之因果關係，而挑選重要解釋變數對模糊迴歸模式之建構成本及其應用上的表現極具影響力。本研究架構於(Chen & Hsueh, 2009)提出之模糊迴歸模式與既定之參數求解方法上，發展兩套模糊迴歸模式之配適度衡量與變數選取法。首先、提出明確值配適度衡量指標(R2 and adjusted R2)，用以衡量所有模糊迴歸式之模式配適情形，作為所有可能模式選擇的判斷準則，並發展能有系統向前及向後選擇之逐步變數選取法，此法利用所提出之平均邊際貢獻率(MF)，達到有效率地尋找適當、精簡之解釋變數集，而不需逐一配適所有模糊迴歸式。
其次、提出模糊值配適度衡量指標(R2 and adjusted R2)，結合擴充定理及應用兩個線性數學規劃模式，求解模式衡量指標之歸屬函數，以評估模糊迴歸式之配適程度，另延伸傳統隨機之模糊隨機數概念，發展近似F統計量作為模式選擇的判斷準則，提出能逐步選擇解釋變數之程序及方法，尋得具有統計顯著性之解釋變數集，而不需逐一檢查所有模糊迴歸式。所提出之統計檢定法，其發展脈絡始於對變異來源之探討。兩種方法論皆可適用於任何資料型態變數及逐步選取，不同於現行變數選取法僅能採用向前選取，本研究所提出之逐步選取法中，向後選取程序之優勢為可避免解釋變數之間的共線性問題。最後，透過範例驗證所提出之兩方法論的適切性及可行性，並與現有文獻進行比較。

Fuzzy linear regression models (FLRMs) are used to describe the contribution of corresponding fuzzy explanatory variables in explaining the fuzzy response variable. The selection of explanatory variables greatly affects the cost of establishing an FLRM and its performance in applications. Based on the existing method of FLRM formulation (Chen & Hsueh, 2009), this study proposes two methodologies to investigate the quality of fit and suitable variable selection for building FLRMs. Firstly, crisp fitness measures, namely R2 and adjusted R2, are proposed to evaluate the fitting performance of potential FLRMs for selecting a suitable model from all possible FLRMs. In addition, a stepwise selection procedure with fuzzy numbers and the proposed index of marginal fit (MF), which includes forward and backward selections, is developed to efficiently find a suitable subset of explanatory variables without having to fit all possible FLRMs.
Secondly, fuzzy fitness measures, namely R2 and adjusted R2, are obtained to evaluate the goodness of fit of FLRMs by solving the mathematical programming problem with the extension principle. In addition, a stepwise selection procedure with fuzzy random numbers and the asymptotic F statistic is developed to select a significant explanatory variable set to establish FLRMs without having to test all possible FLRMs. The sources of variability are well studied to develop the hypothesis test. Two methodologies can accommodate all types of data for evaluating FLRMs, and a stepwise variable selection approach. Unlike the current selection procedure, which only includes forward selection, the backward selection in the proposed stepwise procedure prevents the multicollinearity problem among explanatory variables. The applicability and feasibility of the proposed fitness measures and variable selection procedure are demonstrated using numerical examples and comparisons with existing approaches.

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