區間回歸與模糊樣本分析

傳統的回歸是假設觀測值的不確定性來自於隨機，模糊回歸則是假設不確定性來自隸屬度現象。一般的模糊回歸採用樣本模糊數(X(下標 i), Y(下標 i))來對模糊回歸參數進行估計，其中Y(下標 i)為觀測模糊數，X(下標 i)依舊為實數值。我們認為X(下標 i)的假設不能真實地表達出樣本所蘊含的資訊，本研究將假設X(下標 i)也為模糊數，如此一來對樣本的解釋方式將更為貼近現實，且估計的過程則採用通用的最小平方估計，保留回歸原始精神，但是在模糊數上則有更深入的探究。

關鍵字

區間回歸分析；區間參數估計；最小平方法；區間模糊數距離

並列摘要

The traditional regression is based on the assumption that the uncertainty is from the randomness of the variables, but in fuzzy regression, the uncertainty is assumed from membership grades. Generally, fuzzy regression adopts the fuzzy variables of sample (X(subscript i), Y(subscript i)) to estimate the parameter of fuzzy regression while Y(subscript i) is the fuzzy variable and X(subscript i) is still the real number. We think that the assumption of X(subscript i) can not express factually all the information of the sample, so we assume X(subscript i) is the fuzzy variable in the study. In this way, the explanation of the sample will be pressed close to the reality and by using the least square approximation in estimation process, the original essence of regression is preserved but more investigation in fuzzy variables is given.