迴歸模式在工程應用之探討

The Study of Using Regression Models for Engineering Applications

傳統迴歸模式係由明確的樣本資料與利用最小平方法所配適之模式，主要用以探討與預測變數間的關係。模糊迴歸模式則為一種區間預測模式，適用於分析具有不確定性及含糊性的資料。模糊迴歸分析可視傳統迴歸分析的一種特殊型式。在模糊迴歸分析中，以Tanaka等人基於最小化模糊度的原理所建立之可能性模糊迴歸模式，以及Chang與Ayyub利用最小平方法所建構之複合式模糊迴歸模式，為極具代表性的兩種模式。本文以開挖成本估計為例，探討在不同的可信度下，此三種模式預測結果之異同處。

Nang-Fei Pan The conventional regression model, fitted to crisp sample data and employing the least-squares method, is mainly applied to investigate and predict the relationships between variables. The fuzzy regression model, an interval approach which can be thought of as a variation of conventional regression analysis, is used to fit data containing uncertainty and vagueness. In this paper, two of the most representative fuzzy regression models are evaluated. The first model is the fuzzy possibility regression proposed by Tanaka et al., which is based on minimizing fuzziness. The second approach is called hybrid fuzzy regression, developed by Chang and Ayyub, which utilizes the technique of the least squares of errors as a fitting criterion. A numerical example for cost estimations of a construction excavation is used to compare the similarities and differences of these three models at different degrees of confidence.