模糊線性迴歸模型之穩健式最小平方法

自從Tanaka等人在1982年首次提出模糊線性迴歸模型的研究後，模糊迴歸分析就被廣泛地研究並且應用在許多不同的領域中。一般來說，模糊迴歸模型的分析可以粗略地分成兩個範疇，其中之一是以Tanaka的線性規劃方法為基礎，另一個則是以模糊最小平方法為基礎。在本文中我們提出一個穩健式模糊最小平方法，接著將此方法用在模糊線性迴歸（Fuzzy Linear Regression, FLR）的參數估計上，最後我們將模糊最小平方法和Tanaka線性規劃法對FLR模型的估計作數值的比較分析，根據這些比較，我們發現模糊最小平方法有不錯的估計效果，我們因此建議可以選擇所提出的穩健式模糊最小平方法來做FLR模型的參數估計。

關鍵字

離群值；線性規劃法；健全式；模糊最小平方法；迴歸模型；模糊集；估計法

並列摘要

Since Tanaka et al. in 1982 proposed a study in linear regression with a fuzzy model, fuzzy regression analysis has been widely studied and applied in various areas. In general, the analysis of fuzzy regression models can be roughly divided into two categories. One is based on Tanaka's linear-programming approach. Another category is based on the fuzzy least-squares approach. In this paper, a robust fuzzy least- squares algorithm is considered in the estimation of fuzzy linear regression (FLR) models. Then numerical comparisons between this fuzzy least-square and Tanaka's methods for FLR models are implemented. According to these comparisons, it is suggested that the proposed fuzzy least-square is preferred for use in the parameter estimation of FLR models.

並列關鍵字

outlier ； linear programming ； Fuzzy set ； robust ； estimation ； regression model ； fuzzy least-square

參考文獻

[1] M. Albrecht, “Approximation of functional relationships to fuzzy observations”, Fuzzy Sets and Systems 49 （1992） 301--305.

[2] J. C. Bezdek, “Pattern Recognition with Fuzzy Objective Function Algorithms”. （Plenum Press, New York, 1981）.

[3] A. Celminv s, “A practical approach to nonlinear fuzzy regrssion”, SIAM J. Sci. Stat. Comput. 12（3）（1991） 521--546.

[4] R. N. Dave, “Characterization and detection of noise in clustering”, Pattern Recognition Letters 12 （1991） 657--664.

[5] P. Diamond, “Fuzzy least squares”, Information Science 46 （1988） 141--157.

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模糊線性迴歸模型之穩健式最小平方法

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