政大機構典藏-National Chengchi University Institutional Repository(NCCUR):Item 140.119/32575

政大機構典藏-National Chengchi University Institutional Repository(NCCUR):Item 140.119/32575

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政大典藏 > College of Science > Department of Mathematical Sciences > Theses > Item 140.119/32575

Please use this identifier to cite or link to this item: https://nccur.lib.nccu.edu.tw/handle/140.119/32575

Title:	模糊線性迴歸之研究
Authors:	趙家慶
Contributors:	宋傳欽趙家慶
Keywords:	模糊線性迴歸具影響力觀察值離群值雙重模糊線性迴歸模型隸屬度函數 fuzzy linear regression influence observation outlier doubly fuzzy linear regression membership function
Date:	2005
Issue Date:	2009-09-17 13:46:45 (UTC+8)
Abstract:	使用傳統迴歸的方式對未知事物做預測，往往不能夠精準的做出結論，縱使在相同的條件下實際去操作，也很難得到相同的結果，因此模糊數概念的建立，並運用在迴歸分析上更能有效描述預測結果的不確定性。然而模糊線性迴歸(Fuzzy Linear Regression)在利用最小平方法處理問題時，往往過於著重在模糊區間的中心與分展度上，而忽略了描述資料的模糊性，使得隸屬度函數(membership function)的功能受到相當大的限制。本文在D`Urso和Gastaldi(2000)所提出的雙重模糊線性迴歸(doubly fuzzy linear regression)模型架構下，利用Yang和Ko(1996)在LR空間下所定義模糊數間的距離公式，導出能反映隸屬度函數的最小平方估計，並引進一些傳統迴歸中常用來偵測離群值(outlier)與具影響力觀察值(influence observation)的概念與技巧，應用在模糊線性迴歸資料的偵測上。
Reference:	[1]Draper, N. R. and Smith, H., (1980). Applied Regression Analysis,Wiley, New York. [2]D`Urso, P. and Gastaldi, T., (2000). A least-squares approach to fuzzy linear regression analysis. 34, 427-440. [3]D`Urso, P., (2003). Linear regression analysis for fuzzy/crisp input and fuzzy/crisp output data. 42,47-72. [4]Tanaka, H., (1987). Fuzzy data analysis by possibilistic linear models. [5]Tanaka, H., Uejima, S., Asai, K., (1982). Fuzzy limear regression model.903-907. [6]Xu, R. and Li, C., (2001). Multidimensional least-squares fitting with a fuzzy model.215-223. [7]Yang, M. S. and Ko, C. H., (1996). On a class of $c$-numberrs clustering procedures for fuzzy data.84,49-60. [8]Yang, M. S. and Liu, H. H., (2003). Fuzzy least-squares algorithms for interactive fuzzy linear regression modles.135, 305-316. [9]Yang, M. S. and Liu, H. H., (2005). A new statistic for influence in linear regression.47, 305-316 [10]Zimmermann, H. J., (1991). Fuzzy Set Theory and its Applications,Kluwer,Dordrecht. [11]吳柏林(2005)：模糊統計導論方法與應用。台北，五南圖書出版社。
Description:	碩士國立政治大學應用數學研究所 93751003 94
Source URI:	http://thesis.lib.nccu.edu.tw/record/#G0093751003
Data Type:	thesis
Appears in Collections:	[Department of Mathematical Sciences] Theses

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