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研究生: 陳帥
論文名稱: 模糊數據的局部加權回歸
Locally weighted regression of fuzzy data
指導教授: 吳柏林
學位類別: 碩士
Master
系所名稱: 理學院 - 應用數學系
Department of Mathematical Sciences
論文出版年: 2017
畢業學年度: 105
語文別: 中文
論文頁數: 19
中文關鍵詞: 模糊理論模糊回歸分析局部加權
外文關鍵詞: Fuzzy theory, Fuzzy regression, Locally weighted method
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  • 目標:本文旨在建構一種新型的模糊回歸模式,解決一类較複雜的模糊回歸問題。
    研究方法:推廣局部加權回歸的思想,先從理論上構建新模型;然後借由模拟數據,從多個方面考察新模型的性質,并和其他模型做比較。
    發現:局部加權回歸方法結合模糊隸屬度概念,使模糊回歸理論有更多的應用場合。
    原創性:目前在模糊回歸領域的主流思想是通過線性規劃等方法來構建模型,而本文另闢蹊徑,首次從局部加權的角度構建了模糊回歸的新模型。


    Objective: This paper aims to construct a new fuzzy regression model to solve a more complex fuzzy regression problem.
    Method: Build a new model by promoting the idea of locally weighted regression; Using simulated data to compare the new model with other models.
    Conclusion: The fuzzy membership degree concept combined with the locally weighted regression method makes the fuzzy regression theory have more applications.
    Originality: At present, the main idea in the field of fuzzy regression is to construct models by means of linear programming. In this paper, a new model of fuzzy regression is constructed from the perspective of locally weighted method for the first time.

    1.前言 1
    2.模糊數據的局部加權回歸 5
    2.1 模型的建構 5
    2.2 回歸係數的估計 6
    2.3 殘差分析 7
    2.4 數據模擬 8
    3.實證分析 12
    4.結語 18
    參考文獻 19

    [1] L.A. Zadeh, Fuzzy sets, Information and Control, Volume 8, Issue 3, June 1965, pp.338–353
    [2] H. Tanaka, S. Uejima, K. Asai,Linear regression analysis with fuzzy model, IEEE Trans. Sys., Man. Cyber., 12 (1982), pp. 903–907.
    [5] William S. Cleveland, Robust Locally Weighted Regression and Smoothing Scatterplots, Journal of the American Statistical Association, Vol. 74,No. 368.(Dec., 1979),pp. 829-836.
    [6]Phil Diamond, Fuzzy Least Squares, Information Sciences 46(3), 1988, pp.141
    -157
    [7] Pierpaolo D'Urso, Linear regression analysis for fuzzy/crisp input and fuzzy/crisp output data ,Computational Statistics & Data Analysis, Volume 42, Issues 1–2, (2003), pp.47–72.
    [8] P. Anand Raj, D. Nagesh Kumar, Ranking alternatives with fuzzy weights using maximizing set and minimizing set ,Fuzzy Sets and Systems,1999,pp365-375
    [3]吳柏林,模糊統計導論第二版(2015),五南出版社(台北),p153.
    [4]陳孝煒、吳柏林,區間回歸與模糊樣本分析,管理科學與統計決策, 4(1), 2007

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