傳統線性迴歸與模糊線性迴歸在預測應用方面的比較｜國立臺灣科技大學博碩士論文系統

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研究生：	李鴻毅 Hung-Yi Lee
論文名稱：	傳統線性迴歸與模糊線性迴歸在預測應用方面的比較 A Comparison on the Application of Prediction of Traditional Linear Regression and Fuzzy Linear Regression
指導教授：	徐世輝 Shey-Huei Sheu
口試委員:	陳坤盛 Kun-Sheng Chen 葉瑞徽 Ruey-Huei Yeh
學位類別：	碩士 Master
系所名稱：	管理學院 - 工業管理系 Department of Industrial Management
論文出版年：	2005
畢業學年度：	93
語文別：	中文
論文頁數：	51
中文關鍵詞：	迴歸分析、模糊迴歸分析、隸屬度、殘差值
外文關鍵詞：	Regression analysis, Membership, Fuzzy regression analysis, Residual
相關次數：	點閱：279 下載：7
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迴歸分析為一種利用兩個或多個數量型變數間的關係，使得其中一個變數可以用另外一個或是其他多個變數預測的統計方法。目前，迴歸分析被廣泛的應用於建構領域的模型如商業、工業、社會、教育、體育上。然而，這些模型並非所有的變數都是以單一數值(Crisp Value)的形式呈現，往往含有模糊的特質，也就是多重隸屬的特性，因此就要以模糊迴歸來做分析。傳統迴歸觀測值的不確定性來自於隨機，也就是殘差值是來自量測上的誤差；但是模糊迴歸的不確定性卻是來自於多重隸屬的現象。本論文的主要目的在比較傳統迴歸和模糊迴歸兩種不同的迴歸分析方法，並以臺灣機車工業為例，進行兩種方法在預測應用方面的比較。

Regression analysis is a method that uses the relationship of two or more quantified variables to make one of variables that can be predicted by another. At present, regression analysis is widely used to construct models for business, industry, society, and physical education. However, the variables in these models do not present completely as crisp values. They often have the quality of fuzzy. Hence, we do analysis by fuzzy regression.

The uncertainty of observable values of traditional regression is due to randomness, and residuals of traditional regression come from error of measurement or observation. However the uncertainty of observable values of fuzzy regression is due to the membership.

The objective of this article is to compare these two different analytical methods with the traditional regression and fuzzy regression. Finally, the author takes an example of motor industry in Taiwan to make a comparison on the application of prediction of these two methods.

中文摘要……………………………………………………………………………..Ⅰ
Abstract……………………………………………………………………………….Ⅱ
誌謝…………………………………………………………………………………..Ⅲ
目錄…………………………………………………………………………………..Ⅳ
圖目錄..........................................................................................................................Ⅵ
表目錄..........................................................................................................................Ⅶ
第一章 緒論………………………………………………………………..................1
1.1	研究動機與背景…………………………………………….……………..1
1.2	研究目的……………………………………………………………….….1
1.3	研究方法…………………………………………………………………..2
1.4	論文架構…………………………………………………….…………….2
第二章 文獻探討……………………………………………………………………..3
    2.1 傳統線性迴歸……………………………………………………………….3
        2.1.1 傳統線性迴歸的基本假設…………………………………………..3
        2.1.2 母體分配參數之點估計……………………………………………..5
    2.2 模糊理論…………………………………………………………………….6
        2.2.1 模糊集合……………………………………………………………..6
        2.2.2 模糊集合表示法……………………………………………………..6
        2.2.3  截集………………………………………………………………..7
    2.3 模糊迴歸模式……………………………………………………………...8
        2.3.1 模糊迴歸模式的架構………………………………………………8
        2.3.2 Tanaka提出的線性模糊迴歸模型………………………………….9
        2.3.3 參數估計……………………………………………………………10
第三章 模式的分析比較……………………………………………………………14
    3.1 使用方法的比較…………………………………………………………...14
    3.2 信賴區間與模糊區間……………………………………………………...14
    3.3 模糊區間的分析…………………………………………………………...15
        3.3.1 實際值因變數與實際值自變數……………………………………15
            3.3.1.1 使用線性規劃法求出模糊迴歸模式……………………….16
        3.3.2 模糊因變數與實際值自變數………………………………………18
            3.3.2.1 使用線性規劃法求出模糊迴歸模式……………………….19
    3.4 因變數分配的比較………………………………………………………...23
    3.5 轉換技巧…………………………………………………………………...26
        3.5.1 傳統迴歸的資料轉換………………………………………………26
        3.5.2 模糊迴歸的資料轉換………………………………………………27
    3.6 Tanaka模糊迴歸模式的缺失………………………………………………27
        3.6.1 Tanaka所提出的線性規劃模型在限制式上的缺失……………….27
        3.6.2 Tanaka所提出的線性規劃模型在預測上的缺失………………….28
    3.7 本章之結論與建議…………………………………………………………29
第四章 數值分析-以台灣機車工業為例…………………………………………...30
    4.1台灣車輛工業概述…………………………………………………………30
    4.2 台灣機車工業概況………………………………………………………...30
    4.3 影響國內機車總產值之因素……………………………………………...31
    4.4 兩種迴歸方法之應用……………………………………………………...35
        4.4.1 傳統迴歸模式………………………………………………………35
        4.4.2 模糊迴歸模式………………………………………………………37
    4.5 兩種迴歸方法之分析比較………………………………………………...38
第五章 結論與後續探討……………………………………………………………40
參考文獻……………………………………………………………………………..41
附錄-模糊係數之求解……………………………………………………………….44
作者簡介……………………………………………………………………………..51

                                

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