臺灣博碩士論文加值系統

傳統迴歸分析是一種重要的分析工具，能夠協助決策者了解自變數與因變數之間的因果邏輯關係，但考量到真實社會存在著許多不確定性的現象，進而發展出模糊迴歸分析法 (Fuzzy Regression)，能夠更貼近地分析存在模糊或不確定性的真實社會問題。原始的模糊迴歸分析法會因為觀測值的個數增加時，迴歸係數的模糊度會加大，致使因變數估計值的展度變大，產生迴歸模型之預測準確度下降的問題。因此為了以提升整個模型準確度，本研究以多目標規劃法 (Multi-objective Programming)的數學模式求解二次規劃法 (Quadratic Programming)之模糊迴歸模型，其中考慮了最小平方集中趨勢 (The Property of Central Tendency in Least Squares)、模楜迴歸的可能性質 (The possibilistic Property in Fuzzy Regression)與配適度 (Fitness)作為目標式。採用二次規劃法於模糊迴歸分析中，是由於二次規劃法相較於線性規劃法會有更多的展度 (Spread)係數，且能夠在模糊迴歸中整合集中趨勢 (Integrating Central Tendency)和模糊迴歸的可能性質 (Possibilistic Property of Fuzzy Regression)；其中結合多目標規劃的優點是可考慮對於多個目標衝突時的權衡取捨 (Trade-Off)，以提供決策者更有效地預測不確定性的現象。最後本論文透過三個案例進行實證研究，研究結果顯示此一模式確實能夠改善傳統迴歸的缺點。

The traditional regression analysis is an important analysis tool, it can help the decision makers to know the relationship between the dependent and independant variables. The real world exists a lot of uncertainty, therefore the fuzzy regression is develope. Fuzzy regression can be used to analyze the social problems that exist fuzziness or uncertainty. Original fuzzy regression analysis increases the fuzziness when the number of the observed data increases that causing the spread of estimated value increases, and the forecasting accuracy of fuzzy regression model decreasing. In order to improve the entire model accuracy, this study uses multi-objective programming in quadratic programming of fuzzy regression model, considering the property of central tendency in least squares, the possibilistic property in fuzzy regression and fitness of the model. Comparing with linear programming, the quadratic programming can give more diverse spread coefficient. So this study uses quadratic programming in the interval regression analysis. And in the interval regression that integrating central tendency and possibilistic property of fuzzy regression, combining with multi-objective programming that considers how to trade-off multiple objectives. Providing the decision makers effectively forecast the uncertain phenomenon. Finally, this study uses three empirical examples to prove the usefulness and efficiency. The research results show that the fuzzy regression is able to improve the tradition regression defects.

目錄

摘要 i
ABSTRACT ii
誌謝 iv
目錄 v
表目錄 vii
圖目錄 viii
第一章 緒論 1
1.1研究背景與動機 1
1.2研究目的 3
1.3研究方法 4
1.4研究架構與流程 4
第二章 文獻探討 6
2.1模糊迴歸分析 6
2.2多目標規劃法 14
第三章 研究方法 20
3.1模糊迴歸模式之建構 20
3.1.1 二次模糊迴歸模式 21
3.1.2 二次規劃法整合可能性和必要性模式 22
3.1.3 配適度 25
3.2模糊多目標規劃 26
3.3結合多目標與模糊迴歸分析 29
3.3.1模糊迴歸分析之單目標規劃問題 29
3.3.2多目標規劃之模糊迴歸分析 30
第四章 例題演算與分析 34
4.1例題分析 34
4.1.1案例一 34
4.1.2案例二 40
4.1.3案例三 46
4.2討論 49
第五章 結論與建議 51
5.1結論 51
5.2建議 53
參考文獻 55
附錄
A 線性模糊迴歸模型 61
B 二次模糊迴歸模型 63
C 集中趨勢、模糊迴歸可能性質、配適度三者想上界值與下界值 65
D 多目標規劃法建構糊迴歸模型 71


表目錄

表2.1 模糊迴歸分析相關研究文獻整理 13
表2.2 傳統多目標求解方法 16
表2.3 多目標規劃相關研究文獻整理 18
表3.1 多目標規劃償付表(payoff table) 27
表4.1 日本房屋售價之數據 34
表4.2 線性模糊迴歸係數之參數 35
表4.3 二次模糊迴歸係數之參數 36
表4.4 各目標之理想上界值與下界值 37
表4.5 多目標規劃法建構模糊迴歸模型之模糊係數 38
表4.6 各模型之模糊係數比較表 39
表4.7 Tanka and Lee (1998)二次規劃法建構區間模糊迴歸模型之數據 41
表4.8 二次規劃法整合可能性和必要性模式係數之參數 41
表4.9 配適度數據 42
表4.10 各目標之理想上界值與下界值 42
表4.11 多目標規劃法建構模糊迴歸模型係數之參數 43
表4.12 配適度數據 43
表4.13 模糊迴歸的可能性質比較表 45
表4.14 各品牌鞋子之獲利額數據 46
表4.15 線性模糊迴歸係數之參數 47
表4.16 二次模糊迴歸係數之參數 47
表4.17 各目標之理想上界值與下界值 47
表4.18 多目標規劃法建構模糊迴歸模型係數之參數 47


圖目錄

圖1.1 研究流程圖 5
圖3.1 可能性模型Y*(xj)，必要性模型Y*(xj)和給定的區間Yj 23
圖3.2 目標式隸屬函數圖 28
圖4.1 三種模型之預測區間範圍 39
圖4.2 三種模型之單點預測區間範圍 40
圖4.3 兩種求解方法之可能性與必要性模型 44

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