- 學位論文
以多目標規劃法建構模糊迴歸模型
Constructing the Fuzzy Regression Model by Multi-Objective Programming
摘要
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。
並列摘要
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.