動機與目的：傳統的統計迴歸模式假設觀測值的不確定性來自於隨機現象，而模糊迴歸則考慮不確定性來自於多重隸屬現象。不同的模型建構所得到的估計值也不一致。如何衡量模型的優劣程度，至今仍沒有一套嚴謹的標準。 研究方法：本研究以區間模糊數建構模糊迴歸模式，如此一來對樣本的解釋方式將更為貼近現實，並提出一套區間模糊數距離測度，以衡量估計值與實際值之間的差距。實證分析中（懸浮微粒PM_10濃度預測、台灣加權股價指數預測），我們藉由此距離測度衡量二維模糊迴歸與傳統二項最小平方法對於樣本的配適性。 創新與推廣：提出區間模糊數距離衡量估計值與原樣本之差異程度。在符合傳統統計迴歸精神之下，當距離最小就是差異最小的估計，最能符合所抽取的樣本，也是最佳估計。 重要發現：利用本區間模糊數距離測度，我們發現二維模糊迴歸方法比起傳統二項最小平方法更有效率且廣義殘差（generalized residual）將更小。 結論：過去以來，我們對於模糊迴歸架構一直都沒有完整的衡量標準。文中我們定義區間模糊數區間距離與平均距離，並推導賦距空間等性質。結合實例分析及應用，建構一合適模糊迴歸模式，以利統計決策分析參考。 / Objective: This study concerns how to develop effective fuzzy regression models. In the literature, little is addressed on how to evaluate the effectiveness of fuzzy regression models developed with different regression methods. We consider this issue in this work and present a framework for such evaluation. Method: We consider fuzzy regression models developed with different regression approaches. A method to evaluate the developed models is proposed. We then show that the proposed method possesses desirable mathematical properties and it is applied to compare the two-dimensional regression method and the traditional least square based regression method in our case studies: predicating the concentration of and the volatility of the weighted price index of the Taiwanese stock exchange. Innovation: We propose a new metric to define a distance between two fuzzy numbers. This metric can be used to evaluate the performance of different fuzzy regression models. When a prediction from one model is closest to the sample data measured in terms of the proposed metric, it can be recognized as the optimal predication. Results: Based on the proposed metric, it can be obtained that the two-dimensional fuzzy regression method is better than the traditional least square based regression method. Especially, its resulting generalized residual is smaller. Conclusion: In the literature, no unified framework has been previously proposed in evaluating the effectiveness of developed fuzzy regression models. In this work, we present a metric to achieve this goal. It facilitates the work to determine whether a fuzzy regression model suitably fits obtained samples and whether the model has potential to provide sufficient accuracy for follow-up analysis in a considered problem.

都市發展固然帶動了經濟成長、生活舒適、交通便利等諸多正面效益，但隨著都市不斷向外發展之成果，卻也帶來了都市內的空間擁擠、交通壅塞、空氣汙染、生活環境惡化等現象，以及都市外的分散、無秩序蔓延發展等環境問題。為解決這些問題，都市規劃者提出大眾運輸導向發展理念。從都市化之觀點來看，發展大眾運輸導向能降低都市蔓延，提昇都市內之使用密度，減少私人運具之使用，進而降低能源消耗、改善空氣品質。然而，運輸建設具有改變土地使用模式與活動區位，進而帶動人口、產業在空間上重新分布的特性；當運輸建設的興建促使周邊都市活動頻繁時，少有研究探討到大眾運輸導向帶來的效益，是否會隨著人口、產業往捷運沿線聚集，反而使交通流量增加，進而造成空氣品質愈加惡化之問題。因此，本研究從捷運營運前後台北市空氣品質變化之觀點，以台北市433個里之1995年至2006年為研究範圍，以懸浮微粒為汙染變數，運用空間分析法和長期追蹤資料實證分析法，探討捷運、人口及產業三者對空氣品質之影響程度。 / 研究結果顯示，人口密度和就業密度對懸浮微粒濃度有顯著正向影響，因此，政府在推廣大眾運輸導向理念，鼓勵人口和產業往捷運沿線發展時，需有完善配套措施，否則將導致反效果－空氣品質的惡化。而有捷運經過之村里對懸浮微粒濃度有顯著正相關；但是分析各年度懸浮微粒可發現，台北市年平均懸浮微粒濃度下降，且隨捷運路網愈加完善，空氣品質愈好。因此，捷運建設雖造成沿線懸浮微粒濃度的上升，但卻降低了整體懸浮微粒濃度，提昇台北市空氣品質。 / Urban development is driven by economic growth, comfortable living, convenient transportation and other positive benefits. However, the results of urban development also brought crowdedness, traffic congestion, air pollution, environment degradation inside the city, and sprawl development out of the city. To solve these problems, urban planners proposed mass transit-oriented development (TOD) concept. From the perspective of urbanization, developing TOD can reduce urban sprawl, enhance the use of space inside the city, and reduce the use of cars. Further, these can decrease energy consumption and improve air quality. However, a transportation system can change the land-use patterns and redistribute the population and industries. Few studies have discussed whether the benefits of TOD will gather people and industries along the mass rapid transit (MRT), where results in the increase in traffic and more deterioration of air quality are inconclusive. Therefore, from the perspective of air quality varies over time in Taipei before and after the operation of MRT, this study uses spatial analysis and panel data analysis to investigate the impact of MRT, population and industry on air quality in 433 villages of Taipei City from 1995 to 2006. / The results show that population density and employment density have significant positive effects on the concentrations of PM10. Thus, when promoting the concept of TOD and encouraging the development of population and industry along the rapid transit, the Government should plan and implement the proper procedure; otherwise they will result in rising air pollution. The villages along the rapid transit have significant positive effects on the concentrations of PM10. However, analysis of the annual PM10 concentration can be found that the annual average has declined in Taipei City; the air quality will be better with a more extensive rapid transit network. Although the construction of transit system will cause the increase in the concentration of PM10 along the rapid transit, it has decreases the overall concentration of PM10 in Taipei City.