Loading...
|
Please use this identifier to cite or link to this item:
https://nccur.lib.nccu.edu.tw/handle/140.119/99612
|
Title: | 區間迴歸與模糊資訊分析及應用 Interval regression analysis with fuzzy data |
Authors: | 蔡皓旭 Cai, Hao Xu |
Contributors: | 陳政輝 蔡皓旭 Cai, Hao Xu |
Keywords: | 區間模糊迴歸 懸浮微粒 台灣加權股價指數 區間模糊數 Fuzzy regression Suspended Particulate Matter TAIEX Interval fuzzy number |
Date: | 2016 |
Issue Date: | 2016-08-03 10:15:04 (UTC+8) |
Abstract: | 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. |
Reference: | [1] 吳柏林(2015),模糊統計導論-方法與應用,五南出版社 [2] 陳孝煒、吳柏林(2007),區間迴歸與模糊樣本分析,管理科學與統計決策,4,54-65 [3] 楊敏生(1994),模糊理論簡介,數學傳播季刊,18 [4] 邱鼎泰(2012),學習技術分析,理財周刊,614 [5] 李聯雄、賴嘉祥(2011),大陸沙塵暴對我國室外作業勞工健康影響之研究,行政院勞工委員會勞工安全衛生研究所 [6] 溫志中、蔡立宏、楊尚威(2009)台灣港區大氣能見度特性探討-基隆、台中、高雄,港灣報導,82,31-39 [7] 蔡春進、繆敦耀、簡聰智、陳泰任(1999),裸露地逸散性粒空氣污染物的控制技術研究,第十六屆空氣污染控制技術研討會,台中朝陽科技大學台灣 [8] 細懸浮微粒(PM_2)對人體健康危害之預防策略研究公聽會(2013),國家衛生研究院國家環境毒物研究中心 [9] 江世民(1999),台北地區臭氧及懸浮微粒型態與其他汙染物及氣象條件之分析比較,第十六屆空氣污染控制技術研討會,台中朝陽科技大學 [10] 潘南飛、李思賢(2005),模糊迴歸用於分析作業之工期,工程科技與教育學刊,2,152-160 [11] 台灣十大死因 都是空氣惹的禍,遠見雜誌 [12] Wu, B. & Tseng, N. (2002). A new approach to fuzzy regression models with application to business cycle analysis. Fuzzy Sets and System. 130, 33-42. [13] Zadeh, L.A. (1965). Fuzzy sets, Information and Control 8, 338-353. [14] Tanaka, H. & Uejima, S. & Asai, K. (1980). Fuzzy Linear Regression Model. International Congress on Applied Systems Research and Cybernetics. Aculpoco, Mexico. [15] Tanaka, H. & Uejima, S. & Asai, K. (1982). Linear Regression Analysis with Fuzzy model. IEEE Trans. SystemsMan Cybernet, vol SMC 12, 903-907. [16] Diamond, P. (1988). Fuzzy least squares, Information Sciences 46(3), 141-157. [17] Curtis, R. K, (1990) .Complexity and predictability: The application of chaos theory to economic forecasting. Futures Research Quarterly, 6(4), 57-70. [18] Kacprzyk J. & Fedrizzi M. (1992). Fuzzy Regression Analysis. [19] Tanaka, H. & Ishibuchi, H. (1993). Anarchitecture of neural networks with interval weights and its application to fuzzy regression analysis. Fuzzy Sets and Systems, 57, 27-39. [20] Chang P. T. & Lee E. S., (1994), Fuzzy Linear Regression with spreads Unrestricted in Sign,Computers Math. Applic, 281994, 61-70. [21] Chang P. T. et al, (1996). Applying fuzzy linear regression to VDT legibility, Fuzzy Sets and Systems, 80, 197-204. [22] Chang Yun-His O. & Ayyub, B. M (1996). Hybrid Fuzzy Regression Analysis and Its applications. Uncertainty Modeling and Analysis in Civil Engineering, CRC Press Inc. 33-41. [23] Chang P. T. (1997). Fuzzy Seasonality Forecasting. Fuzzy Sets and Systems, 90, 1-10. [24] Yen K. K. & Ghoshray S. & Roig G. (1999). A Linear Regression Model Using Triangular Fuzzy Number Coefficient, Fuzzy Sets and Systems, 106, 167-177. [25] Wang H. F. & Tsaur R. C. (2000). Insight of a fuzzy regression model, Fuzzy Sets and Systems, 112, 355-369. [26] Lee, H. T. & Chen, S. H. (2001). Fuzzy regression model with fuzzy input and output data for manpower forecasting, Fuzzy Sets and Systems, 119, 205-213. [27] Tseng Yu-Heng & Paul Durbin & Tzeng Gwo-Hshiung (2001). Using a Fuzzy Piecewise Regression Analysis to Predict the Nonlinear Time-Series of Turbulent Flows with Automatic Change-Point Detection, Flow, Turbulence and Combustion, 67, 81–106. [28] Kao Chiang & Chyu Chin - Lu (2002). A fuzzy linear regression model with better explanatory power. Fuzzy Sets and Systems, 126(3), 401-409 [29] Kutner & Nachtsheim & Neter (2004). Applied Linear Regression Model, Fourth Edition. [30] Reza Ghodsi & MohammadSaleh Zakerinia & Mahdi Joka (2010). Neural network and Fuzzy Regression Model for Forecasting Short Term Price in Ontario Electricity Market. Proceedings of the 41st International Conference on Computers & Industrial Engineering.954-959. [31] Ul-Saufie A.Z & Yahya A.S & Ramli N.A (2010). Improving multiple linear regression model using principal component analysis for predicting PM_10 concentration in Seberang Prai, Pulau Pinang, International Journal Of Environmental Sciences Vol2, No 2, 2011. [32] Ghodratollah Emamverdi & Ebrahim Siami Araghi & Fatemeh Fahimifar (2013). Presenting a Fuzzy ARIMA Model for Forecasting Stock Market Price Index of Iran. J. Basic. Appl. Sci. Res, 3(6), 37-43, 2013. [33] Arwa S. Sayegh & Said Munir & Turki M. Habeebullah (2014). Comparing the Performance of Statistical Models for Predicting PM_10 Concentrations, Aerosol and Air Quality Research, 14, 653–665. [34] Liem Tran & Lucien Duckstein (2002). Comparison of fuzzy numbers using a fuzzy distance measure, Fuzzy Sets and Systems, 130, 331-341. |
Description: | 碩士 國立政治大學 應用數學系 103751009 |
Source URI: | http://thesis.lib.nccu.edu.tw/record/#G0103751009 |
Data Type: | thesis |
Appears in Collections: | [應用數學系] 學位論文
|
Files in This Item:
File |
Size | Format | |
100901.pdf | 888Kb | Adobe PDF2 | 416 | View/Open |
|
All items in 政大典藏 are protected by copyright, with all rights reserved.
|