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| Title: | 模糊資料之軟統計分析及檢定 |
| Authors: | 張建瑋
Chang ,Chien-Wei |
| Contributors: | 吳柏林
鄭宇庭
張建瑋
Chang ,Chien-Wei |
| Keywords: | 模糊數
模糊區間
軟統計分析
模糊平均數
模糊變異數
估計
最佳估計
無母數檢定
時間數列
相似性 |
| Date: | 2005 |
| Issue Date: | 2009-09-17 18:47:26 (UTC+8) |
| Abstract: | 本文將模糊理論的觀念，應用在估計、檢定及時間數列分析上。研究重點包括離散型及連續型模糊樣本的定義與度量，模糊參數的最佳估計，模糊排序方法應用於無母數檢定，模糊相似度的定義、性質，以及如何將其應用於辨識不同時間數列間的落差l期相似程度等。我們首先將常見的模糊資料分為離散型及連續型，並針對不同類型的資料，給定對應的模糊平均數、模糊變異數等模糊參數的概念與一些重要性質。接著我們提出幾種估計方法，針對不同的模糊參數進行最佳估計並提出可行的評判準則。進一步地，我們將模糊排序方法應用於無母數檢定推論。最後我們提出模糊相似度的定義與度量。經由系統性的模擬與分析，我們建立兩時間數列間模糊相似度演算法則。實證分析方面，我們利用提出的方法對台灣的股價加權指數、個股股價進行估計及檢定；同時，針對台灣歷年GDP、民間消費、毛投資間的相似性進行偵測，以驗證我們提出的模糊參數估計、模糊無母數檢定及模糊相似度演算法的效率性與實用性。
In this paper, we apply fuzzy theory in estimation, nonparametric test, and time series analysis. Our focus is on: How to define and measure the discrete type fuzzy data and continuous one? How to find the optimal estimators for fuzzy parameters? How to apply fuzzy ranking methods in nonparametric test when the data is vague? How to define and find the degree of fuzzy similarity between two time series? First, fuzzy data is classified according to its type, discrete or continuous. Then we give some definitions and properties on fuzzy mean, fuzzy variance for different type of fuzzy data. Next, we proposed some estimating methods and evaluation rules. Moreover we apply fuzzy ranking methods in nonparametric test, such as Sign test, Wilcoxon signed rank test, Wilcoxon rank sum test, and so on. Finally, we suggest the definitions as well as the algorithm for computing the degree of fuzzy similarity between two time series. We also give some simulate and empirical examples to illustrate the techniques and to analyze fuzzy data. Results show that fuzzy statistics with soft computing are more realistic and reasonable for the social science research. |
| Reference: | 中文部分
[1]. 吳柏林 (1995). 模糊統計分析:問卷調查研究的新方向.國立政治大學研究通訊,2, 65-80.
[2]. 吳柏林 (1997). 社會科學研究中的模糊邏輯與模糊統計分析.國立政治大學研究通訊,7, 17-38.
[3]. 吳柏林, 曾能芳 (1998). 模糊迴歸參數估計及在景氣對策信號之分析應用. 中國統計學報. 36(4), 399-420
[4]. 吳柏林, 楊文山 (1997). 模糊統計在社會調查分析的應用.社會科學計量方法發展與應用. 楊文山主編:中央研究院中山人文社會科學研究所. 289-316
[5]. 李允中, 王小璠, 蘇木春 (2003). 模糊理論及其應用. 全華科技圖書股份有限公司.
[6]. 張建瑋、吳柏林 (1996) “非線性時間數列的分類與預測”，第三屆三軍官校基礎學術研討會，25-46。
英文部分
[1]. Buckley, J. J. (2003). Fuzzy Probabilities: New Approach and Applications, Physics-Verlag, Heidelberg, Germany.
[2]. Buckley, J. J. (2004). Fuzzy Statistics, Springer-Verlag, Heidelberg, Germany.
[3]. Carlsson, C., Fuller, R. (2001). On possibilistic mean value and variance of fuzzy numbers, Fuzzy Sets and Systems, 122, 315-326.
[4]. Casals, M. R., Gil, M. A. and Gil, P. (1986) The fuzzy decision problem: An approach to the problem of testing statistical hypotheses with fuzzy information, European Journal of Operational Research, 27, 371-382.
[5]. Casals, M. R. and Gil, P. (1994) Bayesian sequential test for fuzzy parametric hypotheses from fuzzy information, Information Sciences, 80, 283-298.
[6]. Cheng, C. H. (1998). A new approach for ranking fuzzy numbers by distance method, Fuzzy Sets and Systems, 95, 307-317.
[7]. Chen, L. H., Kao, C., Kuo, S., Wang, T. Y., and Jang, Y. C. (1996), “Productivity Diagnosis via Fuzzy Clustering and Classification: An Application to Machinery Industry,” Omega, Int. J. Mgmt Sci., 24(3), 309-319.
[8]. Chen S. J. and Huang, C. L. (1992). Fuzzy multiple attribute decision making methods and applications, Lecture Notes in Economics and Mathematical Systems, Springer, New York.
[9]. Chen, S. M. (1996). Forecasting enrollments based on fuzzy time series. Fuzzy Sets and Systems, 81, 311-319.
[10]. Dubois, D. and Prade, H (1987). The mean value of a fuzzy number, Fuzzy Sets and Systems, 24, 279-300.
[11]. Dumitrescu, D. and Dumitrescu, A. (1997). A Unified Approach to Fuzzy Pattern recognition, European Journal of Operational Research, 96 , 3, 471-478.
[12]. Freeling, ANS. (1980). Decision analysis and fuzzy sets, Masters Thesis. Cambridge University, England.
[13]. Galvo, T., and Mesiar, R. (2001). Generalized Medians, Fuzzy Sets and Systems, 124, 59-64.
[14]. Gebhardt, J., Gil, M. A., and Kruse, R. (1998). Fuzzy set-theoretic methods in statistics, in: R. Slowinski(Ed.), Handbook on Fuzzy Sets, Fuzzy Sets in Decision Anaysis, Operations Research, and Statistics, vol. 5, Kluwer Academic Publishers, New York, 311-347.
[15]. Gil, M. A., Corral, N. and Gil, P. (1985). The fuzzy decision problem: An approach to the point estimation problem with fuzzy information, European Journal of Operational Research, 22, 26-34.
[16]. Gil, M. A., Corral, N. and Gil P. (1988). The minimum inaccuracy estimates in tests for goodness of fit with fuzzy observations, Journal of Statistical Planning and Inference, 19, 95-115.
[17]. Guegan, D. and Pham, T. D. (1992), “Power of the Score Test Against Bilinear Time Series Models,” Statistica Sinica, Vol. 2, 1, 157-169.
[18]. Hathaway, R. J. and Bezdek, J. C. (1993). Switching Regression Models and Fuzzy Clustering. IEEE Transactions of Fuzzy Systems, 1, 195-204.
[19]. Heilpern, S. (1992). The expected value of a fuzzy number, Fuzzy Sets and Systems, 47, p81–86.
[20]. Hung, W. L. and Wu, J. W., (2002). Correlation of fuzzy numbers by α-cut method, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 10, 725-735.
[21]. Hwang, C.M. and Yao, J.S. (1996). Independent Fuzzy Random Variables and their Application. Fuzzy Sets and Systems, Vol. 82, p335-350.
[22]. Kaufmann A., Gupta M. M. (1988). Fuzzy mathematical models in engineering and management science, Elsevier Science Publishers BV, New York.
[23]. Klir, G. and Yuan, (1995). Fuzzy Sets and Fuzzy Logic－Theory and Applications. Prentice-Hall, Upper Saddle River, NJ.
[24]. Korner, R. (1997). On the Variance of Fuzzy Random Variables. Fuzzy Sets and Systems, Vol. 92, p83-93.
[25]. Kosko, B. (1993). Fuzzy thinking : the new science of fuzzy logic. Hyperion, New York.
[26]. Kumar, K. and Wu, B. (2001). Detection of change points in time series analysis with fuzzy statistics. International Journal of Systems Science. 32( 9), 1185- 1192.
[27]. Lee, T. S., Chiu, C. C., and Lin, F. C. (2001). Prediction of the unemployment rate using fuzzy time series with Box-Jenkins Methodology, International Journal of Fuzzy Systems, 3(4), 577-585.
[28]. Lin C. C., and Chen, A. P.(2004). Fuzzy discriminant analysis with outlier detection by genetic algorithm, Computers & Operations Research, 31(6), 877.
[29]. Liou, T. S., and Wang, M. J. (1992). Ranking fuzzy numbers with integral value, Fuzzy Sets and Systems, 50, 247-255.
[30]. Liu, S. T. and Kao, C. (2002). Fuzzy measures for correlation coefficient of fuzzy numbers. Fuzzy Sets and Systems, 128, 267-275
[31]. Manton¸K. Woodbury¸K. and Tolley, H. (1993). Statistical Applications – Using Fuzzy Set. John Willy & Sons, Inc.¸New York.
[32]. Milan Mares (1994). Computation over Fuzzy Quantities. Boca Raton, Fla: CRC.
[33]. Mitra, S. and Pal, S. K. (1994), “Self-Organizing Neural Network as a Fuzzy Classifier,” IEEE,Transactions on System,Man and Cybernetics, 24:3, 385-399.
[34]. Miyamoto, S. (1990). Fuzzy Sets in Information Retrieval and Cluster Analysis. Kluwer Academic, Boston.
[35]. Nguyen, H and Wu, B. (2000) Fuzzy Mathematics and Statistical Applications. Hua-Tai Book Company, Taipei
[36]. Saade J., and Schwarzlander H. (1990). Fuzzy hypothesis testing with hybrid data, Fuzzy Sets and Systems, 35, 197-212.
[37]. Saade J. (1994). Extension of fuzzy hypothesis testing with hybrid data, Fuzzy Sets and Systems, 63, 57-71.
[38]. Saikonen, P. and Luukkonen, R. (1988). Lagrange Multiplier Testts for Testing Nonlinearities in Time Series Models, Scand Joural of Statistics, 15, 55-68.
[39]. Saikonen, P. and Luukkonen R. (1991). Power Properties of a Time Series Linearity Test Against Some Simple Bilinear Alternatives, Statistica Sinica, 1, (2), 453-464.
[40]. Simpson, P. K. (1993), Fuzzy Min-Max Neural Networks-Part2:Clusting, IEEE, Transactions on Fuzzy System, 1:1, 32-45.
[41]. Song, Q. and B. S. Chissom (1993a). Forecasting enrollments with fuzzy time series—Part I. Fuzzy Sets and Systems, 54, 1-9.
[42]. Song, Q. and B. S. Chissom (1993b). Fuzzy time series and its models. Fuzzy Sets and Systems, 54, 269-277.
[43]. Song, Q., and Chissom, B. S. (1993c). Forecasting Enrollments with Fuzzy Time Series-Part II, Fuzzy Sets and Systems, 54, 1-9.
[44]. Stojakovic, M. (1992). Fuzzy Conditional Expectation. Fuzzy Sets and Systems, Vol. 52, p53-60.
[45]. Stojakovic, M. (1994). Fuzzy Random Variables, Expectation, and Martingales . Journal of Mathematical Analysis and Applications, Vol. 184, p594-606.
[46]. Tsay, R. S. (1991). Detecting and Modeling Nonlinearity in Univariate Time Series Analysis, Statistica Sinica, 1, (2), 431-451.
[47]. Tseng F. M., Tzeng G. H., Yu H. C., and Yuan, J. C. (2001). Fuzzy ARIMA model for for forecasting the foreign exchange market, Fuzzy Sets and Systems, 118, 9-19.
[48]. Watanabe, N. and Imaizumi, T. (1993). A fuzzy statistical test of fuzzy hypotheses. Fuzzy Sets and Systems, 53, 167-178.
[49]. Wilcoxon, F. (1945). Individual comparisons by ranking methods, Biometrics, 3, 80-83.
[50]. Wong, Z. and Klir G. J. (1992). Fuzzy Measure Theory. New York: Plenum Press.
[51]. Wu, B. and Chen, M. (1999). Use fuzzy statistical methods in change periods detection. Applied Mathematics and Computation. 99, 241-254.
[52]. Wu, H. C. (1999). Probability density functions of Fuzzy Random Variables. Fuzzy Sets and Systems, Vol. 105, p139-158.
[53]. Wu, H. C. (2000). The Law of Large Numbers for Fuzzy Random Variables. Fuzzy Sets and Systems, Vol. 116, p245-262.
[54]. Wu, H. C. (2003). The fuzzy estimators of fuzzy parameters based on fuzzy random variables, European Journal of Operational Research, 146(1), 101-114
[55]. Yang, M. (1993). A survey of Fuzzy Clustering. Math. Compu. Modelling, 18(11), 1-16.
[56]. Yang, M. and Ko, C. (1997). On cluster-wise fuzzy regression analysis. IEEE Trans. Systems Man Cybernet, vol 27, 1-13.
[57]. Yun, K. K. (2000). The Strong Law of Large Numbers for Fuzzy Random Variables. Fuzzy Sets and Systems, Vol. 111, p319-323.
[58]. Zadeh, L. A. (1965). Fuzzy Sets. Information and Control, 8, 338-353.
[59]. Zimmermann, H. J. (1991) Fuzzy Set Theory and Its Applications. Boston: Kluwer Academic. |
| Description: | 博士
國立政治大學
統計研究所
88354505
94 |
| Source URI: | http://thesis.lib.nccu.edu.tw/record/#G0883545052 |
| Data Type: | thesis |
| Appears in Collections: | [統計學系] 學位論文
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