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    題名: 模糊資料之無母數檢定法
    Nonparametric test wiht fuzzy data
    作者: 陳思穎
    Chen, Shih Ying
    貢獻者: 吳柏林
    陳思穎
    Chen, Shih Ying
    關鍵詞: 模糊無母數檢定
    日期: 2005
    上傳時間: 2009-09-17 13:47:21 (UTC+8)
    摘要: 傳統的統計方法檢定都假定資料來自於某個分配，但若假設檢定包含著不確定性時，有關模糊數的假設檢定有其重要性。由此可知，模糊統計推論已逐漸受到重視，這是符合現在複雜的社會現象所自然發展的結果。針對模糊資料，本文嘗試以簡易的計算配合模糊理論，定義出模糊數及模糊區間的排序方法，並將此方法應用在檢定上。即針對傳統無母數檢定方法，在無法解決參數假設為模糊數或是模糊區間值的情形下，為改進此一缺點，本文提出模糊Kruskal-Wallis檢定和Run test檢定。由實証的例子顯示，本文提出的檢定方法能有效解決模糊樣本問題。
    再者，傳統的統計迴歸模式，假設觀察值的不確定性來自於隨機現象，但模糊迴歸則考慮不確定性來自於多重隸屬現象。因而以無母數統計方法，配合模糊迴歸理論，進而提出模糊無母數迴歸Theil法，並應用實際的例子，以顯示其存在的實質意義。
    Traditional statistical hypothesis testing is completely assumed that the data are from some statistical distribution. However if the data includes many uncertainties, fuzzy hypothesis testing will be useful in this condition. Thus it can be seen that fuzzy inferential statistics is gradually emphasized in modern world due to the development of complex social phenomenon. In this paper, the ordination technique, based on the fuzzy data, of fuzzy numbers and intervals will be defined by simple computations with fuzzy theories, and this technique will be applied to statistical testing. In another word, traditional nonparametric statistical hypothesis testing could not deal with the data from fuzzy numbers or intervals. To be successful for this, we provide Kruskal-Wallis Test and Run Test in this paper. The testing techniques mentioned by this paper could solve the limitation of fuzzy samples. Some empirical examples will be given to show for this.
    Furthermore, traditional statistical regression models assume that the uncertainty of the observed values is from random sampling. Nevertheless, fuzzy statistical regression models assume that the uncertainty of the observed data is from the phenomenon of Multiple Membership. Therefore we bring up Theil fuzzy nonparametric regression model considering nonparametric statistical techniques and fuzzy regression models. One practical example is given to show the application for this fuzzy nonparametric regression model in this paper.
    參考文獻: 原文部份
    Brown, G. W., & Mood, M. A. (1951). On Median Tests for Linear Hypotheses in J. Neyman(ed), Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability, 159-166. Berkeley and Los Angeles: The University of California Press.
    Cheng, C. H. (1998). A new approach for ranking fuzzy numbers by distance method, Fuzzy Sets and Systems, 95, 307-317.
    Clymer, J., Corey, P., & Gardner, J.(1992). Discrete Event Fuzzy Airport Control. IEEE Transactions on Systems, Man, and Cybernetics, 22(2), 343-351.
    Custem, B. V., & Gath, I. (1993). Detection of outliers and robust estimation using fuzzy clustering. Computational Statistics and Data Analysis, 15, 47-61.
    Chen, S. J.,& Hwang C. L.(1992) . Fuzzy multiple attribute decision making : methods and applications. Berlin ; New York
    Dubois, D., & Prade, H. (1991). Fuzzy sets in approximate reasoning, Part 1：Inference with possibility distribution, Fuzzy Sets and Systems, 40, 143-202.
    Kaufmann, A., & Gupta, Madan M. (1988). Fuzzy mathematical models in engineering and management science. Amsterdam ; New York : North-Holland.
    Lowen, R. (1990) A fuzzy language interpolation theorem. Fuzzy Sets and Systems, 34, 33-38.
    Liou, T. & Wang, J（1992）. Fuzzy Weighted Averag：An Improved Algorithm. Fuzzy Sets And Systems, 87, p307－315.
    Manski, C. (1990) The Use of Intention Data to Predict Behavior：A Best Case Analysis. Journal of the American Statistical Association, 85, 934-940.
    Romer, C., Kandel, A., & Backer, E. (1995). Fuzzy partitions of the sample space and fuzzy parameter hypotheses. IEEE Transs. Systems, Man and Cybernet, 25(9), 1314-1321.
    Ruspini, E.(1991). Approximate Reasoning：past, present, future. Information Sciences, 57, 297-317.
    Tanaka, H., Uejima, S. and Asai, K.(1980). Fuzzy linear regression model. International Congress on Applied Systems Research and Cybernetics. Aclpoco, Mexico.
    Wu, B., & Hung, S. (1999). A fuzzy identification procedure for nonlinear time series：with example on ARCH and bilinear models. Fuzzy Set and System, 108, 275-287.
    Yoshinari, Y., W. Pedrycz and K. Hirota (1993). Construction of Fuzzy Models through Clustering Techniques. Fuzzy Sets and Systems, 54, 157-165.
    中文部份
    吳柏林，（2005）。模糊統計導論方法與應用， 159-173。台北：五南書局。
    阮亨中、吳柏林，（2000）。模糊數學與統計應用， 233-250; 319-341。台北：俊傑書局。
    吳柏林，（1999）。現代統計學，252-255。台北：五南書局。
    顏月珠，（1992）。無母數統計方法。台北: 三民書局。
    描述: 碩士
    國立政治大學
    應用數學研究所
    93751015
    94
    資料來源: http://thesis.lib.nccu.edu.tw/record/#G0093751015
    資料類型: thesis
    顯示於類別:[應用數學系] 學位論文

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