English  |  正體中文  |  简体中文  |  Post-Print筆數 : 27 |  Items with full text/Total items : 109952/140903 (78%)
Visitors : 46048427      Online Users : 592
RC Version 6.0 © Powered By DSPACE, MIT. Enhanced by NTU Library IR team.
Scope Tips:
  • please add "double quotation mark" for query phrases to get precise results
  • please goto advance search for comprehansive author search
  • Adv. Search
    HomeLoginUploadHelpAboutAdminister Goto mobile version
    政大機構典藏 > 理學院 > 應用數學系 > 學位論文 >  Item 140.119/32566
    Please use this identifier to cite or link to this item: https://nccur.lib.nccu.edu.tw/handle/140.119/32566


    Title: 模糊期望值與模糊變異數的檢定方法
    Methods on Testing Hypotheses of Fuzzy Mean and Fuzzy Variance
    Authors: 張曙光
    Shu-Kuang,Chang
    Contributors: 吳柏林
    張曙光
    Shu-Kuang,Chang
    Keywords: 隸屬度函數
    模糊樣本取樣
    模糊樣本期望值
    模糊樣本變異數
    人性思考
    t檢定
    F檢定
    模糊常態分配
    Membership function
    fuzzy sampling survey
    fuzzy mean
    human thought
    t-test
    F-test
    normally distributed
    Date: 2006
    Issue Date: 2009-09-17 13:45:46 (UTC+8)
    Abstract: 在許多實際情形下,傳統的統計檢定方法是不足以應付的。故本論文提出模糊檢定方法,我們定義出模糊樣本期望值與模糊樣本變異數的計算方法,再針對不同的模糊資料,分別提出不同的檢定方法,去解決最實際需要解決的問題,其中包括推廣古典的統計檢定方法與自創的檢定方法。

    關鍵字:隸屬度函數,模糊樣本取樣,模糊樣本期望值,模糊樣本變異數,人性思考,t檢定,F檢定,模糊常態分配。
    In many expositions of fuzzy methods, fuzzy techniques are described as an alternative to a more traditional statistical approach. In this paper, we present a class of fuzzy statistical decision process in which testing hypothesis can be naturally reformulated in terms of interval-valued statistics. We provide the definitions of fuzzy mean, fuzzy distance as well as investigation of their related properties. We also give some empirical examples to illustrate the techniques and to analyze fuzzy data. Empirical studies show that fuzzy hypothesis testing with soft computing for interval data are more realistic and reasonable in the social science research. Finally certain comments are suggested for the further studies. We hope that this reformation will make the corresponding fuzzy techniques more acceptable to researchers whose only experience is in using traditional statistical methods.
    Key words: Membership function, fuzzy sampling survey, fuzzy mean, human thought, t-test, F-test, normally distributed.
    Reference: Delgado, M., J. L. Verdegay, and M. A. Vila, 1985, Testing fuzzy hypothesis: a Bayesian approach, in: M. M. Gupta, A. Kandel, W. Bandler, and J. B. Kiszka (Eds.), Approximate Reasoning In Expert Systems, Elsevier, Amsterdam, 307-316.
    Diamond, P., and P. Kloeden, 1994, Metric Space of Fuzzy Sets, World Scientific, London.
    Dubois, D., and H. Prade, 1991, Fuzzy sets in approximate reasoning, part 1: inference with possibility distributions, Fuzzy Sets and Systems 40, 143-202.
    Fréchet, M., 1948, Les elements aléatoires de natures quelconque dans un espace distancié, Ann. Inst. H. Poincaré 10, 2155-310.
    Gil, M. A., M. Montenegro, G. Gonzáxlez-Rodríguez, A. Colubi, and M. R. Casals, 2006, Bootstrap approach to the classic one way multi-sample test with imprecise data, Comp. Stat. Data Anal., in press.
    González-Rodríguez, G., M. Momtenegro, A. Colubi, M. Á. Gil, 2006, Bootstrap techniques and fuzzy random variables: synergy in hypothesis testing with fuzzy data, Fuzzy Sets and Systems 157, 2608-2613.
    Goutsias, J., R. P. S. Mahler, and H. T. Nguyen (eds.), 1997, Random Sets: Theory and Applications, Springer-Verlag, N.Y.
    Grzegorzewski, P., 2000, Testing statistical hypotheses with vague data, Fuzzy Sets and Systems 112, 501-510.
    Grzegorzewski, P., 2001, Fuzzy test – defuzzification and randomization, Fuzzy Sets and Systems 118, 437-446.
    Körner, R., 2000, An asymptotic -test for the expectation of random fuzzy variables, J. Stat. Plann. Inference 83, 331-346.
    Körner, R., W. Näther, 2002, On the variance of random fuzzy variables, in: C. Bertoluzza, M. A. Gil, D. A. Ralescu (Eds.), Statistical Modeling, Analysis and Management of Fuzzy Data, Physica-Verlag, Heidelberg, 22-39.
    Kruse, R., 1982, The strong low of large numbers for random variables, Information Sciences 28, 233-241.
    Kruse, R. and K. D. Meyer, 1987, Statistics with Vague Data, Reidel, Dordrecht, Boston.
    Kruse, R., K.D. Meyer, 1988, Confidence intervals for the parameters of a linguistic random variable, in: J. Kacprzyk, M. Fedrizzi, (Eds.), Combining Fuzzy Imprecision with Probabilistic Uncertainty in Decision Making, Springer, Berlin, 113-123.
    Lehmann, E. L,1986, Testing Statistical Hypotheses, Berkeley, California.
    Liang, G. S., and M. J. Wang, 1991, A fuzzy multicriteria decision making method for facility site selection, International Journal of Production Research 29(11), 2313-2330.
    Montenegro, M., M. R. Casals, M.A. Gil, 2000, Asymptotic comparison of two fuzzy expected values, Proc. JCIS 2000 - Seventh FT&T Conference, 150-153.
    Montenegro, M., M. R. Casals, M. A. Lubiano, and M. A. Gil, 2001, Two-sample hypothesis tests of means of a fuzzy random variable, Information Sciences 113, 89-100.
    Montenegro, M., A. Colubi, M. R. Casals, and M.A. Gil, 2004a, Introduction to ANOVA with fuzzy random variables, in M. Lopez-Diaz, M. A Gil, P. Grzegorzewski, O.Hryniewicz, and J. Lawry (Eds), Soft Methodology and Random Information System, Springer, Berlin, 487-494.
    Montenegro, M., A. Colubi, M. R. Casals, and M.A. Gil, 2004b, Asymptotic and bootstrap techniques for testing the expected value of a fuzzy random variable, Metrika 59, 31-49.
    Nguyen, H. T., and B. Wu, 2000, Fuzzy Mathematics and Statistical Applications, Hua-Tai Book Company, Taipei.
    Saade, J., 1994, Extension of fuzzy hypotheses testing with hybrid data, Fuzzy Sets and Systems 63, 57-71.
    Saade, J., and H. Schwarzlander, 1990, Fuzzy hypotheses testing with hybrid data, Fuzzy Sets and Systems 35, 197-212.
    Stojakovic, M., 1994, Fuzzy random variables, expectation, and martingales, Journal of Mathematical Analysis and Applications 184, 594-606.
    Watanabe, N., and T. Imaizumi, 1993, A fuzzy statistical test of fuzzy hypotheses, Fuzzy Sets and Systems 53, 167-178.
    Wu , B. and W. Yang, 1998, Application of fuzzy statistics in the sampling survey, in: Development and Application for the Quantity Methods of Social Science, Academic Sinica, Taiwan, 289-316.
    Description: 博士
    國立政治大學
    應用數學研究所
    90751503
    95
    Source URI: http://thesis.lib.nccu.edu.tw/record/#G0090751503
    Data Type: thesis
    Appears in Collections:[應用數學系] 學位論文

    Files in This Item:

    File Description SizeFormat
    75150301.pdf42KbAdobe PDF2780View/Open
    75150302.pdf32KbAdobe PDF2749View/Open
    75150303.pdf31KbAdobe PDF2896View/Open
    75150304.pdf49KbAdobe PDF2866View/Open
    75150305.pdf63KbAdobe PDF2839View/Open
    75150306.pdf38KbAdobe PDF21011View/Open
    75150307.pdf89KbAdobe PDF21159View/Open
    75150308.pdf98KbAdobe PDF2973View/Open
    75150309.pdf167KbAdobe PDF21241View/Open
    75150310.pdf23KbAdobe PDF2714View/Open
    75150311.pdf43KbAdobe PDF21073View/Open


    All items in 政大典藏 are protected by copyright, with all rights reserved.


    社群 sharing

    著作權政策宣告 Copyright Announcement
    1.本網站之數位內容為國立政治大學所收錄之機構典藏,無償提供學術研究與公眾教育等公益性使用,惟仍請適度,合理使用本網站之內容,以尊重著作權人之權益。商業上之利用,則請先取得著作權人之授權。
    The digital content of this website is part of National Chengchi University Institutional Repository. It provides free access to academic research and public education for non-commercial use. Please utilize it in a proper and reasonable manner and respect the rights of copyright owners. For commercial use, please obtain authorization from the copyright owner in advance.

    2.本網站之製作,已盡力防止侵害著作權人之權益,如仍發現本網站之數位內容有侵害著作權人權益情事者,請權利人通知本網站維護人員(nccur@nccu.edu.tw),維護人員將立即採取移除該數位著作等補救措施。
    NCCU Institutional Repository is made to protect the interests of copyright owners. If you believe that any material on the website infringes copyright, please contact our staff(nccur@nccu.edu.tw). We will remove the work from the repository and investigate your claim.
    DSpace Software Copyright © 2002-2004  MIT &  Hewlett-Packard  /   Enhanced by   NTU Library IR team Copyright ©   - Feedback