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| 研究生： |
張曙光 Shu-Kuang,Chang |
|---|---|
| 論文名稱： |
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 |
| 指導教授： | 吳柏林 |
| 學位類別： |
博士
Doctor |
| 系所名稱： |
理學院 - 應用數學系 Department of Mathematical Sciences |
| 論文出版年： | 2007 |
| 畢業學年度： | 95 |
| 語文別： | 英文 |
| 論文頁數： | 66 |
| 中文關鍵詞： | 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 |
| 外文關鍵詞： | Membership function, fuzzy sampling survey, fuzzy mean, human thought, t-test, F-test, normally distributed |
| 相關次數： | 點閱：142 下載：155 |
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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.
Abstract v
摘要 vi
Table of Contents vii
Chapter 1. Introduction 1
1.1 Research Objective 3
1.2 Organization of the Dissertation 8
Chapter 2. Literature Review 10
Chapter 3 Testing on Discrete and Continuous Fuzzy Numbers 16
3.1. Fuzzy Data with Soft Computing 16
3.1.1. Membership Function 16
3.2. Fuzzy Mean 18
3.3. Some Properties and Soft Computing of Fuzzy Data 21
3.3.1. Fuzzy Equal and Fuzzy Belongs for Fuzzy Data 21
3.3.2. Some Properties about Fuzzy Data 24
3.4. Testing Hypothesis with Fuzzy Data 27
3.4.1. Testing Hypothesis for Fuzzy Equal 27
3.4.2. Testing Hypothesis for Fuzzy Belongs 30
3.5. Empirical Studies 31
Chapter 4. Testing on Interval Data (I) 37
4.1. Fuzzy Mean and Fuzzy Variance 37
4.1.1. Definition and properties 37
4.2. Interval’s Confidence Interval 39
4.3. Testing Hypotheses about Mean and Variance with Interval Data 40
4.3.1. Extended Concept 40
4.4. Illustration Examples 42
Chapter 5. Testing on Interval Data (II) 45
5.1. Sample Mean and Sample Variance for Interval Data 45
5.2. Method of computing sample mean for interval data 45
5.2.1. Method of computing sample mean for interval form 46
5.3. Testing hypotheses about mean and variance with interval data 52
5.4. Empirical studies 58
Chapter 6. Conclusions 62
Reference 64
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.