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題名 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作者 張曙光
Shu-Kuang,Chang貢獻者 吳柏林
張曙光
Shu-Kuang,Chang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
Membership function
fuzzy sampling survey
fuzzy mean
human thought
t-test
F-test
normally distributed日期 2006 上傳時間 17-九月-2009 13:45:46 (UTC+8) 摘要 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.參考文獻 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.描述 博士
國立政治大學
應用數學研究所
90751503
95資料來源 http://thesis.lib.nccu.edu.tw/record/#G0090751503 資料類型 thesis dc.contributor.advisor 吳柏林 zh_TW dc.contributor.author (作者) 張曙光 zh_TW dc.contributor.author (作者) Shu-Kuang,Chang en_US dc.creator (作者) 張曙光 zh_TW dc.creator (作者) Shu-Kuang,Chang en_US dc.date (日期) 2006 en_US dc.date.accessioned 17-九月-2009 13:45:46 (UTC+8) - dc.date.available 17-九月-2009 13:45:46 (UTC+8) - dc.date.issued (上傳時間) 17-九月-2009 13:45:46 (UTC+8) - dc.identifier (其他 識別碼) G0090751503 en_US dc.identifier.uri (URI) https://nccur.lib.nccu.edu.tw/handle/140.119/32566 - dc.description (描述) 博士 zh_TW dc.description (描述) 國立政治大學 zh_TW dc.description (描述) 應用數學研究所 zh_TW dc.description (描述) 90751503 zh_TW dc.description (描述) 95 zh_TW dc.description.abstract (摘要) 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。 zh_TW dc.description.abstract (摘要) 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. en_US dc.description.tableofcontents Abstract v摘要 viTable of Contents vii Chapter 1. Introduction 11.1 Research Objective 31.2 Organization of the Dissertation 8Chapter 2. Literature Review 10Chapter 3 Testing on Discrete and Continuous Fuzzy Numbers 163.1. Fuzzy Data with Soft Computing 163.1.1. Membership Function 163.2. Fuzzy Mean 183.3. Some Properties and Soft Computing of Fuzzy Data 213.3.1. Fuzzy Equal and Fuzzy Belongs for Fuzzy Data 213.3.2. Some Properties about Fuzzy Data 243.4. Testing Hypothesis with Fuzzy Data 273.4.1. Testing Hypothesis for Fuzzy Equal 273.4.2. Testing Hypothesis for Fuzzy Belongs 303.5. Empirical Studies 31Chapter 4. Testing on Interval Data (I) 374.1. Fuzzy Mean and Fuzzy Variance 374.1.1. Definition and properties 374.2. Interval’s Confidence Interval 394.3. Testing Hypotheses about Mean and Variance with Interval Data 404.3.1. Extended Concept 404.4. Illustration Examples 42Chapter 5. Testing on Interval Data (II) 455.1. Sample Mean and Sample Variance for Interval Data 455.2. Method of computing sample mean for interval data 455.2.1. Method of computing sample mean for interval form 465.3. Testing hypotheses about mean and variance with interval data 525.4. Empirical studies 58Chapter 6. Conclusions 62Reference 64 zh_TW dc.format.extent 43876 bytes - dc.format.extent 33548 bytes - dc.format.extent 32357 bytes - dc.format.extent 51038 bytes - dc.format.extent 64635 bytes - dc.format.extent 38997 bytes - dc.format.extent 91424 bytes - dc.format.extent 100854 bytes - dc.format.extent 171177 bytes - dc.format.extent 24311 bytes - dc.format.extent 44882 bytes - dc.format.mimetype application/pdf - dc.format.mimetype application/pdf - dc.format.mimetype application/pdf - dc.format.mimetype application/pdf - dc.format.mimetype application/pdf - dc.format.mimetype application/pdf - dc.format.mimetype application/pdf - dc.format.mimetype application/pdf - dc.format.mimetype application/pdf - dc.format.mimetype application/pdf - dc.format.mimetype application/pdf - dc.language.iso en_US - dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0090751503 en_US dc.subject (關鍵詞) 隸屬度函數 zh_TW dc.subject (關鍵詞) 模糊樣本取樣 zh_TW dc.subject (關鍵詞) 模糊樣本期望值 zh_TW dc.subject (關鍵詞) 模糊樣本變異數 zh_TW dc.subject (關鍵詞) 人性思考 zh_TW dc.subject (關鍵詞) t檢定 zh_TW dc.subject (關鍵詞) F檢定 zh_TW dc.subject (關鍵詞) 模糊常態分配 zh_TW dc.subject (關鍵詞) Membership function en_US dc.subject (關鍵詞) fuzzy sampling survey en_US dc.subject (關鍵詞) fuzzy mean en_US dc.subject (關鍵詞) human thought en_US dc.subject (關鍵詞) t-test en_US dc.subject (關鍵詞) F-test en_US dc.subject (關鍵詞) normally distributed en_US dc.title (題名) 模糊期望值與模糊變異數的檢定方法 zh_TW dc.title (題名) Methods on Testing Hypotheses of Fuzzy Mean and Fuzzy Variance en_US dc.type (資料類型) thesis en dc.relation.reference (參考文獻) 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. zh_TW dc.relation.reference (參考文獻) Diamond, P., and P. Kloeden, 1994, Metric Space of Fuzzy Sets, World Scientific, London. zh_TW dc.relation.reference (參考文獻) Dubois, D., and H. Prade, 1991, Fuzzy sets in approximate reasoning, part 1: inference with possibility distributions, Fuzzy Sets and Systems 40, 143-202. zh_TW dc.relation.reference (參考文獻) Fréchet, M., 1948, Les elements aléatoires de natures quelconque dans un espace distancié, Ann. Inst. H. Poincaré 10, 2155-310. zh_TW dc.relation.reference (參考文獻) 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. zh_TW dc.relation.reference (參考文獻) 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. zh_TW dc.relation.reference (參考文獻) Goutsias, J., R. P. S. Mahler, and H. T. Nguyen (eds.), 1997, Random Sets: Theory and Applications, Springer-Verlag, N.Y. zh_TW dc.relation.reference (參考文獻) Grzegorzewski, P., 2000, Testing statistical hypotheses with vague data, Fuzzy Sets and Systems 112, 501-510. zh_TW dc.relation.reference (參考文獻) Grzegorzewski, P., 2001, Fuzzy test – defuzzification and randomization, Fuzzy Sets and Systems 118, 437-446. zh_TW dc.relation.reference (參考文獻) Körner, R., 2000, An asymptotic -test for the expectation of random fuzzy variables, J. Stat. Plann. Inference 83, 331-346. zh_TW dc.relation.reference (參考文獻) 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. zh_TW dc.relation.reference (參考文獻) Kruse, R., 1982, The strong low of large numbers for random variables, Information Sciences 28, 233-241. zh_TW dc.relation.reference (參考文獻) Kruse, R. and K. D. Meyer, 1987, Statistics with Vague Data, Reidel, Dordrecht, Boston. zh_TW dc.relation.reference (參考文獻) 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. zh_TW dc.relation.reference (參考文獻) Lehmann, E. L,1986, Testing Statistical Hypotheses, Berkeley, California. zh_TW dc.relation.reference (參考文獻) 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. zh_TW dc.relation.reference (參考文獻) 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. zh_TW dc.relation.reference (參考文獻) 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. zh_TW dc.relation.reference (參考文獻) 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. zh_TW dc.relation.reference (參考文獻) 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. zh_TW dc.relation.reference (參考文獻) Nguyen, H. T., and B. Wu, 2000, Fuzzy Mathematics and Statistical Applications, Hua-Tai Book Company, Taipei. zh_TW dc.relation.reference (參考文獻) Saade, J., 1994, Extension of fuzzy hypotheses testing with hybrid data, Fuzzy Sets and Systems 63, 57-71. zh_TW dc.relation.reference (參考文獻) Saade, J., and H. Schwarzlander, 1990, Fuzzy hypotheses testing with hybrid data, Fuzzy Sets and Systems 35, 197-212. zh_TW dc.relation.reference (參考文獻) Stojakovic, M., 1994, Fuzzy random variables, expectation, and martingales, Journal of Mathematical Analysis and Applications 184, 594-606. zh_TW dc.relation.reference (參考文獻) Watanabe, N., and T. Imaizumi, 1993, A fuzzy statistical test of fuzzy hypotheses, Fuzzy Sets and Systems 53, 167-178. zh_TW dc.relation.reference (參考文獻) 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. zh_TW
