模糊数据样本统计中的联合扩张问题
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摘要
在大数据的背景下,运用模糊数据统计分析的理论与方法越来越受到重视。本文论述了模糊数据统计中存在的自然扩张和联合扩张问题,指出了统计量自然扩张的错误并给出了联合扩张的解决方案,利用模糊数的结构元表达方法构建了几个重要样本公式,它们是模糊数据统计分析的重要工具。
In the context of big data,theories and methods using statistical analysis of fuzzy data are receiving more and more attention. This paper discusses the problems of natural expansion and joint expansion in fuzzy data statistics,points out the error of natural expansion of statistics and gives the solution of joint expansion.Several important sample formulas are constructed by using the structural element expression method of fuzzy numbers. They are an important tool for statistical analysis of fuzzy data.
In the context of big data,theories and methods using statistical analysis of fuzzy data are receiving more and more attention. This paper discusses the problems of natural expansion and joint expansion in fuzzy data statistics,points out the error of natural expansion of statistics and gives the solution of joint expansion.Several important sample formulas are constructed by using the structural element expression method of fuzzy numbers. They are an important tool for statistical analysis of fuzzy data.
引文
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[13] Jamkhaneh E B,et al.Statistical hypotheses with fuzzy data[J].International Conference on Intelligent Computing and Cognitive Informatics,2010,2(7):86～89.
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[15] 孙旭东,郭嗣琮.模糊数和模糊值函数的等式限定运算[J].模糊系统与数学,2009,(4).
[16] 郭嗣琮著.模糊结构元理论与模糊分析数学原理(国家自然科学基金资助)[M].东北大学出版社,2004.
[17] 郭嗣琮.[-1,1]上同序单调函数的同序变换群与模糊数运算[J].模糊系统与数学,2005,(3):105～110.
[2] Zadeh L A.Fuzzy sets[J].Information and Control,1965,8(5):338～353.
[3] Chang S L,Zadeh L A.On fuzzy mapping and control[J].IEEE Trans.SMC,1972,13(2):30～40.
[4] Mizumoto M,Tanaka K.The four operations of arithmetic on fuzzy numbers[J].Systems Comput Controls,1976,7(5):73～81.
[5] Dubois D,Prade H.Operations on fuzzy numbers[J].Int.J.Systems Sci,1978,9(6):613～626.
[6] Bezdek J C.Cluster validity with fuzzy sets[J].J.Cybernet,1974,3:58～72.
[7] Tanaka H,Hayashi I,Watada J.Possibilistic linear regression analysis for fuzzy data[J].European Journal of Operational Research,1989,40(3):389～396.
[8] Hathaway R J,Bezdek J C,Pedrycz W.A parametric model for fusing heterogeneous fuzzy data[J].IEEE Transactions on Fuzzy Systems,1996,4(3):270～281.
[9] 王振强等.模糊数量化理论的应用与探索[J].系统工程理论与实践,2001,7:64～70.
[10] Viertl R.Statistics with one-dimensional fuzzy data[J].Studies in Fuzziness & Soft Computing,2002,87:199～212.
[11] Huang W L,Yang M S.Fuzzy clustering on LR-type fuzzy numbers with an application in Taiwanese tea evaluation[J].Fuzzy Set and Systems,2005,150:561～577.
[12] Nguyen H T,Wu B.Fundamentals of statistics with fuzzy data(Studies in fuzziness and soft computing)[M].Springer-Verlag New York,Inc.,2006,7(6):575～6.
[13] Jamkhaneh E B,et al.Statistical hypotheses with fuzzy data[J].International Conference on Intelligent Computing and Cognitive Informatics,2010,2(7):86～89.
[14] 郭嗣琮,刘海涛.模糊数的相等、同一与等式限定运算[J].模糊系统与数学,2008,(6):12～33.
[15] 孙旭东,郭嗣琮.模糊数和模糊值函数的等式限定运算[J].模糊系统与数学,2009,(4).
[16] 郭嗣琮著.模糊结构元理论与模糊分析数学原理(国家自然科学基金资助)[M].东北大学出版社,2004.
[17] 郭嗣琮.[-1,1]上同序单调函数的同序变换群与模糊数运算[J].模糊系统与数学,2005,(3):105～110.