关于马田系统若干问题的研究
|
摘要
马田系统(Mahalanobis-Taguchi System,MTS)是由日本著名质量工程学家田口玄一博士首先提出的一种新的模式识别方法,它以基于马氏距离(MahalanobisDistance,MD)的信噪比(Signal to Noise Ratio,R_(SN))为优化指标,应用二水平正交表进行有效特征的选择,通过样品的马氏距离达到数据分类与判别分析的目的。目前,国际上马田系统的应用领域已经非常广泛,创造了巨大的经济效益和社会效益。但是,在我国,关于马田系统的理论与应用研究才刚刚起步,研究基础还相当薄弱。
本论文的研究思路为:首先,系统回顾马田系统理论和应用的国内外最新进展和研究;其次,在对马田系统进行深入分析的基础之上,通过对距离统计量与相似系数统计量的整合,构造一个新的类别可分性指标,使之既能反映样品之间的距离贴近程度,同时又能反映样品之间的形状相似程度;第三,通过计算每个特征变量的熵值,Ⅰ类分析特征变量的有效性,并通过模糊聚类的分析方法,对特征变量进行模糊聚类分析,使得相似的特征变量归为一类,从而达到识别Ⅱ类特征变量的目的;第四,根据分类类型的不同(有序分割类型与一般分割类型),分别通过3σ准则与扰动模糊分析方法,将两类判别的状况发展至多类判别,给出一般意义上的多类判别准则;最后,运用马田系统进行疾病诊断的研究,运用理论指导实践,并为我国的疾病诊断提供新的技术和方法。
本论文主要研究内容及结论有:
1)距离统计量的比较研究
经典马田系统中,类别可分性指标采用的是马氏距离统计量。从理论上讲,相比较其他距离测度,马氏距离有着比较科学的内涵:考虑到相关性、量纲的影响以及线性变换不变性等。试验也表明,马氏距离具有更好的判别效果。
2)类别可分性指标的拓展研究在经典的马田系统中,所用类别可分性指标为距离统计量。应用距离统计量作为类别可分性指标,虽然能够有效地识别出样本之间的距离贴近程度,但却不能准确地衡量样本之间的形状相似程度。在某些识别场合下,样本之间的形状相似较之距离贴近显得更为重要。因此,本论文对经典马田系统的类别可分性指标进行拓展,整合了距离统计量与相似系数统计量,构建了样本近似度统计量,使之既能够体现样本之间的距离贴近程度,也能够衡量样本之间的形状相似程度。
3)特征变量选择方法的研究
经典马田系统采用正交表与信噪比的方法来判定特征变量有效性。这种方法不仅计算繁杂,而且随着特征变量的增多,计算量也随之成倍增大。本论文根据田口玄一的基于数据分析的思想,讨论了熵值法在特征变量优化选择问题中的应用,阐明了应用熵值法进行特征变量选择的基本原理与计算过程,并通过实际的应用算例表明熵值法的有效性。
利用二水平正交表法与熵值原理法能够剔出掉那些对识别效果起负作用或者基本不起作用的特征变量(Ⅰ类特征变量),但是却难以识别出那些对最终识别效果起相似作用的特征变量(Ⅱ类特征变量)。笔者通过模糊聚类的分析方法,对特征变量进行模糊聚类分析,使得相似的特征变量归为一类,从而达到识别Ⅱ类特征变量的目的。
4)马田系统多类判别研究
经典马田系统中,由于基准空间是由一类正常总体所定义,因而对于判别待检样品正常与否的两类判别情形具有良好的效果。然而,对于多类判别的情形,经典的马田系统方法则不能很好的解决此类问题。本论文依据分类两种类型(有序分割类型与一般类型),分别采用3σ准则与扰动模糊的分析方法,对多类判别进行了研究,并阐明了进行多类判别的原理与计算过程。
5)马田系统在医疗诊断中的应用研究
马田系统是基于数据分析的方法而不是基于变量概率分布的方法,它具有良好的应用价值。本论文选取一类典型的、在临床诊断中具有一定难度的疾病——肺病疾病,通过一定数量的健康数据作为训练样品,构造该疾病的基准空间,并通过特征优化方法对基准空间进行优化;通过构造特征变量与疾病类型之间的扰动模糊关系,将待检样品与模糊扰动模糊关系作用,确定样品的疾病类型,达到疾病诊断的目的。
Dr. Taguchi developed the Mahalanobis-Taguchi system (MTS) which is a burgeoning method of pattern recognition based on the quality engineering. MTS is the first method that used the orthogonal array to select variables. MTS regards the SN ratios along with Mahalanobis distances as the optimization target, and select the useful variables by using 2-level orthogonal array. So far, MTS is widely used, and create tremendous economic and social bennifts. In China, the research of MTS in theory and application is just commenced developing, and it needs a great deal of manpower and resource.
The layout of this dissertation is shown as follows: first, the dissertation reviewed the MTS, and gived the latest progress; second, based on the analysis of MTS, by integration of distance and similarity coefficient, the dissertation create a new index for classification which can reflect both the comparability of distance value and the comparability of shapes between samples; third, through entropy value of every variable, the validity of Class I variables can be recognized, and through fuzzy cluster analysis, the validity of Class II variables can be recognized; fourth, according diffirent of classication style, by the method of 3σrule and disturbing fuzzy set, the theory and design model for MTS design in discrimination of multiclass have been studied; finally, as an example, the MTS approach has been applied to the medical diagnosis and a satisfactory result has been obtained, and provide a new teconology and method to disease diagnosis in China.
The research and main conclusion of this dissertation is shown as follows:
1) The research of distance in MTS
In original MTS, Mahalanobis distance is used as classification index. Selecting Mahalanobis distance is proper because it is consider the influence of relativity, relativity and etc. And in practice, Mahalanobis distance has the better discriminant ability than others.
2) The research of extention of classification index
In original MTS, distance is adopted as classification index. Distance index can reflect how close among samples in space. However, in the other hand, distance index can not reflect the similitude of samples' shape. So, this dissertation extends the classification index by integrating the distance and similarity coefficient, and thus it can reflect the similitude of samples in both sides.
3) The research of variable selection
Original MTS is used the method of orthogonal array and SN ratio to select variables. However, this approach would become more complex along with the increase of variable number. According to ideology of Taguchi's data analysis, this dissertation applied entropy into variable selection, and gives an example to show efficiency of entropy method.
The method of experimental design and entropy could identify the harmful variables (Class I variables), but they could not identify the variables which have similar effect (Class II variables). This dissertation uses the fuzzy cluster method to identify the Class II variables.
4) The research of multiple recognition
In original MTS, because the base space is constructed only by normal data, it is more fittable to classification of two models than multiple models. According to two kinds of classification of samples, this dissertation uses the methods of 3σrule and disturbing fuzzy set to solve the problem of discrimination of multiclass.
5) The research of MTS applications in medical diagnosis
MTS is the method based on data analysis rather than probability distribution, and is suitable to be appled in practice. This dissertation chooses pulmonary disease as the object. Through amount of normal and abnormal data, we contruct the base space, select the useful variables; by constructing the disturbing fuzzy relationship between variables and disease types, compute the fuzzy number of samples, and so can achieve the purpose of medical diagnosis.
本论文的研究思路为:首先,系统回顾马田系统理论和应用的国内外最新进展和研究;其次,在对马田系统进行深入分析的基础之上,通过对距离统计量与相似系数统计量的整合,构造一个新的类别可分性指标,使之既能反映样品之间的距离贴近程度,同时又能反映样品之间的形状相似程度;第三,通过计算每个特征变量的熵值,Ⅰ类分析特征变量的有效性,并通过模糊聚类的分析方法,对特征变量进行模糊聚类分析,使得相似的特征变量归为一类,从而达到识别Ⅱ类特征变量的目的;第四,根据分类类型的不同(有序分割类型与一般分割类型),分别通过3σ准则与扰动模糊分析方法,将两类判别的状况发展至多类判别,给出一般意义上的多类判别准则;最后,运用马田系统进行疾病诊断的研究,运用理论指导实践,并为我国的疾病诊断提供新的技术和方法。
本论文主要研究内容及结论有:
1)距离统计量的比较研究
经典马田系统中,类别可分性指标采用的是马氏距离统计量。从理论上讲,相比较其他距离测度,马氏距离有着比较科学的内涵:考虑到相关性、量纲的影响以及线性变换不变性等。试验也表明,马氏距离具有更好的判别效果。
2)类别可分性指标的拓展研究在经典的马田系统中,所用类别可分性指标为距离统计量。应用距离统计量作为类别可分性指标,虽然能够有效地识别出样本之间的距离贴近程度,但却不能准确地衡量样本之间的形状相似程度。在某些识别场合下,样本之间的形状相似较之距离贴近显得更为重要。因此,本论文对经典马田系统的类别可分性指标进行拓展,整合了距离统计量与相似系数统计量,构建了样本近似度统计量,使之既能够体现样本之间的距离贴近程度,也能够衡量样本之间的形状相似程度。
3)特征变量选择方法的研究
经典马田系统采用正交表与信噪比的方法来判定特征变量有效性。这种方法不仅计算繁杂,而且随着特征变量的增多,计算量也随之成倍增大。本论文根据田口玄一的基于数据分析的思想,讨论了熵值法在特征变量优化选择问题中的应用,阐明了应用熵值法进行特征变量选择的基本原理与计算过程,并通过实际的应用算例表明熵值法的有效性。
利用二水平正交表法与熵值原理法能够剔出掉那些对识别效果起负作用或者基本不起作用的特征变量(Ⅰ类特征变量),但是却难以识别出那些对最终识别效果起相似作用的特征变量(Ⅱ类特征变量)。笔者通过模糊聚类的分析方法,对特征变量进行模糊聚类分析,使得相似的特征变量归为一类,从而达到识别Ⅱ类特征变量的目的。
4)马田系统多类判别研究
经典马田系统中,由于基准空间是由一类正常总体所定义,因而对于判别待检样品正常与否的两类判别情形具有良好的效果。然而,对于多类判别的情形,经典的马田系统方法则不能很好的解决此类问题。本论文依据分类两种类型(有序分割类型与一般类型),分别采用3σ准则与扰动模糊的分析方法,对多类判别进行了研究,并阐明了进行多类判别的原理与计算过程。
5)马田系统在医疗诊断中的应用研究
马田系统是基于数据分析的方法而不是基于变量概率分布的方法,它具有良好的应用价值。本论文选取一类典型的、在临床诊断中具有一定难度的疾病——肺病疾病,通过一定数量的健康数据作为训练样品,构造该疾病的基准空间,并通过特征优化方法对基准空间进行优化;通过构造特征变量与疾病类型之间的扰动模糊关系,将待检样品与模糊扰动模糊关系作用,确定样品的疾病类型,达到疾病诊断的目的。
Dr. Taguchi developed the Mahalanobis-Taguchi system (MTS) which is a burgeoning method of pattern recognition based on the quality engineering. MTS is the first method that used the orthogonal array to select variables. MTS regards the SN ratios along with Mahalanobis distances as the optimization target, and select the useful variables by using 2-level orthogonal array. So far, MTS is widely used, and create tremendous economic and social bennifts. In China, the research of MTS in theory and application is just commenced developing, and it needs a great deal of manpower and resource.
The layout of this dissertation is shown as follows: first, the dissertation reviewed the MTS, and gived the latest progress; second, based on the analysis of MTS, by integration of distance and similarity coefficient, the dissertation create a new index for classification which can reflect both the comparability of distance value and the comparability of shapes between samples; third, through entropy value of every variable, the validity of Class I variables can be recognized, and through fuzzy cluster analysis, the validity of Class II variables can be recognized; fourth, according diffirent of classication style, by the method of 3σrule and disturbing fuzzy set, the theory and design model for MTS design in discrimination of multiclass have been studied; finally, as an example, the MTS approach has been applied to the medical diagnosis and a satisfactory result has been obtained, and provide a new teconology and method to disease diagnosis in China.
The research and main conclusion of this dissertation is shown as follows:
1) The research of distance in MTS
In original MTS, Mahalanobis distance is used as classification index. Selecting Mahalanobis distance is proper because it is consider the influence of relativity, relativity and etc. And in practice, Mahalanobis distance has the better discriminant ability than others.
2) The research of extention of classification index
In original MTS, distance is adopted as classification index. Distance index can reflect how close among samples in space. However, in the other hand, distance index can not reflect the similitude of samples' shape. So, this dissertation extends the classification index by integrating the distance and similarity coefficient, and thus it can reflect the similitude of samples in both sides.
3) The research of variable selection
Original MTS is used the method of orthogonal array and SN ratio to select variables. However, this approach would become more complex along with the increase of variable number. According to ideology of Taguchi's data analysis, this dissertation applied entropy into variable selection, and gives an example to show efficiency of entropy method.
The method of experimental design and entropy could identify the harmful variables (Class I variables), but they could not identify the variables which have similar effect (Class II variables). This dissertation uses the fuzzy cluster method to identify the Class II variables.
4) The research of multiple recognition
In original MTS, because the base space is constructed only by normal data, it is more fittable to classification of two models than multiple models. According to two kinds of classification of samples, this dissertation uses the methods of 3σrule and disturbing fuzzy set to solve the problem of discrimination of multiclass.
5) The research of MTS applications in medical diagnosis
MTS is the method based on data analysis rather than probability distribution, and is suitable to be appled in practice. This dissertation chooses pulmonary disease as the object. Through amount of normal and abnormal data, we contruct the base space, select the useful variables; by constructing the disturbing fuzzy relationship between variables and disease types, compute the fuzzy number of samples, and so can achieve the purpose of medical diagnosis.
引文
[1]边肇祺,张学工等编著.模式识别(第二版)[M].北京:清华大学出版社,2000
[2]黄振华.模式识别原理[M].浙江:浙江大学出版社,1991
[3]周冠雄.计算机模式识别——统计方法[M].武昌:华中工学院出版社,1984
[4]陈季稿.统计模式识别[M].北京:北京邮电出版社,1989
[5]帕夫利迪斯.结构模式识别[M].上海:上海科技文献出版社,1981
[6]尼曼.模式分类[M].北京:科学出版社,1988
[7]R.C.Gonzalez.句法模式识别[M].北京:清华大学出版社,1984
[8]厄尔曼.图形识别技术[M].北京:人民邮电出版社,1983
[9]傅京孙.模式识别及其应用[M].北京:科学出版社,1990
[10]黄德双.神经网络模式识别系统理论[M].北京:电子工业出版社,1996
[11]殷勤业.模式识别与神经网络[M].北京:机械工业出版社,1992
[12]包约翰.自适应模式识别与神经网络[M].北京:科学出版社,1992
[13]Genichi Taguchi,Rajesh Jugulum.The Mahalanobis-Taguchi Strategy[M].New York:John Wiley & Sons,Inc.,2002
[14]Genichi Taguchi,Subir Chowdhury,Yuin Wu.The Mahalanobis-Taguchi System [M].New York:The McGraw-Hill Companies,Inc.,2000
[15]李昭阳.马田系统在模式识别中的研究与应用[D].南京:南京理工大学经济管理学院,2001.5
[16]李昭阳,韩之俊.一种新的判别预测方法——马田系统(MTS)[J].管理工程学报,2000.2:54-55
[17]郑称德,韩之俊.MTS原理及其设计模型[J].管理工程学报,2000.3:43-47
[18]薛跃.基于RMTS的上市公司虚假财务报告识别及其扩展应用研究[D].南京:南京理工大学经济管理学院,2005.4
[19]薛跃,韩之俊,王雪荣,盛党红.稳健MTS系统研究[J].统计与决策,2004.12:17-18
[20]薛跃,韩之俊,盛党红.MTS法用于上市公司财务质量评估初探[J].数理统计与管理,2005.1:81-85
[21]王海燕.关于在P-M模糊测度空间构建CSI测评体系的研究[D].南京:南京理工大学经济管理学院,2002.10
[22]王海燕,韩之俊.MTS在CSI测评中的应用[J].中国质量,2003.7:34-35
[23]宗鹏,曾凤章.基于MTS的企业可持续发展评价体系研究[J].科学技术与工程,2006.8:1163-1170
[24]宗鹏,曾凤章.基于马田系统的Mahalanobis距离选择[J].漯河职业技术学院学报,2006.4:1-3
[25]郑称德.质量工程学的新进展[J].科技进步与对策,2002.4:101-104
[26]许前,郑称德,韩之俊.MTS多类判别研究[J].南京:南京理工大学学报,2002.2:92-95
[27]宗鹏.马田系统理论及应用研究[D].北京:北京理工大学经济管理学院,2006.7
[28]曾凤章.稳健性设计[M].北京:兵器工业出版社,1996
[29]王雪,李勇.零件形状误差的MTS测量识别方法[J].电测与仪表,2006.5:7-10
[30]孙文爽,陈兰祥.多元统计分析[M].北京:高等教育出版社,1994
[31]张尧庭,方开泰.多元统计分析引论[M].北京:科学出版社,1982
[32]蒋泽军.模糊数学教程[M].北京:国防工业版社,2004
[33]庄世坚.环境检测中确定最佳点位的关键技术[J].中国环境监测,2001.10:24-29
[34]项可风,吴启光.试验设计与数据分析[M].上海:上海科学技术出版社,1989
[35]Kleijenen,J,P.C.Statistical Techniques in simulation(in two parts)[M].New York:Marcel,Dekker,Inc,1975
[36]李群.隶属函数的扰动问题和算子研究[J].大连理工大学学报,2001.7:371-376
[37]李群.不确定性方法研究及其在社会科学中的应用[M].北京:中国社会科学出版社,2005
[38]冯德益,楼世博等.模糊数学方法与应用[M].北京:地震出版社,1983
[39]马逢时等编著.六西格玛管理统计指南[M].北京:中国人民大学出版社,2007
[40]钟晓芳,韩之俊.评价计测仪器精度的一种新方法[J].计量与测试技术,2004.6:27-28
[41]何桢,韩亚娟.多元系统马氏田口方法的诊断与分析研究[J].数理统计与管理,2007.9.830-839
[42]何桢,韩亚娟,李菊栋.马氏田口两种不同方法的比较研究[J].中国卫生统计,2007.10:531-535
[43]韩亚娟.马氏田口在多元系统优化与分析中的应用研究[D].天津:天津大学,2005.1
[44]王雪,马俊杰,王晟.机械设备状态的经验模式分解统计识别方法[J].中国机械工程,2008.3:704-708
[45]陈湘来,韩之俊.田口方法在太阳能电池刻蚀工序中的应用[J].中国质量,2007.6:88-89
[46]陈湘来,韩之俊.基于MTS的供应商评价体系研究[J].商场现代化,2007.8:23-24
[47]薛跃,盛党红,朱立峰,韩之俊.田口式测量质量工程学与传统MSA的比较分析[J].系统工程理论与实践,2006.8:76-80
[48]Rajesh J,Taguchi S.Direction of Abnormals and Treatment of Noise Factors in Multidimensional Systems:A Discussion[J].Journal of Quality Engineering Forum,2001.3:37-44
[49]Jugulum,Rajesh,Taguchi,Genichi,Taguchi,Shin,Wilkins,James O.Discussion-A Review and Analysis of the Mahalanobis-Taguchi System[J].Technometrics,2003.1:16-21
[50]Yixin Chen,John Phillips,Linson Qiao.Improving Sofeware Subsystem Testing With Mahalanobis-Taguchi System[J].ASI's 20th Annual Symposium,2001.6:35-42
[51]Abraham,B.and Variyath,A.M.Discussion-A Review and Analysis of the Mahalanobis-Taguchi System[J].Technometrics,2003.1:22-24
[52]Woodall,W.H.,Koudelik,R.,Kwok-Leung Tsui,and Seoung Bum Kim.A Review and Analysis of the Mahalanobis-Taguchi System[J].Technometrics,2003.1:1-15
[53]Woodall,W.H.,Koudelik,R.,Kwok-Leung Tsui,Seoung Bum Kim,Stoumbos,Z.G.and Carvounis,C.P.Respoonse-A Review and Analysis of the Mahalanobis-Taguchi System[J].Technometrics,2003.1:29-30
[54]Hawkins,D.M.Discussion-A Review and Analysis of the Mahalanobis-Taguchi System[J].Technometrics,2003.1:25-28
[55]Louis La Vallee,Application of Mahalanobis-Taguchi system to Thermal Ink Jet Image Quality Inspection,Proc.of 4~(th) Annual International TPD Symposium Robust Engineering Conference,1998.8:411-427
[56]Nagao,M.Yamamoto,M.MTS approach to fcial image recognition[J].1999 IEEE international Conference on Systems,Man,and Cybernetics,1999.4:37-42
[57]Asada,M.Wafer yield prediction by the Mahalanobis-Taguchi system[J]..International Workshop on Statistical Metrology,IWSM,2001.4:25-28
[58]Hacker,J.,and Engelhardt,F.,and Frey,D.D.Robust Manufacturing Inspection and Classification with Machine Vision[J].International Journal of Production Research,2002.6:1319-1334
[59]A.Mike Vurton,Paul Miller.Human and automatic face recognition comparisonacross image formats[J].Vision Rseeareh,2001(41):3185-3195
[60]R.De Maesschalck,D.Jouan-Rimband.The Mahalanobis distance[J].Chemometrics and Intelligent Laboratory systems,2000(50):1-18
[61]Nakatsugawa,M.A study on determination of the threshold in MTS algorithm,ransactions of the Institute of Electronics[J].Information and Communication Engineers,2001.4:519-527
[62]Nakatsugawa,M.,and Ohuchi,A.A Study on Selection of the Terms in MTS Algorithm[J].Transactions of the Institute of Electronics,Information and Communication Engineers.2000.4:434-441
[63]Nagao,M.,and Yamamoto,M.,and Suzuki,K.,and Ohuchi,A.A Face Identification System Based on the Mahalanobis-Taguchi system.International Transactions in Operational Research[J],2001.1:31-45
[64]R.Di Mascio,G.W.Barton.The economic assessment of process control quality using a Taguchi-based method[J].Journal of Process control,2001.11:81-88
[65]X.L.Chen,J.L.Chen,Z.J.Han.A Method of Personal Appraisement based on MTS [J].Journal of Science,Technolgy,and Engineering,2007.6:42-45
[66]Genichi Taguchi,J.Rajesh.New Trends in Multivariate Diagnosis[J].Japan:Qulity Enginerring,2001.4:74-85
[67]Jugulum,R.,Taguchi,S.,and Yang,K.New developments in multivariate diagnosis:a comparison between two methods[J].Jouranl of the Japanese Quality Engineering Society,1999.5:62:72
[68]Li Deng-feng,Cheng Chun-tian.New similarity measures of intuitionistic fuzzy sets and application to pattern recognition[J].Pattern Recognition Letters,2002.12:221-225
[69]Chao-yu Chou,Chung-ho Chen & Hui-rong Liu.Acceptance Control Charts for Non-normal Data[J].Journal of Applied Statistics,2005.1:25-36
[70]Philippe Castagliola.(?) Control Chart for Skewed Populations Using a Scaled Weighted Variance Method[J].International Journal of Reliability,Quality and Safety Engineering,2000.3:237-252
[71]X.L.Chen,J.L.Chen,Z.J.Han.Application of Anvoa in Varaible Selection of MTS [J].Natrue Sicences,2007.12:34-36
[72]Douglas M.Hawkins and K.D.Zamba.On Small Shifts in Quality Control[J].Quality Engineering,2004.1:143-149
[73]John Terninko.The QFD,TRIZ and Taguchi Connection:Customer-Driven Robust Innovation[J].TRIZ Journal,http://www.triz-journal.com,1998.1
[74]Huei-Chun Wang.Data Classification Using the Mahalanobis-Taguchi System[J].Journal of the Chinese Institute of Industrial Engineers,2004.11:606-618
[75]Ratna Babu Chinnam,Bharatendra Rai,Nanua Singh.Tool-Condition Monitoring From Degradation Signals Using Mahalanobis-Taguchi System Analysis[J].ASI's 20~(th)Annual Symposium,2004.2343-351
[76]Jugulum R.Monplaisir L.Comparison between Mahalanobis-Taguchi System and Artificial Neural Networks[J].Journal of Quality Engineering Forum,2002.1:60-73
[77]Miki Shinsuke,Okazawa Hiroshi.Diagnosis of the Degradation of Insulating Material Using the Mahalanobis-Taguchi System Method[J].Papers of Technical Meeting on General Industries Division,2001.1:20-26
[78]王雪,马俊杰,王晟.机械设备状态的经验模式分解统计识别方法[J].中国机械工程.2008.6:704-708
[79]田口玄一.MTS法和诊断问题.标准化和品质管理[J].1999.10:63-69
[80]田口玄一.MTS法的信噪比.标准化和品质管理[J].1999.9:63-70
[81]金迟幸彦.MTS法在处理液诊断中的应用.品质工学[J].1998.6:47-52
[82]手岛昌一.基于多变量诊断的SN比.品质工学[J].1999.6:70-74
[83]韩之俊,许前.质量管理[M].北京:科学出版社,2003
[84]韩之俊.测量质量工程学[M].北京:中国计量出版社,2000
[85]陈魁.试验设计与分析[M].北京:清华大学出版社,2005
[86]中国兵器工业质量管理协会.质量工程学应用手册[M].北京:兵器工业出版社,1993
[87]田口玄一.测量技术的实验设计法[M].北京:机械工业出版社,1988
[88]田口玄一.开发、设计阶段的质量工程学[M].北京:兵器工业出版社,1990
[89]吴玉印等.田口式的稳健性设计[M].北京:兵器工业出版社,1997
[90]田口玄一.制造阶段的质量工程学[M].北京:兵器工业出版社,1992
[91]周纪芗等.质量管理统计方法[M].北京:中国统计出版社,1999
[92]马林.六西格玛管理[M].北京:中国人民大学出版社,2004
[93]韩之俊.三次设计[M].北京:机械工业出版社,1992
[94]韩之俊.质量工程学——线外、线内质量管理[M].北京:科学出版社,1991
[95]K.S.Fukunaga.Introduction to Statistical Pattern Recognition[M].New York:Academic Press.Inc,1990
[96]Douglas.C.Montogomery.Design and Analysis of Experiment[M].John Wiley &Sons,Inc,1991
[97]Chao-yu Chou,Chtmg-ho Chen & Hui-rong Liu.Economic-statistical design of(?)charts for non-normal data by considering quality loss[J].Journal of Applied Statistics,2000.8:939-951
[98]Z.Wu,M.Shamsuzzaman and E.S.Pan.Optimization design of control charts based on Tahuchi's loss function and random process shifts[J].INT.J.PROD.RES.,2004.2:379-390
[99]盛骤.概率论与数理统计[M].北京:高等教育出版社,1989
[100]常大勇,张丽丽.经济管理中的模糊数学方法[M].北京:北京经济学院出版社,1995
[101]唐守正.多元统计分析方法[M].北京:中国林业出版社,1989:61-84
[102]马本堃,高尚惠,孙煜.热力学与统计物理学[M].北京:高等教育出版社,1980
[103]王诚泰.统计物理学[M].北京:科学出版社,1979
[104]Kanetaka,Tatsuji.Diagonosis of a Special Health Check Using Mahalanobis Distance.ASI Journal,1990.3:72-76
[105]Thompson A.,Strictland A J.Strategic management:concepts and cases[M].New York:McGraw Hill Companies,lnc,2001
[106]Colan A,Judge G,Miller D.Maximum entropy econometrics:robust estimation with limted data[M].New York:John Wiley and Sons,1996
[107]Shen E Z,Perloff J M.Maximum entropy and Bayesian approaches to the ratio problem[J].Journal of Economtrics,2001.2:289-313
[108]Fraser I.An application of maximum entropy estimation:the demand for meat in the United Kingdom[J].Applied Economics,2000.1:45-59
[109]Lence S.H.,Miller D.J.Estimtion of Multi-Output Production Functions with Incomplete Data:A Generalized Maximum Entropy Approach[J].Eur.Rev.Agr.Econ.1998.1:188-209
[110]]马振华.现代应用数学手册:运筹学与最优化理论卷[M].北京:清华大学出版社,1998
[111]于洋,李一军.基于多策略评价的绩效指标权重确定方法研究[J].系统工程理论与实践,2003.8:8-15
[112]姜璐.熵——系统科学基本概念[M].沈阳:沈阳出版社,1997
[113]霍映宝,韩之俊.基于熵原理的上市公司综合评价研究[J].运筹与管理,2004.4:119-122
[114]张卫民,安景文,韩朝.熵值法在城市可持续发展评价问题中的应用[J].数量经济技术经济研究,2003.6.115-118
[115]B.Turksen.Interval Valued Fuzzy Sets Based on normal Forms[J].Fuzzy Sets and System.1986.10:191-210
[116]刘心,陈图云.扰动模糊逻辑及其“非”算子[J].模糊系统与数学,2002.9:179-182
[117]孟广武.区间值模糊集的基本理论[J].应用数学,1993.2:212-217.
[118]杨伦标,高英仪.模糊数学:原理及应用[M].广州:华南理工大学出版社,1993
[119]刘晋寅,吴孟达.模糊理论及其应用[M].长沙:国防科技大学出版社,1998
[120]冯保成.模糊数学实用集粹[M].北京:中国建筑工业出版社,1991
[121]宋晓秋.模糊数学原理与方法[M].徐州:中国矿业大学出版社,1999
[122]田口玄一.实验设计法[M].北京:机械工业出版社,1987
[123]钟南山,胡文立,何权瀛.严重急性呼吸综合征(SARS)的诊断与治疗[J].疑难病杂志,2003.6:129-131
[124]赵子文,张复春,许敏等.广州地区年春季传染性非典型肺炎 190 例临床分析[J].中国病案,2003.4:73-76
[125]彭国文,何剑峰,郭汝宁等.广东省传染性非典型肺炎流行病学特征分析[J].华南预防医学,2003.6:11-12
[126]中华医学会呼吸病学分会.社区获得性肺炎诊断和治疗指南草案[J].中华结核和呼吸杂志,1999.4:199-201
[127]邹晓颖.140例肺结核临床分析[J].中华临床医学研究杂志,2008.3:671
[128]肖正伦,黎毅敏,陈荣昌等.78例传染性非典型肺炎病例临床分析[J].中华结核和呼吸杂志,2003.6:334-338
[129]王云南,吕嘉春,冯蝶仪等.SARS 与普通肺炎的临床特征对比分析[J].广州医学院学报,2004.6:26-29
[130]蒋捍东.传染性非典型肺炎的临床现状[J].青岛大学医学院学报,2003.6:121-122
[131]彭国文,何剑峰,林锦炎等.广东省传染性非典型肺炎流行病学特征初步研究[J].广东医学,2003.6:36-38
[132]吕军,袁慧军,王敏等.收治 28 例地方传染性非典型肺炎流行病学特征分析[J].广东医学,2003.6:40-41
[2]黄振华.模式识别原理[M].浙江:浙江大学出版社,1991
[3]周冠雄.计算机模式识别——统计方法[M].武昌:华中工学院出版社,1984
[4]陈季稿.统计模式识别[M].北京:北京邮电出版社,1989
[5]帕夫利迪斯.结构模式识别[M].上海:上海科技文献出版社,1981
[6]尼曼.模式分类[M].北京:科学出版社,1988
[7]R.C.Gonzalez.句法模式识别[M].北京:清华大学出版社,1984
[8]厄尔曼.图形识别技术[M].北京:人民邮电出版社,1983
[9]傅京孙.模式识别及其应用[M].北京:科学出版社,1990
[10]黄德双.神经网络模式识别系统理论[M].北京:电子工业出版社,1996
[11]殷勤业.模式识别与神经网络[M].北京:机械工业出版社,1992
[12]包约翰.自适应模式识别与神经网络[M].北京:科学出版社,1992
[13]Genichi Taguchi,Rajesh Jugulum.The Mahalanobis-Taguchi Strategy[M].New York:John Wiley & Sons,Inc.,2002
[14]Genichi Taguchi,Subir Chowdhury,Yuin Wu.The Mahalanobis-Taguchi System [M].New York:The McGraw-Hill Companies,Inc.,2000
[15]李昭阳.马田系统在模式识别中的研究与应用[D].南京:南京理工大学经济管理学院,2001.5
[16]李昭阳,韩之俊.一种新的判别预测方法——马田系统(MTS)[J].管理工程学报,2000.2:54-55
[17]郑称德,韩之俊.MTS原理及其设计模型[J].管理工程学报,2000.3:43-47
[18]薛跃.基于RMTS的上市公司虚假财务报告识别及其扩展应用研究[D].南京:南京理工大学经济管理学院,2005.4
[19]薛跃,韩之俊,王雪荣,盛党红.稳健MTS系统研究[J].统计与决策,2004.12:17-18
[20]薛跃,韩之俊,盛党红.MTS法用于上市公司财务质量评估初探[J].数理统计与管理,2005.1:81-85
[21]王海燕.关于在P-M模糊测度空间构建CSI测评体系的研究[D].南京:南京理工大学经济管理学院,2002.10
[22]王海燕,韩之俊.MTS在CSI测评中的应用[J].中国质量,2003.7:34-35
[23]宗鹏,曾凤章.基于MTS的企业可持续发展评价体系研究[J].科学技术与工程,2006.8:1163-1170
[24]宗鹏,曾凤章.基于马田系统的Mahalanobis距离选择[J].漯河职业技术学院学报,2006.4:1-3
[25]郑称德.质量工程学的新进展[J].科技进步与对策,2002.4:101-104
[26]许前,郑称德,韩之俊.MTS多类判别研究[J].南京:南京理工大学学报,2002.2:92-95
[27]宗鹏.马田系统理论及应用研究[D].北京:北京理工大学经济管理学院,2006.7
[28]曾凤章.稳健性设计[M].北京:兵器工业出版社,1996
[29]王雪,李勇.零件形状误差的MTS测量识别方法[J].电测与仪表,2006.5:7-10
[30]孙文爽,陈兰祥.多元统计分析[M].北京:高等教育出版社,1994
[31]张尧庭,方开泰.多元统计分析引论[M].北京:科学出版社,1982
[32]蒋泽军.模糊数学教程[M].北京:国防工业版社,2004
[33]庄世坚.环境检测中确定最佳点位的关键技术[J].中国环境监测,2001.10:24-29
[34]项可风,吴启光.试验设计与数据分析[M].上海:上海科学技术出版社,1989
[35]Kleijenen,J,P.C.Statistical Techniques in simulation(in two parts)[M].New York:Marcel,Dekker,Inc,1975
[36]李群.隶属函数的扰动问题和算子研究[J].大连理工大学学报,2001.7:371-376
[37]李群.不确定性方法研究及其在社会科学中的应用[M].北京:中国社会科学出版社,2005
[38]冯德益,楼世博等.模糊数学方法与应用[M].北京:地震出版社,1983
[39]马逢时等编著.六西格玛管理统计指南[M].北京:中国人民大学出版社,2007
[40]钟晓芳,韩之俊.评价计测仪器精度的一种新方法[J].计量与测试技术,2004.6:27-28
[41]何桢,韩亚娟.多元系统马氏田口方法的诊断与分析研究[J].数理统计与管理,2007.9.830-839
[42]何桢,韩亚娟,李菊栋.马氏田口两种不同方法的比较研究[J].中国卫生统计,2007.10:531-535
[43]韩亚娟.马氏田口在多元系统优化与分析中的应用研究[D].天津:天津大学,2005.1
[44]王雪,马俊杰,王晟.机械设备状态的经验模式分解统计识别方法[J].中国机械工程,2008.3:704-708
[45]陈湘来,韩之俊.田口方法在太阳能电池刻蚀工序中的应用[J].中国质量,2007.6:88-89
[46]陈湘来,韩之俊.基于MTS的供应商评价体系研究[J].商场现代化,2007.8:23-24
[47]薛跃,盛党红,朱立峰,韩之俊.田口式测量质量工程学与传统MSA的比较分析[J].系统工程理论与实践,2006.8:76-80
[48]Rajesh J,Taguchi S.Direction of Abnormals and Treatment of Noise Factors in Multidimensional Systems:A Discussion[J].Journal of Quality Engineering Forum,2001.3:37-44
[49]Jugulum,Rajesh,Taguchi,Genichi,Taguchi,Shin,Wilkins,James O.Discussion-A Review and Analysis of the Mahalanobis-Taguchi System[J].Technometrics,2003.1:16-21
[50]Yixin Chen,John Phillips,Linson Qiao.Improving Sofeware Subsystem Testing With Mahalanobis-Taguchi System[J].ASI's 20th Annual Symposium,2001.6:35-42
[51]Abraham,B.and Variyath,A.M.Discussion-A Review and Analysis of the Mahalanobis-Taguchi System[J].Technometrics,2003.1:22-24
[52]Woodall,W.H.,Koudelik,R.,Kwok-Leung Tsui,and Seoung Bum Kim.A Review and Analysis of the Mahalanobis-Taguchi System[J].Technometrics,2003.1:1-15
[53]Woodall,W.H.,Koudelik,R.,Kwok-Leung Tsui,Seoung Bum Kim,Stoumbos,Z.G.and Carvounis,C.P.Respoonse-A Review and Analysis of the Mahalanobis-Taguchi System[J].Technometrics,2003.1:29-30
[54]Hawkins,D.M.Discussion-A Review and Analysis of the Mahalanobis-Taguchi System[J].Technometrics,2003.1:25-28
[55]Louis La Vallee,Application of Mahalanobis-Taguchi system to Thermal Ink Jet Image Quality Inspection,Proc.of 4~(th) Annual International TPD Symposium Robust Engineering Conference,1998.8:411-427
[56]Nagao,M.Yamamoto,M.MTS approach to fcial image recognition[J].1999 IEEE international Conference on Systems,Man,and Cybernetics,1999.4:37-42
[57]Asada,M.Wafer yield prediction by the Mahalanobis-Taguchi system[J]..International Workshop on Statistical Metrology,IWSM,2001.4:25-28
[58]Hacker,J.,and Engelhardt,F.,and Frey,D.D.Robust Manufacturing Inspection and Classification with Machine Vision[J].International Journal of Production Research,2002.6:1319-1334
[59]A.Mike Vurton,Paul Miller.Human and automatic face recognition comparisonacross image formats[J].Vision Rseeareh,2001(41):3185-3195
[60]R.De Maesschalck,D.Jouan-Rimband.The Mahalanobis distance[J].Chemometrics and Intelligent Laboratory systems,2000(50):1-18
[61]Nakatsugawa,M.A study on determination of the threshold in MTS algorithm,ransactions of the Institute of Electronics[J].Information and Communication Engineers,2001.4:519-527
[62]Nakatsugawa,M.,and Ohuchi,A.A Study on Selection of the Terms in MTS Algorithm[J].Transactions of the Institute of Electronics,Information and Communication Engineers.2000.4:434-441
[63]Nagao,M.,and Yamamoto,M.,and Suzuki,K.,and Ohuchi,A.A Face Identification System Based on the Mahalanobis-Taguchi system.International Transactions in Operational Research[J],2001.1:31-45
[64]R.Di Mascio,G.W.Barton.The economic assessment of process control quality using a Taguchi-based method[J].Journal of Process control,2001.11:81-88
[65]X.L.Chen,J.L.Chen,Z.J.Han.A Method of Personal Appraisement based on MTS [J].Journal of Science,Technolgy,and Engineering,2007.6:42-45
[66]Genichi Taguchi,J.Rajesh.New Trends in Multivariate Diagnosis[J].Japan:Qulity Enginerring,2001.4:74-85
[67]Jugulum,R.,Taguchi,S.,and Yang,K.New developments in multivariate diagnosis:a comparison between two methods[J].Jouranl of the Japanese Quality Engineering Society,1999.5:62:72
[68]Li Deng-feng,Cheng Chun-tian.New similarity measures of intuitionistic fuzzy sets and application to pattern recognition[J].Pattern Recognition Letters,2002.12:221-225
[69]Chao-yu Chou,Chung-ho Chen & Hui-rong Liu.Acceptance Control Charts for Non-normal Data[J].Journal of Applied Statistics,2005.1:25-36
[70]Philippe Castagliola.(?) Control Chart for Skewed Populations Using a Scaled Weighted Variance Method[J].International Journal of Reliability,Quality and Safety Engineering,2000.3:237-252
[71]X.L.Chen,J.L.Chen,Z.J.Han.Application of Anvoa in Varaible Selection of MTS [J].Natrue Sicences,2007.12:34-36
[72]Douglas M.Hawkins and K.D.Zamba.On Small Shifts in Quality Control[J].Quality Engineering,2004.1:143-149
[73]John Terninko.The QFD,TRIZ and Taguchi Connection:Customer-Driven Robust Innovation[J].TRIZ Journal,http://www.triz-journal.com,1998.1
[74]Huei-Chun Wang.Data Classification Using the Mahalanobis-Taguchi System[J].Journal of the Chinese Institute of Industrial Engineers,2004.11:606-618
[75]Ratna Babu Chinnam,Bharatendra Rai,Nanua Singh.Tool-Condition Monitoring From Degradation Signals Using Mahalanobis-Taguchi System Analysis[J].ASI's 20~(th)Annual Symposium,2004.2343-351
[76]Jugulum R.Monplaisir L.Comparison between Mahalanobis-Taguchi System and Artificial Neural Networks[J].Journal of Quality Engineering Forum,2002.1:60-73
[77]Miki Shinsuke,Okazawa Hiroshi.Diagnosis of the Degradation of Insulating Material Using the Mahalanobis-Taguchi System Method[J].Papers of Technical Meeting on General Industries Division,2001.1:20-26
[78]王雪,马俊杰,王晟.机械设备状态的经验模式分解统计识别方法[J].中国机械工程.2008.6:704-708
[79]田口玄一.MTS法和诊断问题.标准化和品质管理[J].1999.10:63-69
[80]田口玄一.MTS法的信噪比.标准化和品质管理[J].1999.9:63-70
[81]金迟幸彦.MTS法在处理液诊断中的应用.品质工学[J].1998.6:47-52
[82]手岛昌一.基于多变量诊断的SN比.品质工学[J].1999.6:70-74
[83]韩之俊,许前.质量管理[M].北京:科学出版社,2003
[84]韩之俊.测量质量工程学[M].北京:中国计量出版社,2000
[85]陈魁.试验设计与分析[M].北京:清华大学出版社,2005
[86]中国兵器工业质量管理协会.质量工程学应用手册[M].北京:兵器工业出版社,1993
[87]田口玄一.测量技术的实验设计法[M].北京:机械工业出版社,1988
[88]田口玄一.开发、设计阶段的质量工程学[M].北京:兵器工业出版社,1990
[89]吴玉印等.田口式的稳健性设计[M].北京:兵器工业出版社,1997
[90]田口玄一.制造阶段的质量工程学[M].北京:兵器工业出版社,1992
[91]周纪芗等.质量管理统计方法[M].北京:中国统计出版社,1999
[92]马林.六西格玛管理[M].北京:中国人民大学出版社,2004
[93]韩之俊.三次设计[M].北京:机械工业出版社,1992
[94]韩之俊.质量工程学——线外、线内质量管理[M].北京:科学出版社,1991
[95]K.S.Fukunaga.Introduction to Statistical Pattern Recognition[M].New York:Academic Press.Inc,1990
[96]Douglas.C.Montogomery.Design and Analysis of Experiment[M].John Wiley &Sons,Inc,1991
[97]Chao-yu Chou,Chtmg-ho Chen & Hui-rong Liu.Economic-statistical design of(?)charts for non-normal data by considering quality loss[J].Journal of Applied Statistics,2000.8:939-951
[98]Z.Wu,M.Shamsuzzaman and E.S.Pan.Optimization design of control charts based on Tahuchi's loss function and random process shifts[J].INT.J.PROD.RES.,2004.2:379-390
[99]盛骤.概率论与数理统计[M].北京:高等教育出版社,1989
[100]常大勇,张丽丽.经济管理中的模糊数学方法[M].北京:北京经济学院出版社,1995
[101]唐守正.多元统计分析方法[M].北京:中国林业出版社,1989:61-84
[102]马本堃,高尚惠,孙煜.热力学与统计物理学[M].北京:高等教育出版社,1980
[103]王诚泰.统计物理学[M].北京:科学出版社,1979
[104]Kanetaka,Tatsuji.Diagonosis of a Special Health Check Using Mahalanobis Distance.ASI Journal,1990.3:72-76
[105]Thompson A.,Strictland A J.Strategic management:concepts and cases[M].New York:McGraw Hill Companies,lnc,2001
[106]Colan A,Judge G,Miller D.Maximum entropy econometrics:robust estimation with limted data[M].New York:John Wiley and Sons,1996
[107]Shen E Z,Perloff J M.Maximum entropy and Bayesian approaches to the ratio problem[J].Journal of Economtrics,2001.2:289-313
[108]Fraser I.An application of maximum entropy estimation:the demand for meat in the United Kingdom[J].Applied Economics,2000.1:45-59
[109]Lence S.H.,Miller D.J.Estimtion of Multi-Output Production Functions with Incomplete Data:A Generalized Maximum Entropy Approach[J].Eur.Rev.Agr.Econ.1998.1:188-209
[110]]马振华.现代应用数学手册:运筹学与最优化理论卷[M].北京:清华大学出版社,1998
[111]于洋,李一军.基于多策略评价的绩效指标权重确定方法研究[J].系统工程理论与实践,2003.8:8-15
[112]姜璐.熵——系统科学基本概念[M].沈阳:沈阳出版社,1997
[113]霍映宝,韩之俊.基于熵原理的上市公司综合评价研究[J].运筹与管理,2004.4:119-122
[114]张卫民,安景文,韩朝.熵值法在城市可持续发展评价问题中的应用[J].数量经济技术经济研究,2003.6.115-118
[115]B.Turksen.Interval Valued Fuzzy Sets Based on normal Forms[J].Fuzzy Sets and System.1986.10:191-210
[116]刘心,陈图云.扰动模糊逻辑及其“非”算子[J].模糊系统与数学,2002.9:179-182
[117]孟广武.区间值模糊集的基本理论[J].应用数学,1993.2:212-217.
[118]杨伦标,高英仪.模糊数学:原理及应用[M].广州:华南理工大学出版社,1993
[119]刘晋寅,吴孟达.模糊理论及其应用[M].长沙:国防科技大学出版社,1998
[120]冯保成.模糊数学实用集粹[M].北京:中国建筑工业出版社,1991
[121]宋晓秋.模糊数学原理与方法[M].徐州:中国矿业大学出版社,1999
[122]田口玄一.实验设计法[M].北京:机械工业出版社,1987
[123]钟南山,胡文立,何权瀛.严重急性呼吸综合征(SARS)的诊断与治疗[J].疑难病杂志,2003.6:129-131
[124]赵子文,张复春,许敏等.广州地区年春季传染性非典型肺炎 190 例临床分析[J].中国病案,2003.4:73-76
[125]彭国文,何剑峰,郭汝宁等.广东省传染性非典型肺炎流行病学特征分析[J].华南预防医学,2003.6:11-12
[126]中华医学会呼吸病学分会.社区获得性肺炎诊断和治疗指南草案[J].中华结核和呼吸杂志,1999.4:199-201
[127]邹晓颖.140例肺结核临床分析[J].中华临床医学研究杂志,2008.3:671
[128]肖正伦,黎毅敏,陈荣昌等.78例传染性非典型肺炎病例临床分析[J].中华结核和呼吸杂志,2003.6:334-338
[129]王云南,吕嘉春,冯蝶仪等.SARS 与普通肺炎的临床特征对比分析[J].广州医学院学报,2004.6:26-29
[130]蒋捍东.传染性非典型肺炎的临床现状[J].青岛大学医学院学报,2003.6:121-122
[131]彭国文,何剑峰,林锦炎等.广东省传染性非典型肺炎流行病学特征初步研究[J].广东医学,2003.6:36-38
[132]吕军,袁慧军,王敏等.收治 28 例地方传染性非典型肺炎流行病学特征分析[J].广东医学,2003.6:40-41