【作者】 王一任；

【导师】 孙振球；

【作者基本信息】 中南大学 ， 流行病与卫生统计学， 2012， 博士

【摘要】 目的：(1)拟解决目前综合评价领域中亟待解决的几个重要问题：①综合评价方法一般是对总体资料(特定空间和时间)进行评价,但某些特殊情形下,需要对样本资料评价,那么在综合排序时有必要考虑抽样误差对排序结果的影响,但目前综合评价方法对评价结果只能是描述,而不能进行统计推断,因此存在着抽样误差的估计问题。②多方法评价结论的非一致性困扰问题。③多指标综合评价若干方法中的逆序问题。④常用综合评价方法的软件系统缺乏问题。(2)从方法学上进一步改进和完善医疗卫生领域应用最为广泛的静态TOPSIS (Technique for Order Preference by Similarity to Ideal Solution)法并提出新的动态TOPSIS法。方法：通过广泛查阅文献,参考国内外相关研究成果,利用Monte Carlo模拟技术,针对样本资料,构建综合评价的抽样误差随机模拟模型。基于该模型的模拟结果,提出一种解决“多方法评价结论非一致性困扰问题”的新思路,即对综合评价的“概率结论”组合。通过研究理想点法、TOPSIS法、密切值法、SAW(Simple Additive Weighting)法、优序法、秩和比法以及信息熵客观定权法的逆序现象,找出各种方法产生逆序的原因,并提出解决方案。通过分析探讨传统的静态的TOPSIS存在的缺陷,提出静态TOPSIS法的改良方法。通过文献检索,发现目前医学科研中存在大量的含有时间因素的“立体时序数据集”,而目前对此种三维数据(含有“评价对象”、“评价指标”、“评价时间”)的评价,大多采用静态综合评价方法,不能反映事物动态变化。基于医学科研的综合评价需求,提出一种新的动态TOPSIS法。广泛参考国内外多种统计软件,听取广泛相关人员组成的议题小组的意见,基于Microsoft Excel2002软件,利用Microsoft Visual Basic6.0、Microsoft Visio2002和Visual Basic for Application语言开发了综合评价方法的简体中文版软件包(Comprehensive Evaluation Software,简称CES)。并用SAS6.12for Windows自行编制相应方法的SAS程序(TOPSIS法SAS程序己发表,见文献[143]；其余SAS程序己收入教材[144]),将SAS程序与CES在同一个计算机平台上对同一资料用各种综合评价方法进行分析,然后把两种分析结果一并列出,对每个数据均比较到小数点后15位,进行SAS与CES统计分析结果的比较。结果：1.本文建立了综合评价的抽样误差随机模拟模型并给出了相应的Mablab程序。2.本文提出了“整体排序优先度”与“整体排序平均优先度”的概念,因此提出了一种综合评价结果的排序的新方法：按照“整体排序(平均)优先度”,从大到小排序。3.对于样本资料,本文将综合评价的传统“绝对结论”改为“概率结论”,并依据“整体排序(平均)优先度”可对任何综合评价方法的结果分档。4.本文模拟了TOPSIS法、SAW法、RSR法的抽样误差,发现：①即使指标独立、均服从正态分布,TOPSIS法与SAW法某些评价对象的综合评价值可能会服从正态分布,而另一些评价对象的综合评价值不服从正态分布。而RSR法的模拟RSRi值均不服从正态分布。②TOPSIS法、SAW法、RSR法的综合评价值均有上下限：0≤Ci≤1,0≤Ai≤m,0<RSRi≤1。当某评价对象的综合评价值靠近上限或下限时,则此时综合评价值可能呈偏态分布。5.本文提出了一种解决“多方法评价结论非一致性困扰问题”的新思路——从现有的组合方法中挑选合适的方法对“整体排序平均优先度”组合。即对综合评价的“概率结论”组合。6.理想点法、TOPSIS法、密切值法、SAW法、优序法、秩和比法以及信息熵客观定权法均存在逆序问题。7.理想点法产生逆序的原因：理想点的计算与评价对象紧密相连,当增加或删除含有最优点或最劣点的评价对象时,理想解选择的范围扩大或缩小了,理想点改变了,每个评价对象到理想点的距离就会发生变化,各评价对象之间的优劣顺序也很容易发生变化,从而产生逆序。TOPSIS法产生逆序的原因：①归一化矩阵的计算；②最优方案与最劣方案的计算。密切值法产生逆序的原因：①标准化矩阵的计算；②最优点与最劣点的计算；③密切值Ci=di/d-li/l的计算。SAW法产生逆序的原因：指标的标准化法中最大值与最小值的选取。优序法产生逆序的原因：优序数的给定方法与评价对象紧密相连,当增加或删除不含最大值的评价对象时,优序数必然改变,则排序结果也会改变。秩和比法产生逆序的原因：指标秩的编制方法与评价对象紧密相连,当增加或删除不含最大值的评价对象时,指标秩和秩和比必然改变,则排序结果也会改变。信息熵定权法产生逆序的原因：①归一化矩阵的计算；②信息熵的计算。8.本文提出了绝对理想点法、改进TOPSIS法、改进密切值法、改进SAW法可解决其逆序问题。9.本文提出了一种新的改良静态TOPSIS法。10.本文提出了一种基于指标值及指标增量的新的动态TOPSIS法。11.编制了综合评价软件包CES简体中文1.1版。主要包括：层次分析法、TOPSIS法、密切值法、模糊综合评价、灰色关联分析、功效系数法、秩和比法等模块。CES1.1大小约2.78M.CES1.1可在Microsoft Excel97以上版本运行,运行后成为Excel的一个菜单。自编的SAS程序与CES1.1对同一资料用不同综合评价方法的分析结果均非常接近,除了秩和比法两者主要指标的结果差异小于10-7,其余方法两者差异均小于10-12。结论：1.本文建立的综合评价的抽样误差随机模拟模型,具有通用性,灵活方便。对任何抽样资料,任何综合评价方法,该模型都适用。依据本文提出的“整体排序优先度”与“整体排序平均优先度”的概念,按照“整体排序(平均)优先度”排序,是一种有效的综合评价结果排序的新方法。2.在抽样研究中,即使指标独立、均服从正态分布,TOPSIS法、SAW法、RSR法各评价对象的综合评价值不一定会服从正态分布。当某评价对象的综合评价值靠近其上限或下限时,则此时综合评价值可能呈偏态分布。3.本文提出的综合评价结论的新表达方法与方式——“概率结论”,相对于传统的“绝对结论”,它具有更好的开放性,也更贴近实际。4.基于“概率结论”的组合法不仅包含了“绝对结论”的信息,还考虑了抽样误差的影响,其组合结果更合理、可信。5.理想点法、TOPSIS法、密切值法、SAW法、优序法、秩和比法以及信息熵客观定权法均存在逆序问题。6.本文提出的绝对理想点法、改进TOPSIS法、改进密切值法、改进SAW法均具有强保序性。7.对于逆序问题不能消除的方法,如优序法、秩和比法等,应用时应慎重考虑其评价有效范围及具体资料情况,最好适用于一个绝对无任何变动的评价对象集,当决策者合理地变更评价对象时,它们就不再适用了。对于逆序现象合理存在的信息熵定权法没有必要去消除逆序问题。可与主观赋权法结合采用组合赋权,减少逆序的发生。8.本文提出的新的改良静态TOPSIS法,它具有强保序性,并且很好的解决了传统TOPSIS法Ci值的缺陷。9.本文提出的新的动态TOPSIS法,继承了传统静态TOPSIS法的所有优点,是一种有效的综合评价方法,适用于包含了“评价对象”、“评价指标”及“评价时间”的三维资料。它可既考虑“过去情况”、“现在状况”,也关注“将来发展趋势”。10.本文研制的CES1.1,其分析结果是可靠的,它使广大实际工作者从繁杂的计算中解放出来,极大促进了综合评价方法的推广与应用。它继承了目前人们普遍使用和熟知的办公软件Excel的风格,应用界面友好,操作简单易用,对统计专业人士与非统计专业人士均适用。更多还原

【Abstract】 Objective:(1)To Solve the four problems of the comprehensive evaluation field in the world at present:①Because of lack of the accuracy measure of the sensitivity and stability of all kinds of comprehensive evaluation methods, the sampling errors cannot be estimated in the sampling research usually.②Inconsistency among the evaluation conclusions drawn by different evaluation methods exists in the multi-attribute evaluation.③The Problem of Inverted Sequence in Synthetic Appraisal.④The problem of lack of comprehensive evalution softwarepackage.(2) To further improve and perfect the static TOPSIS approach which is applied widely in the medicine and hygiene fields. What’s more, a novel dynamic TOPSIS method is presented.Methods:By reviewing the domestic and foreign research and considering the suggestions of experts, we make use of the Monte Carlo simulation technology to develop a stochastic simulation model of the sampling errors of comprehensive evaluation methods.Based on the results of this model,a novel thinking which can work out the problem of inconsistency among the evaluation conclusions drawn by different evaluation methods is proposed. That is combination of probability results.We find out the reasons of reverse order phenomenon of a variety of methods and put forward the solving solution by studying Ideal Point method,TOPSIS method, Osculating Value method, SAW method, Precedence Order method,RSR method and information entropy method.By means of analyzing and dicussing the defaults of the traditional static TOPSIS method, a novel modified TOPSIS approach is raised. Literature retrieval reveals that there are plentiful Multi-Dimensional Time Series Data which contains the time factor.But most researches adot the static synthetical evaluation methods which cannot reflect the dynamic changes of things. Based on the needs of comprehensive evaluation in medical scientific research, we come up with a fresh dynamic TOPSIS method, we studied the structure of many domestic and international excellent statistical softwares,and consulted ideas and suggestions from nominal group. Then we use Microsoft Visual Basic6.0、Microsoft Visio2002and VBA (Visual Basic for Application) to develop a comprehensive evaluation software (CES) based on Microsoft Excel2002. Moreover,we use CES1.0and SAS6.12to analyze the same data file on the same PC, One of the SAS programs has been published[143],the others have been adopted by book[144]. Main indexes with15-bit decimal fraction of different comprehensive evaluation methods was given by CES1.1and SAS6.12,which enabled us to compare the accuracy of CES1.1and SAS6.12.Results:1.This paper develops a stochastic simulation model of the sampling errors of comprehensive evaluation methods and gives the matlab programs of the model.2. This paper advances the conceptions of "The Overall Scheduling Priority"and "The Overall Average Scheduling Priority", and proposes a new sorting method of the results of comprehensive evaluation methods that is sorting the results in a ascending order according to " The Overall (Average)Scheduling Priority".3.This paper changes the conventional "Absolute conclusion" of comprehensive evaluation methods to "probability results " for the sample data.We can staple any results of comprehensive evaluation methods in accordance with "The Overall (Average)Scheduling Priority".4. This paper simulating the sampling errors of TOPSIS method, SAW method and RSR method finds that:①Even if the variables are independent and obey the normal distribution, the comprehensive evaluation values of some objects of TOPSIS method and SAW method may follow the normal distribution,while other objects may not comply with the normal distribution.Especially, all objects of RSR method disobey the normal distribution.②The comprehensive evaluation values of TOPSIS method, SAW method, RSR method have upper and lower limits:0≤Ci≤1,0≤Ai≤m,0<RSRi≤1o When the comprehensive evaluation values are close to the upper limit or lower limit, the comprehensive evaluation values may appear skew distribution.5.This paper proposes a novel thinking which can work out the problem of inconsistency among the evaluation conclusions drawn by different evaluation methods. That is, selecting proper methods from the existing combinatorial methods to combine " The Overall (Average)Scheduling Priority", in other words combination of probability results.6. The Ideal Point method, TOPSIS method, Osculating Value method, SAW method, Precedence Order method,RSR method and Information Entropy method all have reversal phenomena.7. The reasons of the Ideal Point method generating reverse are as follows:The ideal point calculation and the evaluation objects are closely linked.When the evaluation objects containing the optimum point or the pessimum point are added or deleted, the selection range of ideal solution is enlarged or reduced.Once the ideal points change,the distance between the evaluation objects and the ideal points change correspondingly.Then the order among the evaluation objects will easily alter, which leads to produce the reversal order.The reasons of the TOPSIS method generating reverse are as follows:①The computation of uniformization matrix;②The computation of the optimal decision schema and the inferior decision schema。The reasons of the Osculating Value method generating reverse are as follows:①The computation of standardization matrix;②The computation of the optimal point and the inferior point;③The computation of Ci=di/d-li/lThe reasons of the SAW method generating reverse are as follows:The selection of the maximum and minimum in standardized method of index.The reasons of the Precedence Order method generating reverse are as follows:The given method of preferential ordinal number and the evaluation objects are closely linked.When the evaluation objects that don’t contain maximum are added or deleted, the preferential ordinal numbers change inevitably,and the sorting results alter correspondingly.The reasons of the RSR method generating reverse are as follows:Index rank establishment method and the evaluation objects are closely linked.When the evaluation objects that don’t contain maximum are added or deleted, the rank and Rank Sum Ratio (RSR) change inevitably, and the sorting results alter correspondingly.The reasons of the Information Entropy method generating reverse are as follows:①The computation of uniformization matrix;②The computation of information entropy.8. The Absolute Ideal Point method, improved TOPSIS method,improved Osculating Value method and improved SAW method which presented by this paper can solve the reversal problem.9.This paper puts forward a novel modified TOPSIS approach.10. This paper proposes a new dynamic TOPSIS method basing on the index value and index increment.11. The Chinese comprehensive evaluation software (version1.1) has been successfully developed. It consists of modules of AHP, TOPSIS, RSR, grey correlation analysis, efficacy coefficient method and fuzzy comprehensive evaluation. The size of CES1.1is about2.78MB. CES1.1can run on Microsoft Exce197or later and becomes a menu of Excel. The results of CES1.1are close to the results of SAS. The differences of the two softwares are lower than10-2, except that the differences between the results of RSR module of CES1.1and the results of SAS program of RSR are lower than10-7.Conclusions:1. The stochastic simulation model of the sampling errors of comprehensive evaluation methods developed by this paper is universal, flexible and convenient.This model is suitable for any sampling data and any comprehensive evaluation methods. It is an effective method to sort resulits according to "The Overall Average Scheduling Priority" noted by this paper.2. Even if the variables are independent and obey the normal distribution, the comprehensive evaluation values of TOPSIS method and SAW method may follow the normal distribution in sampling study,while other objects may not comply with the normal distribution.Especially, all objects of RSR method disobey the normal distribution. When the comprehensive evaluation values are close to the upper limit or lower limit, the comprehensive evaluation values may appear skew distribution.3. The new expression method and way of conclusions of comprehensive evaluation methods——"probability results " is more open and more practicable comparing with the conventional "Absolute conclusion".4. The combination method based on"probability results " is more scientific, reasonable and credible.5.The Ideal Point method, TOPSIS method, Osculating Value method, SAW method, Precedence Order method,RSR method and Information Entropy method all have reversal phenomena.6.The Absolute Ideal Point method, improved TOPSIS method,improved Osculating Value method and improved SAW method which presented by this paper all have strong rank preservation.7. For the methods which cannot eliminate the reverse problem such as Precedence Order method,RSR method etc, we should look round their valid range and conditions of actual data, and select a Evaluation objects set which has no change absolutely. There is no need for eliminating the reversed order problem of Information Entropy method whose reversed order problem is reasonable.We can adopt combination weighting approach combining with subjective weight which can reduce the reversal phenomena.8. The novel modified TOPSIS approach raised by this paper have strong rank preservation and can sovle the defects of Ci in traditional TOPSIS method.9. The new dynamic TOPSIS method raised by this paper not only inherits all the merits of the traditional static TOPSIS method,but also is an effective method.This method is suitable for three-dimensional data containing "evaluation objects"," evaluation index" and "evaluation time". It pay attention to "the past","the present" and " the future development trends".10. The results of CES1.1are reliable, which fills the blank that different demestic and international statistical softwares cannot process comprehensive evaluation data, lightens the researcher’s burden and promote the popularization of comprehensive evaluation methods.CES1.1is of better useful,friendly interface,easy operation in that it succeeded the style of a office software-Excel.It can meet the needs of person majored in statistics or not.更多还原