不完全信息下的综合评价方法研究
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摘要
综合评价问题广泛存在于社会、经济、管理等各个领域中,其理论与方法的研究有着广阔的应用前景。由于客观事物的复杂性,以及人们思维能力、知识结构和知识水平的局限性,在评价活动的实践中经常会遇到评价信息不完全的问题,如评价参数的线性不等式信息形式、评价参数的评价信息缺失、残缺判断矩阵、基于分布式结构的不完全综合评价信息及基于被评价对象子集的偏好信息等形式的不完全信息综合评价问题。传统的完全信息综合评价方法对不完全信息综合评价问题难以直接发挥作用,因此有必要对不完全信息下的综合评价方法进行研究。
Dempster-Shafer (D-S)证据理论是处理不完全信息综合评价问题的常见理论方法。那么,D-S证据理论处理不完全信息综合评价问题需要哪些步骤,D-S证据理论都可以处理什么形式的不完全信息综合评价问题,已有的基于D-S证据理论的不完全信息综合评价处理方法是否完善等,都是值得思考的问题。属性赋权问题是多属性综合评价的一个核心问题,那么属性权系数不完全信息的综合评价问题如何处理；综合评价问题除了单人的、静态的评价之外,还可以向群组、时序范围扩展,那么群体评价下的不完全信息如何集结,不完全信息的动态综合评价问题如何处理等,都是需要深入研究的问题。相对于完全信息综合评价的丰富成果,不完全信息综合评价还有很多问题亟需深入研究、解决。基于以上思考,本文做了如下工作。
(1)不完全信息综合评价建模研究。针对属性评价信息缺失的综合评价问题,以D-S证据理论为理论工具,对已有研究在模型建立上的合理性进行分析,提出了一个处理属性评价信息缺失的多属性综合评价问题的改进模型。对改进模型的求解方法、决策规则及优良特性进行研究。
(2)不完全信息综合评价属性权重确定方法研究。①将“协商”评价与“自主式”评价两种评价环境相结合,提出了具有自主式特征的多属性协商综合评价问题。将该问题提炼为属性权重为线性不等式不完全信息的综合评价问题,提出了一个基于多维诱导有序加权平均(MIOWA)算子的信息集结方法。②对部分属性偏好信息的综合评价群体赋权问题进行了研究,提出了一个基于D-S证据理论的解决方法。所给出的证据推理方法能够对属性权重的不完全偏好信息进行直接处理,不仅与残缺判断矩阵的研究思路不同,而且能够处理残缺判断矩阵中不可接受的残缺的情况；对群体赋权信息的集结方法进行了研究,集结过程可以通过相应的解析表达式在计算机上程式化,实现高效率。
(3)基于残缺判断矩阵形式、评价等级的分布式结构形式及被评价对象子集的偏好信息形式的不完全信息群体评价问题研究。将OWA算子理论运用到不完全信息群体评价中,结合“大多数”模糊语义量化算子,提出了对不完全信息进行有序合成的信息集结方法,体现了群体评价中采用多数人意见的思想。①以语言偏好关系的残缺判断矩阵群体评价问题为背景,提出了一个改进的群体评价方法。对专家偏好信息进行预处理,给出了将偏好信息形式统一的转换公式,定义了基于二元语义的诱导有序加权平均算子对群体信息进行集结。②针对评价等级的分布式结构的群体评价问题,研究了其在评价群体成员权重未知情况下的群体信息集结方法。在Yang等的ER方法的基础上,提出了一种基于位置权向量的证据的有序集结方法。③针对基于被评价对象子集的偏好信息的群体评价问题,研究了其在评价群体成员权重未知情况下的群体信息集结方法。对DS/AHP方法进行了分析改进,定义了证据的综合距离,同时,综合运用位置权重向量与“大多数”模糊语义量化算子,对证据进行有序合成形成群体评价结果。
(4)研究了不完全属性偏好信息的动态综合评价问题,建立了一个属性权重为线性不等式不完全信息形式的动态综合评价模型。所建立的模型在属性权重确定中结合了“差异驱动”和“功能驱动”的赋权思想,对动态综合评价时间因素的考虑上运用了“时间度”的概念,并对“时间度”的功能及其求解模型进行了分析说明。将所建立的动态综合评价模型运用到辽宁省14个省辖市的公共支出综合绩效评价中,进行实证研究。
最后,对全文进行了总结,对进一步的研究作了展望。
The comprehensive evaluation problems could be found abroad in the areas of sociology, economics and management. The research on the theory and method of comprehensive evaluation has an extensive prospect. Duing to the complexity of the objective world, the limitation of people's ideation and knowledge, people will often encount the comprehensive evaluation problems with incomplete information in practice. For example, the evaluation parameter presenting as linear inequation, being short of segmental evaluation information, the incomplete judgement matrix, the distributed structure of evaluation information and preference information with the subset of alternatives. They are all could be found in comprehensive evaluation problems with incomplete information. The conventional methods could not be used directly to the comprehensive evaluation problems with incomplete information. So it is necessary to do research on the methods of comprehensive evaluation problems with incomplete information.
Dempster-Shafer theory is used to deal with the comprehensive evaluation problems with incomplete information frequently. So it is important to know that how does the Dempster-Shafer theory being used to deal with the problems, what kind of problems with incomplete information could be done with Dempster-Shafer theory, and if the existent methods based on Dempster-Shafer theory is proper. The determination of attribute weights is a nuclear problem of comprehensive evaluation, so it also should be considered under the condition of attribute weights with incomplete preference information. The comprehensive evaluation problem could be extended to group evaluation environment and time series environment, and it is necessary to consider the management of incomplete information under group evaluation environment and the time series environment. Corresponding to the affluent production of conventional comprehensive evaluation, there are many work need to be done with the comprehensive evaluation with incomplete information. The main research works of this dissertation are as follows:
(1) The research of modeling of comprehensive evaluation with incomplete information. For multi-attribute comprehensive evaluation problems with segmental evaluation information, this dissertation analyzes the appropriateness of modeling in existing literature and proposes an improved model with Dempster-Shafer theory. The resolution method, decision-making rule and excellent characteristics of this improved model are then studied.
(2) The research of determination of attribute weights with comprehensive evaluation with incomplete information.①a kind of multi-attribute bargaining evaluation problem is considered which combines the bargaining evaluation and self-profit evaluation. The problem is described as attribute weights with linear inequation, and a multi-variable Induced Ordered Weighted Averaging (MIOWA) operator is proposed to solve the problem.②The determination of attribute weights is studied under group evaluation with segmental attribute evaluation information. And a method is proposed based on Dempster-Shafer theory which could deal with the segmental attribute evaluation information directly. This is distinct with the means of incomplete judgement matrix and could tackle the situation of unacceptable incomplete judgement matrix. The information synthesizing process is deduced, so it could be treated in program and efficiently.
(3) The group evaluation problem with incomplete information is considered in the form of incomplete judgement matrix, the distributed structure of evaluation information and preference information with the subsets of alternatives. The relative theory of OWA operator is used to solve the problems. Combining the "most of fuzzy linguistic quantifier, the incomplete preference informations of expert group are integrated with the weighting vector, and the integration process embodys the "majority rule" of group evaluation.①For problems in the form of incomplete judgement matrix with linguistic preference information, an improved group evaluation method is proposed. The conversion formulas are given for the pretreatment of experts'preference information, and two induced ordered weighted averaging aggregation operators for two-tuple linguistic preference information are defined for the integration of experts'preference information.②For group evaluation problems in the form of the distributed structure of evaluation information, an information integration method is presented while the experts' weight coefficients are unknown. Based on the Evidential Reasoning approach by Yang J B et.al, the information integration process is deduced with the weighting vector, which is used to adjust the basic belief assignment of envidence from every expert.③For group evaluation problems in the form of preference information with the subsets of alternatives, an information integration method is presented while the experts'weight coefficients are unknown. The improvement work is done to DS/AHP, and the collective distance measure of the evidence from individual expert is defined, then the integration of experts'preference information is done combining the weighting vector and "most of fuzzy linguistic quantifier.
(4) For a dynamic comprehensive evaluation problem with incomplete attribute preference information, a model is set up with the attribute weight in the form of linear inequation. During the determination of attribute weights, the "difference drive" and "function drive" are used. The time-orness index is used to reflect the time factor in dynamic comprehensive evaluation, and the meaning of time-orness index is analyzed further. The dynamic comprehensive evaluation model is used to check the public expenditure performances of fourteen cities in Liaoning province.
Finally, the whole dissertation is summarized, as well as future research problems.
Dempster-Shafer (D-S)证据理论是处理不完全信息综合评价问题的常见理论方法。那么,D-S证据理论处理不完全信息综合评价问题需要哪些步骤,D-S证据理论都可以处理什么形式的不完全信息综合评价问题,已有的基于D-S证据理论的不完全信息综合评价处理方法是否完善等,都是值得思考的问题。属性赋权问题是多属性综合评价的一个核心问题,那么属性权系数不完全信息的综合评价问题如何处理；综合评价问题除了单人的、静态的评价之外,还可以向群组、时序范围扩展,那么群体评价下的不完全信息如何集结,不完全信息的动态综合评价问题如何处理等,都是需要深入研究的问题。相对于完全信息综合评价的丰富成果,不完全信息综合评价还有很多问题亟需深入研究、解决。基于以上思考,本文做了如下工作。
(1)不完全信息综合评价建模研究。针对属性评价信息缺失的综合评价问题,以D-S证据理论为理论工具,对已有研究在模型建立上的合理性进行分析,提出了一个处理属性评价信息缺失的多属性综合评价问题的改进模型。对改进模型的求解方法、决策规则及优良特性进行研究。
(2)不完全信息综合评价属性权重确定方法研究。①将“协商”评价与“自主式”评价两种评价环境相结合,提出了具有自主式特征的多属性协商综合评价问题。将该问题提炼为属性权重为线性不等式不完全信息的综合评价问题,提出了一个基于多维诱导有序加权平均(MIOWA)算子的信息集结方法。②对部分属性偏好信息的综合评价群体赋权问题进行了研究,提出了一个基于D-S证据理论的解决方法。所给出的证据推理方法能够对属性权重的不完全偏好信息进行直接处理,不仅与残缺判断矩阵的研究思路不同,而且能够处理残缺判断矩阵中不可接受的残缺的情况；对群体赋权信息的集结方法进行了研究,集结过程可以通过相应的解析表达式在计算机上程式化,实现高效率。
(3)基于残缺判断矩阵形式、评价等级的分布式结构形式及被评价对象子集的偏好信息形式的不完全信息群体评价问题研究。将OWA算子理论运用到不完全信息群体评价中,结合“大多数”模糊语义量化算子,提出了对不完全信息进行有序合成的信息集结方法,体现了群体评价中采用多数人意见的思想。①以语言偏好关系的残缺判断矩阵群体评价问题为背景,提出了一个改进的群体评价方法。对专家偏好信息进行预处理,给出了将偏好信息形式统一的转换公式,定义了基于二元语义的诱导有序加权平均算子对群体信息进行集结。②针对评价等级的分布式结构的群体评价问题,研究了其在评价群体成员权重未知情况下的群体信息集结方法。在Yang等的ER方法的基础上,提出了一种基于位置权向量的证据的有序集结方法。③针对基于被评价对象子集的偏好信息的群体评价问题,研究了其在评价群体成员权重未知情况下的群体信息集结方法。对DS/AHP方法进行了分析改进,定义了证据的综合距离,同时,综合运用位置权重向量与“大多数”模糊语义量化算子,对证据进行有序合成形成群体评价结果。
(4)研究了不完全属性偏好信息的动态综合评价问题,建立了一个属性权重为线性不等式不完全信息形式的动态综合评价模型。所建立的模型在属性权重确定中结合了“差异驱动”和“功能驱动”的赋权思想,对动态综合评价时间因素的考虑上运用了“时间度”的概念,并对“时间度”的功能及其求解模型进行了分析说明。将所建立的动态综合评价模型运用到辽宁省14个省辖市的公共支出综合绩效评价中,进行实证研究。
最后,对全文进行了总结,对进一步的研究作了展望。
The comprehensive evaluation problems could be found abroad in the areas of sociology, economics and management. The research on the theory and method of comprehensive evaluation has an extensive prospect. Duing to the complexity of the objective world, the limitation of people's ideation and knowledge, people will often encount the comprehensive evaluation problems with incomplete information in practice. For example, the evaluation parameter presenting as linear inequation, being short of segmental evaluation information, the incomplete judgement matrix, the distributed structure of evaluation information and preference information with the subset of alternatives. They are all could be found in comprehensive evaluation problems with incomplete information. The conventional methods could not be used directly to the comprehensive evaluation problems with incomplete information. So it is necessary to do research on the methods of comprehensive evaluation problems with incomplete information.
Dempster-Shafer theory is used to deal with the comprehensive evaluation problems with incomplete information frequently. So it is important to know that how does the Dempster-Shafer theory being used to deal with the problems, what kind of problems with incomplete information could be done with Dempster-Shafer theory, and if the existent methods based on Dempster-Shafer theory is proper. The determination of attribute weights is a nuclear problem of comprehensive evaluation, so it also should be considered under the condition of attribute weights with incomplete preference information. The comprehensive evaluation problem could be extended to group evaluation environment and time series environment, and it is necessary to consider the management of incomplete information under group evaluation environment and the time series environment. Corresponding to the affluent production of conventional comprehensive evaluation, there are many work need to be done with the comprehensive evaluation with incomplete information. The main research works of this dissertation are as follows:
(1) The research of modeling of comprehensive evaluation with incomplete information. For multi-attribute comprehensive evaluation problems with segmental evaluation information, this dissertation analyzes the appropriateness of modeling in existing literature and proposes an improved model with Dempster-Shafer theory. The resolution method, decision-making rule and excellent characteristics of this improved model are then studied.
(2) The research of determination of attribute weights with comprehensive evaluation with incomplete information.①a kind of multi-attribute bargaining evaluation problem is considered which combines the bargaining evaluation and self-profit evaluation. The problem is described as attribute weights with linear inequation, and a multi-variable Induced Ordered Weighted Averaging (MIOWA) operator is proposed to solve the problem.②The determination of attribute weights is studied under group evaluation with segmental attribute evaluation information. And a method is proposed based on Dempster-Shafer theory which could deal with the segmental attribute evaluation information directly. This is distinct with the means of incomplete judgement matrix and could tackle the situation of unacceptable incomplete judgement matrix. The information synthesizing process is deduced, so it could be treated in program and efficiently.
(3) The group evaluation problem with incomplete information is considered in the form of incomplete judgement matrix, the distributed structure of evaluation information and preference information with the subsets of alternatives. The relative theory of OWA operator is used to solve the problems. Combining the "most of fuzzy linguistic quantifier, the incomplete preference informations of expert group are integrated with the weighting vector, and the integration process embodys the "majority rule" of group evaluation.①For problems in the form of incomplete judgement matrix with linguistic preference information, an improved group evaluation method is proposed. The conversion formulas are given for the pretreatment of experts'preference information, and two induced ordered weighted averaging aggregation operators for two-tuple linguistic preference information are defined for the integration of experts'preference information.②For group evaluation problems in the form of the distributed structure of evaluation information, an information integration method is presented while the experts' weight coefficients are unknown. Based on the Evidential Reasoning approach by Yang J B et.al, the information integration process is deduced with the weighting vector, which is used to adjust the basic belief assignment of envidence from every expert.③For group evaluation problems in the form of preference information with the subsets of alternatives, an information integration method is presented while the experts'weight coefficients are unknown. The improvement work is done to DS/AHP, and the collective distance measure of the evidence from individual expert is defined, then the integration of experts'preference information is done combining the weighting vector and "most of fuzzy linguistic quantifier.
(4) For a dynamic comprehensive evaluation problem with incomplete attribute preference information, a model is set up with the attribute weight in the form of linear inequation. During the determination of attribute weights, the "difference drive" and "function drive" are used. The time-orness index is used to reflect the time factor in dynamic comprehensive evaluation, and the meaning of time-orness index is analyzed further. The dynamic comprehensive evaluation model is used to check the public expenditure performances of fourteen cities in Liaoning province.
Finally, the whole dissertation is summarized, as well as future research problems.
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