基于证据理论的不完全信息多属性决策方法研究
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摘要
在社会经济生活中，存在着大量多属性决策问题。目前，对于完全信息下的多属性决策问题研究已经较为完善。但在实际决策过程中，由于决策信息大多数具有不精确、不完备、模糊等性质，加上决策者对问题认识或信息处理能力的局限性等原因，决策者往往只愿意或只能够提供不完全信息。因此，对不完全信息多属性决策理论与方法进行系统研究，具有重要的理论和实际意义。本文以证据理论为基本理论工具，对不完全信息多属性决策问题进行深入研究，给出了一些新的决策模型与方法。
本文共分八章，主要内容如下：
第1章主要对不完全信息多属性决策问题的相关文献进行回顾，说明了本论文研究的意义、内容与方法。
第2章主要介绍了证据理论的基本概念，并给出基于信任区间的多属性决策规则。文章首先描述了证据理论的基本概念；然后对现有的基于证据结构的决策规则存在不足进行分析；最后综合考虑信度函数和似真函数两个方面对决策方案的影响，给出基于信任区间的多属性决策规则。
第3章提出一种不完全信息多属性决策的证据推理方法。该方法首先对决策矩阵中属性值进行处理；然后根据决策矩阵中属性值的特征对不同属性下焦元进行识别，并计算每个焦元的基本效用分配值；最后得到所有决策方案的效用区间与排序。
第4章对具有层次结构的不完全信息多属性决策问题展开研究，提出了一种不完全信息多属性决策的DS-AHP方法。该方法首先对决策矩阵中属性值进行识别，生成DS-AHP方法的焦元集合；然后构造DS-AHP的判断矩阵，并运用Dempster合成法则对判断值进行合成，从而确定方案排序。
第5章对基于证据理论的群决策过程进行分析。文章首先给出一种任意两个焦元属性间相似程度的测量方法，并运用该测量方法对群决策过程中专家意见一致性进行分析；然后引入专家相对可靠度的概念，对Dempster合成法则进行改进，提出一种新的合成方法。
第6章对不完全信息下决策属性由定性和定量两类指标构成的混合型多属性群决策问题展开研究，提出一种不完全信息的混合型多属性群决策方法。该方法首先对决策矩阵中的属性值进行处理，得到不同属性下各焦元的专家信任度；然后通过Dempster合成法则对专家信任度进行合成；最后根据合成的结果对决策方案进行排序。
第7章提出一种不完全信息的群体语言多属性决策方法。该方法首先首先对多个专家给出的不同语言变量进行转化处理；然后计算各焦元的基本概率分配函数值，最后通过Dempster合成法则对其值进行合成，依据合成后的信度函数值和似真函数值对方案进行排序。
最后一章对整篇论文的主要内容和主要结论进行归纳，总结出本论文的主要研究工作与创新点，指出今后需要进一步开展的工作。
本论文的主要创新性工作如下：
(1)引入隶属度函数的概念，提出了一种不完全信息多属性决策的证据推理方法；
(2)将证据理论(DST)与层次分析法(AHP)方法结合，提出了一种不完全信息多属性决策DS-AHP方法；
(3)将模糊数学理论与证据理论结合，分别给出了决策属性值为混合型和语言型等两类不完全信息的多属性群决策问题的处理方法。
In social life or economic activities, there exist a great many multi-attribute decision making (MADM) problems. Many perfect methods have been proposed to solve MADM problems with complete information. But in the real case of the MADM problems, decision maker (DM) is willing or able to provide only incomplete information because of decision making information's imprecise, incomplete, fuzzy, and or decision maker's limitations of attention and information processing capabilities, etc. Thus it is necessary and significant to find new theories and methods for MADM problem with incomplete information systemically. This paper focuses on MADM problems with incomplete information, and mainly researches some theories and methods based on Dempster- Shafer theory (DST).
This paper involves eight chapters, and the main contents are organized as follows.
In Chapter 1, the related decision making methods for MADM problems with imcomplete information are reviewed. Then the research significance, the main contents, and the research methods are also given.
In Chapter 2, the basic concepts of Dempster-Shafer theory are introduced, and a MADM rule based on belief interval is proposed. The paper first reviews the basic concepts of Dempster-Shafer theory, and then analyzes the deficiency of the existing decision making rules based on evidence structure. Finally the paper synthetically considers the role of belief function (Bel) and plausibility function (Pls) to the alternatives, and proposes a MADM rule based on belief interval.
In Chapter 3, an evidential reasoning approach for MADM problem with incomplete information is proposed. The approach converts quantitative values into qualitative values in decision matrix, determines all possible focal elements based on the decision matrix, and calculates the basic utility assignment of each focal element and the utility interval of each decision alternative. Ranking of decision alternative is then obtained by comparing their utility intervals.
In Chapter 4, the MADM problems with hierarchical structure under incomplete information are investigated, and a DS-AHP approach for MADM problems is proposed. The approach identifies all possible focal elements from the incomplete decision matrix, then constructs the DS-AHP's hierarchical structure model, calculates the basic probability assignment (bpa) of each focal element and the belief interval of each decision alternative. Preference relations among all decision alternatives are determined by comparing their belief intervals.
In Chapter 5, the process of group multi-attribute decision making (GMADM) is analyzed based on Dempster-Shafer theory. A measuring method of similarity degree for two different evidences is given, and the consistency of experts based on the measuring method is analyzed in the process of GMADM. The expert's relative reliability is introduced, Dempster's rule of combination is improved, and a new expertise aggregation approach is proposed.
In Chapter 6, hybrid group multi-attribute decision making (GMADM) problems having both quantitative and qualitative attributes under incomplete information are investigated. An approach for hybrid GMADM problems is developed. By dealing with the incomplete decision matrix given by decision makers, the bpa values of attribute's focal elements are computed and integrated according to Dempster's rule of combination. The bpa values of expert's focal elements are integrated, and the values of Bel and Pls are calculated and used to rank all decision alternatives.
In Chapter 7, a new approach is developed for GMADM problems with incomplete linguistic information. The approach converts linguistic variables and calculates the basic utility assignment value of each focal element. The values are integrated according to Dempster's rule of combination. Alternatives are then ranked by comparing the values of belief function and plausibility function.
The last chapter summarizes all the work of this paper, and gives some useful suggestions for future research.
This paper proposes the innovation as follows:
(1) The membership function is introduced, and an evidential reasoning approach for MADM problem with incomplete information is proposed.
(2) The DS-AHP method for MADM problems with incomplete information is proposed, which incorporates Dempster-Shafer theory of evidence with Analytic Hierarchy Process (AHP).
(3) Dempster-Shafer theory of evidence with Fuzzy Theory is incorporated, and two approaches are developed for hybrid GMADM problem with incomplete information and linguistic GMADM problem with incomplete information, respectively.
本文共分八章，主要内容如下：
第1章主要对不完全信息多属性决策问题的相关文献进行回顾，说明了本论文研究的意义、内容与方法。
第2章主要介绍了证据理论的基本概念，并给出基于信任区间的多属性决策规则。文章首先描述了证据理论的基本概念；然后对现有的基于证据结构的决策规则存在不足进行分析；最后综合考虑信度函数和似真函数两个方面对决策方案的影响，给出基于信任区间的多属性决策规则。
第3章提出一种不完全信息多属性决策的证据推理方法。该方法首先对决策矩阵中属性值进行处理；然后根据决策矩阵中属性值的特征对不同属性下焦元进行识别，并计算每个焦元的基本效用分配值；最后得到所有决策方案的效用区间与排序。
第4章对具有层次结构的不完全信息多属性决策问题展开研究，提出了一种不完全信息多属性决策的DS-AHP方法。该方法首先对决策矩阵中属性值进行识别，生成DS-AHP方法的焦元集合；然后构造DS-AHP的判断矩阵，并运用Dempster合成法则对判断值进行合成，从而确定方案排序。
第5章对基于证据理论的群决策过程进行分析。文章首先给出一种任意两个焦元属性间相似程度的测量方法，并运用该测量方法对群决策过程中专家意见一致性进行分析；然后引入专家相对可靠度的概念，对Dempster合成法则进行改进，提出一种新的合成方法。
第6章对不完全信息下决策属性由定性和定量两类指标构成的混合型多属性群决策问题展开研究，提出一种不完全信息的混合型多属性群决策方法。该方法首先对决策矩阵中的属性值进行处理，得到不同属性下各焦元的专家信任度；然后通过Dempster合成法则对专家信任度进行合成；最后根据合成的结果对决策方案进行排序。
第7章提出一种不完全信息的群体语言多属性决策方法。该方法首先首先对多个专家给出的不同语言变量进行转化处理；然后计算各焦元的基本概率分配函数值，最后通过Dempster合成法则对其值进行合成，依据合成后的信度函数值和似真函数值对方案进行排序。
最后一章对整篇论文的主要内容和主要结论进行归纳，总结出本论文的主要研究工作与创新点，指出今后需要进一步开展的工作。
本论文的主要创新性工作如下：
(1)引入隶属度函数的概念，提出了一种不完全信息多属性决策的证据推理方法；
(2)将证据理论(DST)与层次分析法(AHP)方法结合，提出了一种不完全信息多属性决策DS-AHP方法；
(3)将模糊数学理论与证据理论结合，分别给出了决策属性值为混合型和语言型等两类不完全信息的多属性群决策问题的处理方法。
In social life or economic activities, there exist a great many multi-attribute decision making (MADM) problems. Many perfect methods have been proposed to solve MADM problems with complete information. But in the real case of the MADM problems, decision maker (DM) is willing or able to provide only incomplete information because of decision making information's imprecise, incomplete, fuzzy, and or decision maker's limitations of attention and information processing capabilities, etc. Thus it is necessary and significant to find new theories and methods for MADM problem with incomplete information systemically. This paper focuses on MADM problems with incomplete information, and mainly researches some theories and methods based on Dempster- Shafer theory (DST).
This paper involves eight chapters, and the main contents are organized as follows.
In Chapter 1, the related decision making methods for MADM problems with imcomplete information are reviewed. Then the research significance, the main contents, and the research methods are also given.
In Chapter 2, the basic concepts of Dempster-Shafer theory are introduced, and a MADM rule based on belief interval is proposed. The paper first reviews the basic concepts of Dempster-Shafer theory, and then analyzes the deficiency of the existing decision making rules based on evidence structure. Finally the paper synthetically considers the role of belief function (Bel) and plausibility function (Pls) to the alternatives, and proposes a MADM rule based on belief interval.
In Chapter 3, an evidential reasoning approach for MADM problem with incomplete information is proposed. The approach converts quantitative values into qualitative values in decision matrix, determines all possible focal elements based on the decision matrix, and calculates the basic utility assignment of each focal element and the utility interval of each decision alternative. Ranking of decision alternative is then obtained by comparing their utility intervals.
In Chapter 4, the MADM problems with hierarchical structure under incomplete information are investigated, and a DS-AHP approach for MADM problems is proposed. The approach identifies all possible focal elements from the incomplete decision matrix, then constructs the DS-AHP's hierarchical structure model, calculates the basic probability assignment (bpa) of each focal element and the belief interval of each decision alternative. Preference relations among all decision alternatives are determined by comparing their belief intervals.
In Chapter 5, the process of group multi-attribute decision making (GMADM) is analyzed based on Dempster-Shafer theory. A measuring method of similarity degree for two different evidences is given, and the consistency of experts based on the measuring method is analyzed in the process of GMADM. The expert's relative reliability is introduced, Dempster's rule of combination is improved, and a new expertise aggregation approach is proposed.
In Chapter 6, hybrid group multi-attribute decision making (GMADM) problems having both quantitative and qualitative attributes under incomplete information are investigated. An approach for hybrid GMADM problems is developed. By dealing with the incomplete decision matrix given by decision makers, the bpa values of attribute's focal elements are computed and integrated according to Dempster's rule of combination. The bpa values of expert's focal elements are integrated, and the values of Bel and Pls are calculated and used to rank all decision alternatives.
In Chapter 7, a new approach is developed for GMADM problems with incomplete linguistic information. The approach converts linguistic variables and calculates the basic utility assignment value of each focal element. The values are integrated according to Dempster's rule of combination. Alternatives are then ranked by comparing the values of belief function and plausibility function.
The last chapter summarizes all the work of this paper, and gives some useful suggestions for future research.
This paper proposes the innovation as follows:
(1) The membership function is introduced, and an evidential reasoning approach for MADM problem with incomplete information is proposed.
(2) The DS-AHP method for MADM problems with incomplete information is proposed, which incorporates Dempster-Shafer theory of evidence with Analytic Hierarchy Process (AHP).
(3) Dempster-Shafer theory of evidence with Fuzzy Theory is incorporated, and two approaches are developed for hybrid GMADM problem with incomplete information and linguistic GMADM problem with incomplete information, respectively.
引文
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