群体决策的共识模型研究
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摘要
在现实生活中，人们经常会面临各种各样的决策，由于各人的社会经历、文化水准、社会地位等方面的差异，对同一问题往往有不同的理解和看法，因而所做的决策不尽相同甚至相反。群体共识模型主要研究如何协调各种不同意见和看法以形成群体总的看法和意见。本文对群体决策中的一些共识问题进行了研究，主要工作与创新点如下：
1.在最小共识成本的概念基础上，提出了基于集结算子的最小成本共识模型。当集结算子选择加权向量为(1/2,...,0,...1/2)T的OWA算子时，提出的新的共识模型退化到Ben-Arieh等的共识模型。同时，论文研究了在一般的集结算子（例如加权平均算子和OWA算子）下带线性成本的最小成本共识模型，并给了求解这些模型的线性规划方法。
2.在群体决策中，基于偏好关系的一致性度量一般包括两个问题：个体偏好关系的一致性和群体共识。在AHP中，决策者用判断矩阵（即：乘性偏好关系）来表达他们的偏好。当采用加权几何平均综合排序向量法（RGMM）来进行AHP群体决策时，几何一致性指标通常被用来度量个体判断矩阵的一致性。本文进一步定义了度量群体判断矩阵和个体判断矩阵间共识度的共识指标。在Chiclana等的共识框及Xu和Wei的个体一致性改进模型的基础上，论文提出了基于RGMM法的AHP共识模型。仿真表明提出的两个共识模型都能改进判断矩阵的共识度，从而帮助决策者达到共识。同时，提出的AHP群体决策共识模型有两个优点1）在达到共识的同时，个体判断的矩阵的一致性也得到改进；2）共识模型满足Pareto准则。
3.提出解决模糊偏好关系的一致性问题（比如个体一致性的构建、共识模型和不完全偏好关系的管理）的线性优化模型。提出的方法在构建个体一致性和达成共识时最优保存原始偏好信息，在计算不完全模糊偏好关系时最大化了模糊偏好关系的一致性水平。由于线性优化模型的求解简单花费时间少，因此，在群体决策问题中，本文得到的结果对模糊偏好关系的一致性问题的应用来说是简单和方便的。
4.通过引进区间数值标度的概念和定义区间数值标度的逆运算，提出了区间二元语义模型及相关的处理二元语义的计算模型。区间二元语义模型通过区间数来匹配语言标签集中的标签，是已有的二元语义模型的推广。此外，通过定义传递性构造矩阵的区间一致性，论文提出了由传递性构造矩阵得到区间数值标度的一致性方法。
5.提出了语言标签集上的分布评价的概念并研究了它的运算规则。提出了语义的分布评价的加权平均算子和OWA算子。进一步，提出了基于分布评价的语言偏好关系，研究了基于分布式的语言偏好关系的共识测度，讨论了共识测度的两个性质。最后，提出了基于分布评价的语言偏好关系的共识模型。研究结果为基于分布评价的语言偏好关系的应用提供了基础。
论文最后对研究结果进行总结，并提出需要进一步深入研究的问题。
The main aim of this dissertation is to study the consensus model in group decision making (GDM). In GDM, consensus models are decision aid tools and help experts modify their individual opinions to reach a closer agreement. We have proposed different consensus approaches to reach consensus in GDM problems. Our main results are summarized as follows.
1. Based on the concept of minimum-cost consensus, we propose a novel framework to achieve minimum-cost consensus under aggregation operators. Analytical results indicate that the proposed framework reduces to the consensus model of Ben-Arieh et al. when the selected aggregation operator is the ordered weighted averaging (OWA) operator with weight vector (1/2,...,0,...1/2)T. Furthermore, this paper closely examines the minimum-cost consensus models with a linear cost function under the common aggregation operators (e.g., the weighted veraging operator and the OWA operator) Linear-programming-based approaches are also developed to solve these models.
2. For consensus models of group decision making using preference relations, the consistency measure includes two subproblems:individual consistency measure and consensus measure. In the analytic hierarchy process (AHP), the decision makers express their preferences using judgement matrices (i.e., multiplicative preference relations). Also, the geometric consistency index is suggested to measure the individual consistency of judgement matrices, when using row geometric mean prioritization method (RGMM), one of the most extended AHP prioritization procedures. This paper further defines the consensus indexes to measure consensus degree among judgement matrices (or decision makers) for the AHP group decision making using RGMM. By using Chiclana et al.'s consensus framework, and by extending Xu and Wei's individual consistency improving method, we present two AHP consensus models under RGMM. Simulation experiments show that the proposed two consensus models can improve the consensus indexes of judgement matrices to help AHP decision makers reach consensus. Moreover, our proposal has two desired features:(1) in reaching consensus, the adjusted judgement matrix has a better individual consistency index (i.e., geometric consistency index) than the corresponding original judgement matrix;(2) this proposal satisfies the Pareto principle of social choice theory.
3. We propose linear optimization models for solving some issues on consistency of fuzzy preference relations, such as individual consistency construction, consensus model and management of incomplete fuzzy preference relations. Our proposal optimally preserves original preference information in constructing individual consistency and reaching consensus (in Manhattan distance sense), and maximizes the consistency level of fuzzy preference relations in calculating the missing values of incomplete fuzzy preference relations. Linear optimization models can be solved in very little computational time using readily available softwares. Therefore, the results in this paper are also of simplicity and convenience for the application of consistent fuzzy preference relations in GDM problems.
4. By introducing the concept of the interval numerical scale and by defining a generalized inverse operation of the interval numerical scale, we propose an interval version of2-tuple fuzzy linguistic representation model and develop the corresponding computational model to deal with the linguistic2-tuples. The interval version of2-tuple fuzzy linguistic representation model uses interval numbers to match the terms in a linguistic terms set, and generalizes the existing2-tuple fuzzy linguistic representation models. Further, by defining the interval consistency of the transitive calibration matrix,this paper proposes a consistency-based approach to derive the interval numerical scale from the transitive calibration matrix. Under established interval numerical scale, the transitive calibration matrix is of perfect consistency in terms of the interval sense.
5. We propose the concept of distribution assessments in a linguistic term set, and study the operational laws of linguistic distribution assessments. The weighted averaging operator and the ordered weighted averaging operator for linguistic distribution assessments are presented. We also develop the concept of distribution linguistic preference relations, whose elements are distribution assessments. Further, we study the consensus measures for group decision making based on distribution linguistic preference relations. Two desirable properties of the proposed consensus measures are shown. A consensus model also has been developed to help decision makers improve the consensus level among distribution linguistic preference relations. Finally, illustrative numerical examples are given. The results in this paper provide a theoretic basis for the application of linguistic preference relations based on distribution assessment in group decision making.
1.在最小共识成本的概念基础上，提出了基于集结算子的最小成本共识模型。当集结算子选择加权向量为(1/2,...,0,...1/2)T的OWA算子时，提出的新的共识模型退化到Ben-Arieh等的共识模型。同时，论文研究了在一般的集结算子（例如加权平均算子和OWA算子）下带线性成本的最小成本共识模型，并给了求解这些模型的线性规划方法。
2.在群体决策中，基于偏好关系的一致性度量一般包括两个问题：个体偏好关系的一致性和群体共识。在AHP中，决策者用判断矩阵（即：乘性偏好关系）来表达他们的偏好。当采用加权几何平均综合排序向量法（RGMM）来进行AHP群体决策时，几何一致性指标通常被用来度量个体判断矩阵的一致性。本文进一步定义了度量群体判断矩阵和个体判断矩阵间共识度的共识指标。在Chiclana等的共识框及Xu和Wei的个体一致性改进模型的基础上，论文提出了基于RGMM法的AHP共识模型。仿真表明提出的两个共识模型都能改进判断矩阵的共识度，从而帮助决策者达到共识。同时，提出的AHP群体决策共识模型有两个优点1）在达到共识的同时，个体判断的矩阵的一致性也得到改进；2）共识模型满足Pareto准则。
3.提出解决模糊偏好关系的一致性问题（比如个体一致性的构建、共识模型和不完全偏好关系的管理）的线性优化模型。提出的方法在构建个体一致性和达成共识时最优保存原始偏好信息，在计算不完全模糊偏好关系时最大化了模糊偏好关系的一致性水平。由于线性优化模型的求解简单花费时间少，因此，在群体决策问题中，本文得到的结果对模糊偏好关系的一致性问题的应用来说是简单和方便的。
4.通过引进区间数值标度的概念和定义区间数值标度的逆运算，提出了区间二元语义模型及相关的处理二元语义的计算模型。区间二元语义模型通过区间数来匹配语言标签集中的标签，是已有的二元语义模型的推广。此外，通过定义传递性构造矩阵的区间一致性，论文提出了由传递性构造矩阵得到区间数值标度的一致性方法。
5.提出了语言标签集上的分布评价的概念并研究了它的运算规则。提出了语义的分布评价的加权平均算子和OWA算子。进一步，提出了基于分布评价的语言偏好关系，研究了基于分布式的语言偏好关系的共识测度，讨论了共识测度的两个性质。最后，提出了基于分布评价的语言偏好关系的共识模型。研究结果为基于分布评价的语言偏好关系的应用提供了基础。
论文最后对研究结果进行总结，并提出需要进一步深入研究的问题。
The main aim of this dissertation is to study the consensus model in group decision making (GDM). In GDM, consensus models are decision aid tools and help experts modify their individual opinions to reach a closer agreement. We have proposed different consensus approaches to reach consensus in GDM problems. Our main results are summarized as follows.
1. Based on the concept of minimum-cost consensus, we propose a novel framework to achieve minimum-cost consensus under aggregation operators. Analytical results indicate that the proposed framework reduces to the consensus model of Ben-Arieh et al. when the selected aggregation operator is the ordered weighted averaging (OWA) operator with weight vector (1/2,...,0,...1/2)T. Furthermore, this paper closely examines the minimum-cost consensus models with a linear cost function under the common aggregation operators (e.g., the weighted veraging operator and the OWA operator) Linear-programming-based approaches are also developed to solve these models.
2. For consensus models of group decision making using preference relations, the consistency measure includes two subproblems:individual consistency measure and consensus measure. In the analytic hierarchy process (AHP), the decision makers express their preferences using judgement matrices (i.e., multiplicative preference relations). Also, the geometric consistency index is suggested to measure the individual consistency of judgement matrices, when using row geometric mean prioritization method (RGMM), one of the most extended AHP prioritization procedures. This paper further defines the consensus indexes to measure consensus degree among judgement matrices (or decision makers) for the AHP group decision making using RGMM. By using Chiclana et al.'s consensus framework, and by extending Xu and Wei's individual consistency improving method, we present two AHP consensus models under RGMM. Simulation experiments show that the proposed two consensus models can improve the consensus indexes of judgement matrices to help AHP decision makers reach consensus. Moreover, our proposal has two desired features:(1) in reaching consensus, the adjusted judgement matrix has a better individual consistency index (i.e., geometric consistency index) than the corresponding original judgement matrix;(2) this proposal satisfies the Pareto principle of social choice theory.
3. We propose linear optimization models for solving some issues on consistency of fuzzy preference relations, such as individual consistency construction, consensus model and management of incomplete fuzzy preference relations. Our proposal optimally preserves original preference information in constructing individual consistency and reaching consensus (in Manhattan distance sense), and maximizes the consistency level of fuzzy preference relations in calculating the missing values of incomplete fuzzy preference relations. Linear optimization models can be solved in very little computational time using readily available softwares. Therefore, the results in this paper are also of simplicity and convenience for the application of consistent fuzzy preference relations in GDM problems.
4. By introducing the concept of the interval numerical scale and by defining a generalized inverse operation of the interval numerical scale, we propose an interval version of2-tuple fuzzy linguistic representation model and develop the corresponding computational model to deal with the linguistic2-tuples. The interval version of2-tuple fuzzy linguistic representation model uses interval numbers to match the terms in a linguistic terms set, and generalizes the existing2-tuple fuzzy linguistic representation models. Further, by defining the interval consistency of the transitive calibration matrix,this paper proposes a consistency-based approach to derive the interval numerical scale from the transitive calibration matrix. Under established interval numerical scale, the transitive calibration matrix is of perfect consistency in terms of the interval sense.
5. We propose the concept of distribution assessments in a linguistic term set, and study the operational laws of linguistic distribution assessments. The weighted averaging operator and the ordered weighted averaging operator for linguistic distribution assessments are presented. We also develop the concept of distribution linguistic preference relations, whose elements are distribution assessments. Further, we study the consensus measures for group decision making based on distribution linguistic preference relations. Two desirable properties of the proposed consensus measures are shown. A consensus model also has been developed to help decision makers improve the consensus level among distribution linguistic preference relations. Finally, illustrative numerical examples are given. The results in this paper provide a theoretic basis for the application of linguistic preference relations based on distribution assessment in group decision making.
引文
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