【作者】 王武平；

【导师】 杜纲；

【作者基本信息】 天津大学 ， 管理科学与工程， 2008， 博士

【摘要】 当前群决策的研究越来越受到广泛的关注,其中多属性群决策研究也成为近年来决策科学的一个重要研究领域。多属性群决策解决的问题是集结群体成员的判断以形成群的判断,然后通过某种决策技术集成群的判断,对决策方案进行评价、比较、排序或从中选择相对满意的方案。在实际的决策活动中不可避免地会遇到同时需要定量分析和定性分析的混合多属性群决策问题。本文面向群评价的混合多属性群决策方法研究的是在决策者给出方案属性评价信息后如何进行信息处理、如何确定属性权重和决策者权重和如何进行信息集结得到方案的最终评价结果。研究目就是在理论分析的基础上,给出对不同类型混合多属性群决策问题进行决策的具体方法。文章采用数学推理和理论分析相结合、定性分析与定量说明相结合和具体问题与相关理论相结合的方法进行研究。在背景介绍和文献综述的基础上首先研究了混合多属性群决策的基本问题,然后对不同类型的混合多属性群决策问题提出了相应方法模型。文章对混合多属性群决策问题综合考虑属性值和属性权重、决策者权重和偏好等信息进行分类。其中按照混合问题的混合程度提出了属性值低度混合、中度混合和高度混合的分类;按照属性权重重新定义了偏好的概念,基于属性权重给出组数的不同对混合多属性群决策问题提出了无偏好、对属性有偏好和对方案有偏好的分类;提出了对区间数属性值规范化的新方法,即区间数极差正规化法,并运用于全文决策方法的研究中;提出了新的群体数字理想点的概念并给出了基于群体数字理想点的新的规范化方法;针对混合型问题中混合数据的特点,分别研究了在属性权重和决策者权重已知和未知条件下的决策步骤,对专家信息前置法和专家信息后置法的适用性进行了分析;给出几种求解混合型多属性群决策问题的具体方法,即基于群体数字理想点的混合多属性群决策TOPSIS方法;基于联系数的混合多属性群决策方法;基于加权集值统计的混合多属性群决策方法;基于熵权灰色关联分析的混合多属性群决策方法;基于Borda粗排序的混合多属性群决策方法;提出了确定属性权重和决策者权重的离差最小化方法、差值最小化法、三元联系数法、相似度法和广义标度法。更多还原

【Abstract】 Nowadays studies on group decision making are more and more concerned by people, and thereinto the study on multiple attribute group decision making (MAGDM) becomes an important field on the science of decision making. The problems that MAGDM try to solve are to aggregate individual judgment to form group judgment, then to synthesize the group judgment using certain decision making technique to compare, to evaluate and to sort the order of candidate solutions or to select the relative satisfactory solutions. In decision making activities, it is inevitable to meet hybrid MAGDM problems that need quantitative analysis and qualitative analysis simultaneously.Study on methods for hybrid MADGM facing group evaluation researches on how to manage the datum information, how to make certain the important weights of attributes and decision makers and how to aggregate the information to form the final result of candidate solutions after decision makers have presented the evaluation information on attributes of candidate solutions. The purpose of the study is to present the concrete solution methods for different types of hybrid MAGDM problems based on theoretical analysis. The methodologies of this dissertation are mathematical reasoning along with theory analysis, quantitative analysis together with qualitative investigation, and concrete problem combined with correlative theories. After background introduction and review of literatures, the basic problems of hybrid MAGDM problems are studied firstly; then corresponding arithmetic models are presented to solve different types of hybrid MAGDM problems.The hybrid MAGDM problems are classified basing on attributes values, the importance weights of attributes and the importance weights of decision makers synthetically. Thereinto the hybrid MAGDM problems are classified into low, medium and high-hybrid attribute values problems based on the hybrid degree of attribute values; they are also classified into none preference, with preference on attributes and with preference on candidate solutions based on the number of known attribute weights after redefinition of the concept of preference. New normalization method for attribute values is presented, that is, the interval range difference normalization method (IRDN method), and is used in the method study of hybrid MAGDM problems all-around. The concept of new group numerical ideal point and its normalization methods is also presented. Aiming at the characteristic of hybrid datum of hybrid MAGDM problems, the process of hybrid MAGDM problems are introduced respectively under known or unknown importance weights of attributes and decision makers. The applicability of‘expert information pre-treatment method’and‘expert information post-treatment method’is discussed. Many concrete methods are put forward to solve the hybrid MAGDM problems, they are, the hybrid MAGDM TOPSIS method based the group numerical ideal point, the hybrid MAGDM method based on three-unit connection number; the hybrid MAGDM method based on weighted set-valued statistics, the hybrid MAGDM method based on entropy weight grey related analysis, the hybrid MAGDM method based on Borda coarse sequence. Several methods to make sure the objective and subjective importance weights of attributes and decision makers are also presented, they are, the minimizing deviation method, the minimizing difference-value method, the three-unit connection number method, the similarity degree method and the generalized scale method.更多还原