一个基于夹角测度的群决策结果稳定性的定量分析方法研究  

Quantitative Stability Analysis Method on the Result of Group Decision Making Based on Inclined Angle of Vectors

作　　者：吴凡[1] 赵勇[2] 陈阳[2] 

机构地区：[1]安徽工业大学管理科学与工程学院,马鞍山243000 [2]华中科技大学自动化学院,武汉430074

出　　处：《系统科学与数学》2017年第4期1063-1071,共9页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金(61273206;71071063)资助课题

摘　　要：群决策结果的稳定性分析是决策分析的一个重要内容或环节,也是群决策问题研究的热点和难点之一.一类常见的、基于序数偏好表达的群决策问题,通常采用加权计分规则(weighted scoring rules,简称WSRs)来求解.对其结果稳定性的评价或度量,文章提出了一个基于评分向量夹角测度的定量分析方法,论证了其合理性和可行性,给出了具体的求解方法;并考虑到实际分析中偏好或排序要求的复杂性,进一步探讨了复合关系下的相关概念及度量方法.与基于距离测度的稳定性度量相比,文章提出的方法具有较好的直观几何意义、可公度性和规模不变性等特点.Stability analysis of a decision result is an important step for a group decision making problem. It＇s also a hot and difficult topic. The weighted scoring rules （WSRs） are usually used to solve a class of group decision problems based on ordinal preferences. A measuring method based on the inclined angle of two scores vectors is proposed in this paper, in order to measure the stability degrees of the results of weighted scoring rules. Rationality and feasibility of this method are elaborated, and its calculation method are also proposed. Considering the complexity of preferences or ranking requirements in the practical analyses, the concept and measuring method of stability measurements with complex relations are discussed. Compared with the stability degrees based on the distance measurements, the measuring method proposed in this paper is more visualized, commensurable and scale-invariant.

关 键 词：群决策 向量夹角 加权计分规则 稳定性 

分 类 号：O225[理学—运筹学与控制论]