基于交叉效率DEA与群体共识的区间乘性语言偏好关系群决策

针对区间乘性语言偏好关系群决策问题，提出了一种基于交叉效率DEA和群体共识的群决策方法。首先，提出乘性语言偏好关系导出函数的定义，并构建产出导向的DEA模型，证明了一致性乘性语言偏好关系的DEA效率得分与排序向量之间存在比例关系。在此基础上，建立基于理想值的交叉效率DEA模型，提出乘性语言偏好关系的通用排序方法。同时，基于群体共识建立目标规划模型来计算各语言偏好关系的权重系数。最后，利用Monte Carlo随机模拟的方法对群体语言偏好空间进行统计分析，得到群决策期望排序向量及其可信度。算例分析表明本文方法能够有效的避免信息损失，具有较强的适用性和较高的可信度。

Group Decision Making with Interval Multiplicative Linguistic Preference Relations based on Cross-efficiency DEA and Group Consensus

Group decision making with interval linguistic preference relations has attracted a great deal of attention in the literatures of management science. In order to obtain the group decision making result, the consistency of linguistic preference relations given by the decision makers need to be improved according to some existing approaches, so a variety of consistency adjustment methods have been proposed. However, these consistency adjustment methods of deriving acceptable consistent linguistic preference relation have changed the original evaluation information given by the decision makers, which may distort the given decision making information and make the decision result less reliable. Besides, some existing approaches transform the interval linguistic information into a simple linguistic evaluation value, which may cause the loss of decision information.In order to resolve these problems, a novel approach is proposed to group decision making based on cross-efficiency DEA and group consensus with interval multiplicative linguistic preference relations. First, the definition of derived function of multiplicative linguistic preference relation is given and the output-oriented DEA model is constructed. It is proved that there is a proportional relationship between DEA efficiency scores and the ranking vector of the consistent multiplicative linguistic preference relation. Based on this, a cross-efficiency DEA model based on ideal value is developed. Then, a general ranking method for the multiplicative linguistic preference relation is proposed. Meanwhile, a goal programming model is established to obtain the weight coefficient of each linguistic preference relationship based on group consensus. Finally, the stochastic simulation method is used to statistical analysis of the group's preference space, and the group decision expected ranking vector and the confidence degree are obtained. The numerical results show that the proposed approach can effectively avoid information loss and is of great applicability and high credibility.The problems of information distortion and loss in some existing group decision making methods are solved with interval linguistic preference relations, the relevant theories of group decision making is enriched, and a new technical framework for group decision making with interval multiplicative linguistic preference relations is provided.