Abstract: 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.

Key words: group decision making, cross-efficiency DEA, interval linguistic preference relation, group consensus, stochastic simulation