Group decision making with linguistic preference relations based on fuzzy measures

Linguistic preference relation is a useful tool for expressing preferences of decision makers in group decision making according to linguistic scales. But in the real decision problems, there usually exist interactive phenomena among the preference of decision makers so that it is not suitable for us to aggregate preference information by conventional additive aggregation operators. Thus, to approximate the human subjective preference evaluation process, it would be more suitable to apply non-additive measures tool, where it is not necessary to assume additivity and independence among preference of decision makers. In this paper, based on the fuzzy measure, we developed a new linguistic ordered geometric averaging operator to aggregate the multiplicative linguistic preference relations, where interactions or dependence among subjective preference of decision makers are considered. Further, the procedure and algorithm of group decision making based on the new linguistic aggregation operators is given. Finally, a practical example is provided to illustrate the developed approaches.