Grey relational analysis method for 2-tuple linguistic multiple attribute group decision making with incomplete weight information

With respect to 2-tuple linguistic multiple attribute group decision making problems with incomplete weight information, some basic concepts and operational laws of 2-tuple linguistic variables are introduced. An optimization model based on the maximizing deviation method, by which the attribute weights can be determined, is established. According to the traditional ideas of grey relational analysis (GRA), the optimal alternative(s) is determined by calculating the linguistic degree of grey relation of every alternative and 2-tuple linguistic positive ideal solution and 2-tuple linguistic negative ideal solution. It is based on the concept that the optimal alternative should have the largest degree of grey relation from positive ideal solution and the smallest degree of grey relation from the negative ideal solution. The method has exact characteristic in linguistic information processing. It avoided information distortion and losing which occur formerly in the linguistic information processing. Finally, a numerical example is used to illustrate the use of the proposed method. The result shows the approach is simple, effective and easy to calculate.