The linguistic group decision making method of decision makers having incomplete caregory preferences on some properties is studied. Firstly, according to the case-based framework, the values for all attributes of public mention factor are calculated and the information gain coefficient is presented. Then according to the grey target decision framework, attribute weights are optimized from the minimum of the objective optimization model. Based on the decision-making relevance of individuals and groups, the weights of decision-makers are determined, and the ranking of the scheme is given. An example is provided to illustrate the effectiveness of the proposed method.