Identification of consensus in group decision-making with multi-granularity linguistic information and compromise for discrepancy

A method is proposed to analyze the consensus in group decision-making, based on the multi-granularity linguistic preference in terms of identifying information matrix. According to the different multi-granularity linguistic identifying information matrices given by experts, the relational vector for ranking individual schemes is determined by LOWA aggregation operators. Then, an objective programming model is developed to minimize the discrepancy between the opinions of group and experts, and the relational vector for ranking group schemes is obtained by solving the model. Defining the closeness index between the opinions of experts or individuals and of a group, a method to identify and improve their consensus is proposed. An example is given to show the feasibility and effectiveness of the methods proposed.