This article puts forward a consensus framework for multi-criteria group decision-making (MCGDM) with multi-granular uncertain linguistic information, where different decision-makers employ different linguistic scales to express their opinions on alternatives. In this framework, we first establish a relative projection model for two interval linguistic 2-tuples denoted by linguistic term sets with different granularities, and then extend it to multi-granular interval 2-tuple linguistic matrices. Based on this, the similarity measurement between two individual matrices as well as the consensus degree of an individual matrix to a group one is defined. Furthermore, the similarity degrees are applied to determine the importance weights of decision-makers. Besides, a concept of acceptable consensus is introduced to assist in devising an iterative procedure for the purpose of promoting the group consensus and reaching a satisfactory agreement. Finally, to demonstrate the validity and advantages of our proposed framework, an illustrative example which has been examined is furnished.
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