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As a result of the heterogeneity of decision-makers, it is more suitable to use multi-granular linguistic information to express assessing information over alternatives for decision-makers. Decision-makers may only provide partial preference information as the limitation of knowledge over the alternatives. Thus, the incomplete multi-granular 2-tuple fuzzy linguistic preference relations (IMGFLPRs) can be applied to manage the GDM problems in complex environments. In this paper, we propose a novel group decision-making (GDM) model based on mathematical programming with IMGFLPRs. It is more important that the proposed mathematical programming can directly deal with IMGFLPRs and does not need to be converted into a uniform form. By this means, we construct a consensus reaching process based on IMGFLPRs, considering simultaneously dynamic adjustment of experts’ weight. Finally, an emergency plan selection problem is solved by the proposed model, which shows the result of GDM is effectiveness.

An Interactive Consensus Model for Group Decision-Making with Incomplete Multi-Granular 2-Tuple Fuzzy Linguistic Preference Relations