An incomplete multi-granular linguistic model and its application in emergency decision of unconventional outburst incidents

Unconventional outburst incidents are unpredictable and also have no emergency plans, they can bring huge economic losses and social issues, so we should find optimal emergency decision scheme. In this paper, we study the group decision making (GDM) problems with incomplete fuzzy linguistic preference relations (FLPRs), and the linguistic information provided by different experts are assessed in linguistic term sets with different granularity. We first develop a four-way procedure to estimate missing preference values when dealing with 2-tuple incomplete FLPRs. We propose the transformation rules for multi-granular FLPRs, and devise a transformation function which satisfies the transformation rules. The transformation can transform any linguistic term set to another linguistic term set. Furthermore, we study the properties and advantages of the transformation function. Finally, we integrate the revised estimation procedure for incomplete 2-tuple FLPRs and the multi-granular linguistic decision model to deal with emergency decision of unconventional outburst incidents. It is showed that the proposed method is straightforward and without loss of information.