A consensus approach to multi-granular linguistic MCGDM with hesitant fuzzy linguistic information by using projection

The hesitant linguistic term set, defined as a set that includes several linguistic terms, is a useful tool to describe the hesitancy and reflect the cognition of decision makers when evaluating alternatives in real-life decision making processes. To fully take advantage of this strength, we conduct a study on multi-criteria group decision making (MCGDM) with hesitant linguistic information, where decision makers employ multi-granular linguistic term sets to express opinions. Aiming to avoid information loss, we employ hesitant 2-tuple sets to make computations of hesitant fuzzy linguistic term sets (HFLTSs). The contributions of this article are summarized as follows. First, we introduce the relative projection model for hesitant 2-tuple sets. This model is further extended to a situation where hesitant 2-tuple sets are denoted by multi-granular linguistic term sets. Second, to measure the similarity degree between two individual decision matrices, a similarity measurement is presented by using the relative projection model for two multi-granular hesitant 2-tuple linguistic matrices. Third, some aggregation operators are developed to aggregate individual multi-granular hesitant 2-tuple linguistic information. Subsequently, a consensus measure and definitions for group consensus are presented to handle consensus problems in the MCGDM proceeding. Finally, a consensus approach that comprises the proposed models and a feedback mechanism is developed to handle multi-granular hesitant fuzzy linguistic MCGDM problems. To demonstrate the validity and applicability of the proposed approach, an examined example on the selection of treatment technologies for disposing healthcare waste management is provided.