Signed distance-based consensus in multi-criteria group decision-making with multi-granular hesitant unbalanced linguistic information

Abstract This study aims to deal with hesitant fuzzy linguistic multi-criteria group decision-making (MCGDM) problems with multi-granular unbalanced linguistic term sets. Firstly, a signed distance measure is developed as the support tool for hesitant fuzzy linguistic term sets. This measure is based on the ordinal semantics of linguistic terms and the possibility distribution method. In this manner, the signed distance measure can release the strict constraint of symmetric and uniform linguistic term sets in qualitative decision-making. Secondly, a signed distance-based transformation function is proposed to unify the multi-granular hesitant unbalanced linguistic assessments. Moreover, comprehensive consensus measures on three levels are proposed to measure the consensus degree. These measures simultaneously consider the consensus degree between individual and collective preference and between experts. Subsequently, a consensus reaching algorithm is designed and incorporated into the proposed MCGDM approach. Lastly, an illustrative example, followed by an in-depth comparative analysis and discussion is presented to demonstrate the proposed approach. Results show that the proposed approach can flexibly and effectively tackle MCGDM problems with multi-granular hesitant unbalanced linguistic information.