An optimal Best-Worst prioritization method under a 2-tuple linguistic environment in decision making

Multi-criteria group decision making (MCGDM) deals with decision makers who evaluate alternatives over several criteria. MCGDM problems evolve in tandem with the progress of our society. Such progress has given rise to the large-scale group decision making (LS-GDM) problems in which hundreds of decision makers may participate in the decision process and new challenges to face such as groups' formation and polarization opinions. Most real world MCGDM problems present changing contexts with uncertainty that cannot be modeled by numerical values. Under these circumstances, the use of linguistic variables and computing with words (CW) processes have provided successfully results. Concretely, the 2-tuple linguistic computational model stands out because its precise linguistic computations and high interpretability. On the other hand, pairwise comparison is a widely used elicitation technique in MCGDM, but a large number of comparisons might lead inconsistent decision makers' preferences. The Best-Worst method (BWM) reduces the number of pairwise comparisons and the inconsistency in decision makers' opinions. Several BWM approaches have been proposed to manage linguistic information but none of them take advantage of the 2-tuple linguistic computational process based on the CW approach, which would allow to obtain precise and understandable results. This paper aims to present an extended 2-tuple BWM to reduce the number of pairwise comparisons in MCGDM problems and model the uncertainty associated with them to accomplish accuracy computations and obtaining interpretable results. Moreover, we apply our proposal to LS-GDM scenarios in which polarization opinions and sub-groups identification, ignored from any of BWM proposals, are considered. Finally, the new model is applied to several illustrative MCGDM problems.