A new probabilistic linguistic decision-making process based on PL-BWM and improved three-way TODIM methods

Probabilistic linguistic term sets (PLTSs) provide a flexible tool to express linguistic preferences, which allow decision-makers to label linguistic information with different probabilities. In this paper, a method based on a PLTS is proposed to address multi-criteria decision-making problems (MCDM). We develop the theory of PLTSs and put forward a novel best–worst method (BWM), termed PL-BWM, based on PLTS. Our method fully reflects the preference information of decision-makers and accurately provides the importance level of the criteria. The combined weight of the criteria is obtained by merging PL-BWM-based subjective weights and similarity minimization-based objective weights. Upon introducing a three-way decision system to improve the TODIM method, a novel three-way TODIM method is proposed and showcased on an optimal new energy vehicle selection problem. The effectiveness and accuracy of the proposed method are verified by sensitivity analysis and comparative analysis. Our approach paves the way for new developments in solving MCDM problems and for novel applications in otherwise difficult ranking problems.