Improved TODIM method for Probabilistic Linguistic MAGDM based on New Distance Measure

Probabilistic linguistic term sets (PLTSs) offer a superior means of capturing decision-makers’ evaluations, accurately and reliably reflecting their opinions. It account for both the inherent ambiguity of linguistic terms and the uncertainty associated with those terms. In this article, we elaborate on the application of the Frank operator within the context of probabilistic linguistic multiple attribute group decision making (MAGDM), leveraging its adjusted rules. In addition, we introduce a novel distance measure, rooted in linguistic scale functions, to address the limitations of existing distance metrics. Based on this new distance measure, we develop an extended TODIM method specific to the PLTSs environment.Concurrently, we enhance the rationality of attribute weighting by integrating the criteria importance though intercrieria correlation(CRITIC) method and the best-worst method (BWM) within the PLTSs framework. To demonstrate the practical application of our proposed approach, the purchase selection of electric vehicles was taken as an example to show the procedure of the proposed method. We outline the step-by-step procedure and conduct sensitivity and comparative analyses to validate the effectiveness and rationality of our methodology.