Improved TODIM Method for Probabilistic Linguistic MAGDM Based on New Distance Measure

Abstract Probabilistic linguistic term sets (PLTSs), which assign different weights to various linguistic terms, offer an efficient framework for expressing preferences. Meanwhile, the TODIM method, grounded in prospect theory, is adept at incorporating the cognitive behaviors of decision-makers into the decision-making process. In this paper, we extend the TODIM method to solve multi-attribute group decision making (MAGDM) problems with PLTSs. At first, we extend the Frank operators to PLTSs and propose the probabilistic linguistic Frank weighted averaging (PLFWA) operator based on adjusted rules of PLTSs. Further, some desirable properties of them are studied. Meanwhile, we present an innovative distance measure, deeply anchored in linguistic scale functions, designed to overcome the shortcomings of current distance metrics. What’s more, the combined weights for attributes can be obtained by the criteria importance though intercriteria correlation (CRITIC) method and the best-worst method (BWM) and the steps of the extended TODIM method for PLTSs are proposed. Finally, a numerical example for the purchase selection of electric vehicles is given, and some sensitivity and comparative analysis are used to illustrate the effectiveness and rationality of this new method.