Probabilistic linguistic TODIM approach for multiple attribute decision-making

Probabilistic linguistic term sets (PLTSs) are an effective tool to express preferences with different weights for different linguistic terms, and the TODIM method is based on prospect theory and could consider the decision maker's cognitive behavior. In this paper, we extend the TODIM to solve the multi-attribute decision-making (MADM) problems with PLTSs. First of all, the definition, operations, comparative method, and deviation degrees of PLTSs are introduced; a new standardization method for the attribute values was proposed with respect to the situation in which the probabilistic sum for all linguistic terms is less than 1. Then, the objective weights for criteria can be obtained by information entropy theory and the steps of the extended TODIM method for PLTSs are proposed. Finally, an example is to verify the developed approach.