A novel probabilistic linguistic multi-attribute decision-making method based on Mahalanobis–Taguchi system and fuzzy measure

Probabilistic linguistic term sets (PLTSs) may convey flexible and accurate qualitative information to decision-makers, and it has been widely utilized to handle multi-attribute decision-making (MADM) issues. This article presents a novel technique for MADM using probabilistic linguistic information where attribute weights are entirely unknown and interactive. Firstly, we define the covariance matrix for the set of PLTSs and investigate its properties. Secondly, we propose the probabilistic linguistic Mahalanobis–Taguchi System (PL-MTS) by extending the Mahalanobis–Taguchi System (MTS) to the probabilistic linguistic environment. Using PL-MTS, fuzzy measures of attributes are then computed. Thirdly, this article modifies the current probabilistic linguistic Choquet integral (PLCI) operator and proposes the probabilistic linguistic geometric Choquet integral (PLGCI) operator and the probabilistic linguistic average Choquet integral (PLACI) operator. Fourthly, the decision information of all alternatives is aggregated using PLGCI and PLACI operators, and the alternatives are ordered according to the comparison rules of PLTSs. Finally, an illustration of supplier selection is provided to validate the efficacy of the method.