A Probabilistic Linguistic Three-Way Decision Method With Regret Theory via Fuzzy c-Means Clustering Algorithm

Aiming at multiattribute decision-making (MADM) problems with probabilistic linguistic term sets (PLTSs), and considering the effective rationality of a decision-maker (DM) in complex decision environments, this article proposes a probabilistic linguistic three-way decision (TWD) method based on the regret theory (RT), namely, PL-TWDR. First, a probabilistic linguistic attribute weight determination method is developed that considers probabilistic linguistic information entropies and the weighted total deviation of all objects from the negative ideal solution (NIS). Then, a new group satisfaction index is designed to replace the utility function in RT, which overcomes the limitation of the RT calculation in PLTSs. Second, the fuzzy c-means (FCM) algorithm is extended to PLTSs for obtaining equivalent objects under different clusters and calculate conditional probabilities in corresponding TWD models, which makes up for the shortage of the PLTS evaluation matrix when dividing equivalence classes. Third, RT is introduced into PLTSs to rank objects according to utility perception values. At the same time, a new TWD model constructed by average utility perception values is used to realize object domains in probabilistic linguistic environments. Finally, the proposed method is applied to realistic cases, and the effectiveness and superiority of the PL-TWDR method are verified via comparative analysis and sensitivity analysis in terms of other nine popular decision-making methods.