Probabilistic reliable linguistic term sets applied to investment project selection with the gained and lost dominance score method

Probabilistic linguistic term sets (PLTSs) are an effective tool in keeping with the habits of decision makers (DMs). However, in multi-criteria group decision making (MCGDM) problems, it is necessary to deal with the information reliability problem because of the difference of the DMs’ knowledge backgrounds and knowledge structures. Therefore, this paper proposes a novel concept called probabilistic reliable linguistic term sets. Based on which, some basic operations, comparison laws, distance measures, similarity measures and aggregation operators are defined. After that, we propose the probabilistic reliable linguistic gained and lost dominance score method to cope with MCGDM problems, and we further apply the proposed method to solve an investment project selection problem about lucky bag machine. Finally, we make some comparative analyses to verify the effectiveness and highlight the strength of the proposed method compared with four methods, i.e., the aggregation-based method, the TOPSIS method under probabilistic reliable linguistic environment, the gained and lost dominance score (GLDS) method with probabilistic linguistic information and the GLDS method with hesitant linguistic information.