A Novel Decision-Making Method Based on Probabilistic Linguistic Information

The Maclaurin symmetric mean (MSM) operator has the characteristic of capturing the interrelationship among multi-input arguments, the probabilistic linguistic terms set (PLTS) can reflect the different degrees of importance or weights of all possible evaluation values, and the improved operational laws of probabilistic linguistic information (PLI) can not only avoid the operational values out of bounds for the linguistic terms set (LTS) but also keep the probability information complete after operations; hence, it is very meaningful to extend the MSM operator to PLTS based on the operational laws. To fully take advantage of the MSM operator and the improved operational laws of PLI, the MSM operator is extended to PLI. At the same time, two new aggregated operators are proposed, including the probabilistic linguistic MSM (PLMSM) operator and the weighted probabilistic linguistic MSM (WPLMSM) operator. Simultaneously, the properties and the special cases of these operators are discussed. Further, based on the proposed WPLMSM operator, a novel approach for multiple attribute decision-making (MADM) problems with PLI is proposed. With a given numerical example, the feasibility of the proposed method is proven, and a comparison with the existing methods can show the advantages of the new method in this paper. The developed method adopts the new operational rules with the accurate operations, and it can overcome some existing weaknesses and capture the interrelationship among the multi-input PLTSs, which easily express the qualitative information given by the decision-makers’ cognition.