The opinion dynamics model for group decision making with probabilistic uncertain linguistic information

Multi-criteria group decision making (MCGDM) is the important part in decision-making process, which has been used in many industries. Coordinating differing opinions and ultimately reaching group consensus in a group decision-making process has become an important area of research. This paper uses probabilistic uncertain linguistic term sets (PULTSs) to express the uncertainty of evaluation information, and proposes a group consensus reaching method based on the opinion dynamics model which exhaustively considers how decision-makers’ (DMs) viewpoints can influence each other and evolve over time in MCGDM environments. First, we gathers the group’s preference information regarding the alternatives and their stubbornness to peer influence. Next, an influence matrix is determined based on the authority index of the DMs, and a probabilistic uncertain linguistic Friedkin–Johnsen model (PUL-FJ) is constructed. Then, a group consensus reaching method based on the PUL-Friedkin-Johnsen model is proposed to address the feedback mechanism in the consensus-reaching process (CRP). Finally, we proposes a novel approach for ranking. To better achieve group decision-making, we constructs an improved PUL similarity measure that based on the Wasserstein distance. Additionally, this paper proposes a new approach for expert weight, resulting in a comprehensive expert weight that balances individual expertise of the different criteria and group consensus. In the end, an example is provided, and the method’s feasibility is validated through sensitivity analysis and comparative analysis.