A three-way large-scale group decision-making model based on rewards-and-punishments mechanism for triple-path consensus reaching process in high-end equipment project selection

In high-end equipment project selection, which involves high technical complexity, significant capital investment, and cross-industry applications, it is essential to involve experts from diverse fields in the decision-making process. To address the challenge of large-scale group decision-making, this paper proposes a three-way large-scale group decision-making model for triple-path consensus reaching process based on a rewards-and-punishments mechanism. The model consists of three stages. Firstly, the group consensus degree is calculated based on the initial input. If the specified threshold is not met, the consensus adjustment iteration stage is entered and decision makers are divided into three regions based on the Pareto principle. Secondly, separate calculations are conducted for the moving benefits and costs of decision makers in different regions, with the total benefits and costs used as targets for the NSGA-II algorithm. The Pareto solution set is obtained, and the solution with the least number of moving objects is selected as the three-way decision-making movement strategy. This process is repeated until the consensus threshold is reached or one of the regions is empty. Finally, based on the final adjustment results, scores are calculated for each project and a ranking is established as a selection suggestion. To demonstrate the feasibility and effectiveness of the model, ten high-end equipment projects are taken as examples, and the sensitivity of the model is tested by adjusting the number of decision makers. In conclusion, the proposed three-way large-scale group decision-making model based on a rewards-and-punishments mechanism for triple-path consensus reaching process is an effective and feasible approach for high-end equipment project selection.