Game-theoretic approach to consensus building in multi-objective optimization within multi-scale information systems

In modern industrial management, integrating heterogeneous data and achieving consensus among decision-makers (DMs) are crucial for optimizing complex systems. Multi-scale information systems (MSISs) have emerged as a powerful tool for managing and fusing diverse data sources. However, reaching consensus in multi-scale environments remains challenging due to data complexity and varying DM preferences. This paper proposes a consensus-reaching process (CRP) method based on MSISs, called MSIS-CRP. Specifically, the sequential clustering-based approach for constructing MSISs stands as the bedrock of this innovative framework. Through the meticulous development of a clustering-driven construction strategy, it excels at precisely discerning the surjective connections among various scales. This not only enables comprehensive data integration at a profound level but also paves the way for robust decision-making analysis, laying a reliable groundwork for subsequent steps in the process. Subsequently, scale weights and DMs’ weights are meticulously calculated according to the characteristics of decision information, thereby effectively reflecting the divergent importance levels of different information dimensions. A calculus-based consensus measure is introduced to quantitatively evaluate DMs’ opinions. To facilitate CRP, global and local consensus feedback mechanisms are established using a multi-objective programming model that balances consensus improvement and adjustment costs. The model is solved from a game-theoretic perspective, leveraging equilibrium concepts to enhance robustness. Comparative and experimental analyses demonstrate that MSIS-CRP effectively improves consensus levels while maintaining computational efficiency, outperforming existing approaches by providing more integrated and comprehensive decision results, especially in dynamic environments. Notably, in numerical experiments involving 48 alternatives and 5 DMs, the MSIS-CRP method achieves a group consensus level of 0.9662 after global feedback, followed by local feedback to reach the final consensus. It demonstrates an adjustment distance of 50.8850 and a running time of 3.7031 s, significantly outperforming seven comparative methods in both efficiency and consensus quality. Overall, this research offers a novel solution for complex decision-making challenges in industrial management by integrating MSISs with CRP.