A novel local adjustment approach to improve multiplicative consistency of additive reciprocal matrices with an optimal allocation of information granularity

In decision-making processes, ensuring the consistency of additive reciprocal matrices (ARMs) is critical for obtaining reliable rankings. However, achieving multiplicative consistency in real-world applications is often difficult due to the inherent complexities of human judgment. This paper introduces a novel local adjustment approach to enhance multiplicative consistency in ARMs by leveraging an optimal allocation of information granularity. Firstly, a sequential model of ARMs is proposed to quickly determine which entries need to be modified. Secondly, with a given average level of information granularity, a new optimization model, which aims to maximize multiplicative consistency and is solved via Gaussian quantum-behaved particle swarm optimization, is employed to optimally allocate information granularity to the necessary revisions. Then, a new algorithm is proposed to ensure that the adjusted ARM not only achieves acceptable multiplicative consistency but also minimizes the loss of initial preference information. Finally, numerical experiments and extensive simulations are conducted to demonstrate the effectiveness of the proposed approach. These findings highlight the efficiency and applicability of the method in complex decision-making scenarios, offering a practical solution for improving ARM consistency with minimal information loss.