Improving inconsistency in pairwise comparison matrices using normalized euclidean distance and grey wolf optimization in multicriteria decision making

Ensuring the Consistency of the Pairwise Comparison Matrix (PCM) is crucial in the Multicriteria Decision Making (MCDM) process. This study not only addresses inconsistency correction in PCM but also identifies a substitute matrix that closely approximates the original. To achieve this, we propose a novel distance metric, the Normalized Euclidean Distance (NED), which helps determine the substitute matrix within a maximum correction range. It ensures that the modified matrix remains as close as possible to the original while improving Consistency. Additionally, we introduce an advanced swarm intelligence technique, Grey Wolf Optimization (GWO), which researchers have widely adopted for various optimization problems due to its efficiency. Unlike many other swarm-based methods, GWO requires relatively few parameters and does not rely on derivatives during the initial search. By integrating the NED formula, the maximum correction range, and GWO, our approach achieves better consistency repair than existing methods while minimizing deviations from the original matrix. Experimental results demonstrate the effectiveness and improved performance of the proposed method.