Consensus reaching process using the KI method from Incomplete Pairwise Comparison Matrix

The pairwise comparison matrix (PCM) is an important method commonly used in decision-making, where the relative importance of pairwise elements is compared. However, due to some special circumstances, sometimes the complete PCM cannot be obtained directly. In this regard, this paper develops a method of complementary and correction matrices based on the Katz Index (KI). Firstly, the incomplete pairwise comparison matrix (iPCM) is converted into a direct relationship matrix, and the total relationship matrix is calculated by the KI method; then the inconsistent data processing model is used to check and correct the total relationship matrix data to obtain the complete PCM; finally, the eigenvalue method is used to find the ranking vector. The method is simple and flexible, and this paper applies it to the emergency decision-making of natural disaster emergencies to further verify the superiority and accuracy of the method.