Ant algorithm for modifying an inconsistent pairwise weighting matrix in an analytic hierarchy process

One important issue in the analytic hierarchy process (AHP) is confirming the consistency of comparison matrix to verify the logical respondent opinion. As inconsistent comparison matrix cannot be used as reference to make decisions, this paper proposes a method using an ant algorithm to modify an inconsistent pairwise weight matrix to be consistent in AHP, called ANTAHP. This method employs the matrix element as the path in an ant colony optimization to construct the tour. By laying pheromone information on their path, the ants can find the optimal matrix (or tour), which satisfies the consistency and closer to the original judgment of the decision makers. The experimental results demonstrate that the proposed algorithm is able to make consistent matrices, as well as minimize the difference index.