A discrete region-based approach to improve the consistency of pair-wise comparison matrix

The consistency of pair-wise comparison matrix is a serious challenge for the multiple-criteria decision-making problem. However, existing methods are either too complicated to be applied in the revising process of the inconsistent comparison matrix or are difficult to preserve most of the original comparison information due to the use of a new pairwise comparison matrix. In this paper, a discrete region-based approach is proposed to improve the consistency of the pair-wise comparison matrix. When the decision makers feel confused or uncertain, they could express their evaluation as a discrete region containing multiple judgments, instead of a single result. A new data structure, named as set-matrix, is designed to store the combinations of those multiple judgments. An iterative searching algorithm is designed to find the pair-wise comparison matrix with approximate optimal consistency from the set-matrix. The experiments show that: 1) the consistency is significantly improved when the experts apply the discrete region evaluation instead of the single evaluation; and 2) the users can find the matrix with approximate optimal consistency quickly exploiting the iterative searching algorithm.