A new approach to improve the consistency of linguistic pair-wise comparison matrix and derive interval weight vector

H. Zhang, Q. Zheng, and T. Liu et al. proposed a discrete region based approach to improve the consistency of the pair-wise comparison matrix. The approach is able to significantly improve the consistency of pair-wise comparison matrix without to revise the decision maker's opinion. In the approach, a discrete region matrix is transformed into a set-matrix in which the elements are the real number set. In this paper, a discrete region matrix is transformed into a reciprocal interval matrix. A new iterative searching algorithm (NISA) is proposed to find the pair-wise comparison matrix with approximate optimum consistency from the reciprocal interval matrix. Based on the similarly principle, a new algorithm is proposed to derive the interval weight vector for the reciprocal interval matrix. The key character of this algorithm is that the derived interval weight vector includes the weight vector got by NISA for the same reciprocal interval matrix. In the experiment, five experimental strategies are designed, and the experimental results show that H. Zhang et al. proposed approach and NISA can get approximately similar weight vector according to the same pair-wise comparison matrix used the discrete region.