A new and simple method to get the priority vector for reciprocal matrices

A new optimization method is proposed to find the priority vector of a non-consistent reciprocal matrix, which leads to the solution of a constrained least-squares problem, specially suited for large matrices. Two different approaches are used to solve this problem: the first approach uses QR decomposition, and the second approach performs the singular value decomposition, leading to simple solutions. In addition, a comparison of the proposed method with other methods used in the consulted bibliography is made to obtain the priority vector, and finally, an illustrative example is shown.