A new algorithm to improve the inconsistent comparison matrix

The inconsistent comparison matrix has to be improved often when using the analytic hierarchy process (AHP). There are three shortcomings in the existing methods. First, the most inconsistent element one can find using these methods is not always the same and the result is that the improvement to the inconsistent matrix is not the same. Second, the improvement extent is not clear after one element is improved. Third, one can not be sure of the improvement step. In this paper, a new algorithm is proposed and it calculates the value of the element when the matrix can obtain the best consistency, analyzes the distance of original value and improved value, then finds in two examples an effective way to improve the most inconsistent element.