Definition 1. The initial direct-relation matrix Z is a n
×
n matrix
obtained by pair-wise comparisons in terms of influences and
directions between criteria, in which Zij is denoted as the degree
to which the criterion i affects the criterion j, i.e., Z = [Zij]n×n.
Definition 2. The normalized direct-relation matrix X, i.e.,
X = [Xij]n×n and 0
≤
xij ≤
1 can be obtained through formulas (1) and
(2), in which all principal diagonal elements are equal to zero.