"A Linear Programming Based Decomposition Approach in Evaluating
Priorities from Pairwise Comparisons and Error Analysis"
Journal of Optimization Theory and Applications,
1995, Vol. 84, No. 1, pp. 207-234.
One of the most difficult issues in many real life decision- making
problems is how to estimate the pertinent data. An approach which
uses pairwise comparisons was proposed by Saaty and is widely
accepted as an effective way of determining these data. Suppose
that two matrices with pairwise comparisons are available.
Furthermore, suppose that there is an overlapping of the elements
compared in these two matrices. The problem examined in this
paper is how to combine the comparisons of the two matrices in
order to derive the priorities of the elements considered in both
matrices. A simple approach and a linear programming approach are
formulated and analyzed in solving this problem. Computational
results suggest that the LP approach, under certain conditions, is
an effective way for dealing with this problem. The proposed
approach is of critical importance because it can also result in a
reduction of the total required number of comparisons.