"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.

Evangelos Triantaphyllou

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.

Key Words:
Pairwise comparisons, eigenvectors, analytic hierarchy process, linear programming, fuzzy sets, membership values, artificial intelligence.

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