How to overcome the instability of AHP weight? —Partial order analysis method based on the lower limit of the proportion

Abstract

In the AHP method, it is essential to control the uncertainty in obtaining weight. The paper aims to reduce the uncertainty introduced when using the AHP method, so as to improve the stability of the weight. Firstly, the paper ranks the indicators according to their importance, and the lowest lower limits of the importance ratio of two adjacent indicators are obtained, which can replace the accurate values of the indicator comparison in the AHP method and significantly reduce the introduced uncertainty. Secondly, the schemes are compared under infinite groups of weights, avoiding the blindness and instability of the comparison results obtained by only one group of weights. At the same time, the schemes’ comprehensive comparison results are displayed in the partial order Hasse diagram, which can clearly identify whether the comparison between scheme pairs is stable and evaluate the stability of the weight. Finally, an example is given to show the specific operation process of the proposed method, and simulation is used to verify the method’s superiority.