The Properties of Priority Preservation for Different Prioritization Methods

In this paper, the priority preservation concept for adding a new element under a criterion is proposed. Then we proved that both eigenvector prioritization method and additive normalization prioritization method are weak priority preservation. In the same time, it is also proved that least deviation prioritization method, logarithmic least- squares prioritization method, least-squares prioritization method and gradient eigenvector prioritization method are strong priority preservation. The results are of importance for selecting a fitting prioritization method in the analytic hierarchy process.