Abstract: In order to evaluate the comprehensive national strength correctly,PCA-TOPSIS is given.Firstly,PCA is used to reduce dimensionality and get the scores of the countries related to a few aggregate variables;Then,the contribution rate of each principal component is used to be weighted and get the weighting decision-making matrix;Finally,TOPSIS is used for evaluation.For 11 important counties in the world,25 evaluation indexes are selected and used for evaluation.The results show that the method overcomes the deficiencies of the simple TOPSIS characterized by the computational complexity and necessity of determining the weights.

Key words: comprehensive national strength, principal component, ideal point method, evaluation