In order to overcome the shortcoming of sensitivity to the original clustering center in ordinary fuzzy C-mean clustering algorithm

the homotopy theory is introduced to combine with this algorithm to establish a new method of homotopy fuzzy C-mean Clustering algorithm for evaluation of slope stability. Then the method is applied to studying stability of 36 slopes at banks of the Three Gorges Reservoir; and then some characteristics such as the best sample classification and convergence effect of homotopy fuzzy C-mean clustering algorithm are discussed. Clustering results show that the proposed method is a reasonable classification algorithm with global optimization and superior to the ordinary fuzzy C-mean clustering algorithm.