The representation and processing of uncertain concepts are key issue for both the study of artificial intelligence with uncertainty and human knowledge processing. The intension and extension of a concept can be transformed automatically in the human cognition process, while it is difficult for computers. A Gaussian cloud model (GCM) is used to realize the cognitive transformation between intension and extension of a concept through computer algorithms, including forward Gaussian cloud transformation (FGCT) algorithms and backward Gaussian cloud transformation (BGCT) algorithms. A FGCT algorithm can transform a concept's intension into extension, and a BGCT algorithm can implement the cognitive transformation from a concept's extension to intension. In this paper, the authors perform a thorough analysis on the existing BGCT algorithms firstly, and find that these BGCT algorithms have some drawbacks. They cannot obtain the stable intension of a concept sometimes. For this reason, a new backward Gaussian cloud cognitive transformation algorithm based on sample division is proposed. The effectiveness and convergence of the proposed method is analyzed in detail, and some comparison experiments on obtaining the concept's intension and applications to image segmentation are conducted to evaluate this method. The results show the stability and performance of our method.