Comparing partitions is one of the open-ended questions in data analysis. The need to compare two partitions occurs during the study of two surveys of different units based on the same questionnaires but with the same structure. The goal of our work is to study this approach and to find formal procedures based on probabilistic models that are realistic in the case of comparing close partitions. For this purpose, we propose a method of projection of partitions using linear discriminant analysis on one of the partitions and allocating the units of the other partition in the classes of the first one. The comparison is done by the association measures. We present another approach based on the use of the classification of variables for which the procedure consists in comparing these classification according to consensus indices