In this paper, we define hesitant fuzzy partitions (H-fuzzy partitions) to consider the results of standard fuzzy clustering family (e.g. fuzzy c-means and intuitionistic fuzzy c-means). We define a method to construct H-fuzzy partitions from a set of fuzzy clusters obtained from several executions of fuzzy clustering algorithms with various initialization of their parameters. Our purpose is to consider some local optimal solutions to find a global optimal solution also letting the user to consider various reliable membership values and cluster centers to evaluate her/his problem using different cluster validity indices.