In this paper, we combine two famous fuzzy data clustering algorithms called fuzzy C-means and intuitionistic fuzzy C-means with a metaheuristic called fuzzy firefly algorithm. The resultant hybrid clustering algorithms (FCMFFA and IFCMFFA) are used for image segmentation. We compare the performance of the proposed algorithms with FCM, IFCM, FCMFA (fuzzy C-means fused with firefly algorithm), and IFCMFA (intuitionistic fuzzy C-means fused with firefly algorithm). The centroid values returned by firefly algorithm and fuzzy firefly algorithm are compared. Two performance indices, namely Davies–Bouldin (DB) index and Dunn index, have also been used to judge the quality of the clustering output. Different types of images have been used for the empirical analysis. Our experimental results prove that the proposed clustering algorithms outperform the existing contemporary clustering algorithms. © 2019, Springer Nature Singapore Pte Ltd.