Generalized picture distance measure and applications to picture fuzzy clustering

• We focused on the clustering problem in picture fuzzy sets.
• A generalized picture distance measure was proposed.
• A novel hierarchical picture clustering method based on the measure was presented.
• Its clustering quality is better than those of relevant clustering algorithms.
• A clustering system for picture fuzzy sets was designed.

Picture fuzzy set (PFS), which is a generalization of traditional fuzzy set and intuitionistic fuzzy set, shows great promises of better adaptation to many practical problems in pattern recognition, artificial life, robotic, expert and knowledge-based systems than existing types of fuzzy sets. An emerging research trend in PFS is development of clustering algorithms which can exploit and investigate hidden knowledge from a mass of datasets. Distance measure is one of the most important tools in clustering that determine the degree of relationship between two objects. In this paper, we propose a generalized picture distance measure and integrate it to a novel hierarchical picture fuzzy clustering method called Hierarchical Picture Clustering (HPC). Experimental results show that the clustering quality of the proposed algorithm is better than those of the relevant ones.

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