Picture fuzzy sets (PFSs), as a generalization of fuzzy sets (FSs) and intuitionistic fuzzy sets (IFSs), have better advantages in representing ambiguous information and have been applied in many fields. The distance measures and similarity measures of PFSs have attracted widespread attention. How to reasonably measure the similarities between PFSs in decision-making is still an open question. Therefore, in this paper, we first propose a new distance measure of PFSs, and based on this, we also propose a new similarity measure of PFSs. we applied the proposed distance and similarity measures to two applications, pattern recognition and medical diagnosis, to prove our proposed measures performance is better than previous ones.
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