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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.<\/jats:p>","DOI":"10.1177\/18724981241295947","type":"journal-article","created":{"date-parts":[[2025,3,19]],"date-time":"2025-03-19T12:05:22Z","timestamp":1742385922000},"page":"1158-1181","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":1,"title":["New distance and similarity measures of picture fuzzy sets and applications"],"prefix":"10.1177","volume":"19","author":[{"given":"Henan","family":"Li","sequence":"first","affiliation":[{"name":"School of Computer Science and Technology, Jiangsu Normal University, Xuzhou, 221116, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Sijia","family":"Zhu","sequence":"additional","affiliation":[{"name":"Cw Chu College, Jiangsu Normal University, Xuzhou 221116, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8580-9655","authenticated-orcid":false,"given":"Zhe","family":"Liu","sequence":"additional","affiliation":[{"name":"College of Mathematics and Computer, Xinyu University, Xinyu 338004, China"},{"name":"School of Computer Sciences, Universiti Sains Malaysia, Penang 11800, Malaysia"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"179","published-online":{"date-parts":[[2025,3,19]]},"reference":[{"key":"e_1_3_3_2_2","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1145\/3638061","article-title":"Enhanced fuzzy clustering for incomplete instance with evidence combination","volume":"18","author":"Liu Z","year":"2023","unstructured":"Liu Z, Letchmunan S. 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