{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,26]],"date-time":"2026-06-26T01:01:57Z","timestamp":1782435717117,"version":"3.54.5"},"reference-count":35,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2021,3,8]],"date-time":"2021-03-08T00:00:00Z","timestamp":1615161600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61773019"],"award-info":[{"award-number":["61773019"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11771263"],"award-info":[{"award-number":["11771263"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds For the Central Universities","doi-asserted-by":"publisher","award":["2018TS059"],"award-info":[{"award-number":["2018TS059"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds For the Central Universities","doi-asserted-by":"publisher","award":["GK201503013"],"award-info":[{"award-number":["GK201503013"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Picture fuzzy sets, which are the extension of intuitionistic fuzzy sets, can deal with inconsistent information better in practical applications. A distance measure is an important mathematical tool to calculate the difference degree between picture fuzzy sets. Although some distance measures of picture fuzzy sets have been constructed, there are some unreasonable and counterintuitive cases. The main reason is that the existing distance measures do not or seldom consider the refusal degree of picture fuzzy sets. In order to solve these unreasonable and counterintuitive cases, in this paper, we propose a dynamic distance measure of picture fuzzy sets based on a picture fuzzy point operator. Through a numerical comparison and multi-criteria decision-making problems, we show that the proposed distance measure is reasonable and effective.<\/jats:p>","DOI":"10.3390\/sym13030436","type":"journal-article","created":{"date-parts":[[2021,3,8]],"date-time":"2021-03-08T23:04:39Z","timestamp":1615244679000},"page":"436","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":32,"title":["A Dynamic Distance Measure of Picture Fuzzy Sets and Its Application"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5337-5813","authenticated-orcid":false,"given":"Ruirui","family":"Zhao","sequence":"first","affiliation":[{"name":"College of Mathematics and Information Science, Shaanxi Normal University, Xi\u2019an 710062, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9400-3533","authenticated-orcid":false,"given":"Minxia","family":"Luo","sequence":"additional","affiliation":[{"name":"Department of Information and Computing Science, China Jiliang University, Hangzhou 310018, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Shenggang","family":"Li","sequence":"additional","affiliation":[{"name":"College of Mathematics and Information Science, Shaanxi Normal University, Xi\u2019an 710062, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2021,3,8]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"338","DOI":"10.1016\/S0019-9958(65)90241-X","article-title":"Fuzzy sets","volume":"8","author":"Zadeh","year":"1965","journal-title":"Inf. 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