{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,14]],"date-time":"2025-11-14T21:02:19Z","timestamp":1763154139089,"version":"build-2065373602"},"reference-count":24,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2016,12,14]],"date-time":"2016-12-14T00:00:00Z","timestamp":1481673600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"the National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["71601002"],"award-info":[{"award-number":["71601002"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"the major project of Humanities and Social Sciences of Ministry of Education of China","award":["16JJD840008"],"award-info":[{"award-number":["16JJD840008"]}]},{"name":"the Humanities and Social Sciences Foundation of Ministry of Education of China","award":["16YJC630077"],"award-info":[{"award-number":["16YJC630077"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Recently, a novel hesitant fuzzy set (HFS) ranking technique based on the idea of lexicographical ordering is proposed and an example is presented to demonstrate that the proposed ranking method is invariant with multiple occurrences of any element of a hesitant fuzzy element (HFE). In this paper, we show by examples that the HFS lexicographical ordering method is sometimes invalid, and a modified ranking method is presented. In comparison with the HFS lexicographical ordering method, the modified ranking method is more reasonable in more general cases.<\/jats:p>","DOI":"10.3390\/sym8120153","type":"journal-article","created":{"date-parts":[[2016,12,14]],"date-time":"2016-12-14T10:14:47Z","timestamp":1481710487000},"page":"153","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["A Modification on the Hesitant Fuzzy Set Lexicographical Ranking Method"],"prefix":"10.3390","volume":"8","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4922-9503","authenticated-orcid":false,"given":"Xiaodi","family":"Liu","sequence":"first","affiliation":[{"name":"School of Mathematics and Physics, Anhui University of Technology, Ma\u2019anshan 243002, Anhui, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zengwen","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Government, Nanjing University, Nanjing 210023, Jiangsu, China"},{"name":"Researching Center of Social Security, Wuhan University, Wuhan 430072, Hubei, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shitao","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Mathematics and Physics, Anhui University of Technology, Ma\u2019anshan 243002, Anhui, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2016,12,14]]},"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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