{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,7]],"date-time":"2026-03-07T18:15:20Z","timestamp":1772907320396,"version":"3.50.1"},"reference-count":58,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2023,2,10]],"date-time":"2023-02-10T00:00:00Z","timestamp":1675987200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The dual hesitant fuzzy linguistic term set (DHFLTS) is defined by two functions that express the grade of membership and the grade of non-membership using a set of linguistic terms. In the present work, we first quote an example to point out that the existing complement operation of DHFLTS is on the wrong track. Meanwhile, we redefine this operation to fill the holes in the existing ones. Next, the notion of information energy under a dual hesitant fuzzy linguistic background is provided in order to build the criteria weight determination model. To further facilitate the theory of DHFLTS, we propose two vector similarity measures, i.e., Jaccard and Dice similarity measures, and their weighted forms for DHFLTS. In addition, we pioneer some generalized similarity measures of DHFLTSs and indicate that the Dice similarity measures are particular instances of the generalized similarity measures for some parameter values. Afterward, the similarity measures-based model with unknown weight information under the background of dual hesitant fuzzy linguistic environment is constructed. Lastly, an illustrated example is included to validate the method\u2019s application, along with sensitivity analysis and comparative analysis, demonstrating the practicality and validity of its results.<\/jats:p>","DOI":"10.3390\/sym15020471","type":"journal-article","created":{"date-parts":[[2023,2,10]],"date-time":"2023-02-10T03:52:49Z","timestamp":1676001169000},"page":"471","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["Vector Similarity Measures of Dual Hesitant Fuzzy Linguistic Term Sets and Their Applications"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3372-0034","authenticated-orcid":false,"given":"Jawad","family":"Ali","sequence":"first","affiliation":[{"name":"Institute of Numerical Sciences, Kohat University of Science and Technology, Kohat 26000, KPK, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ahmad N.","family":"Al-kenani","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80219, Jeddah 21589, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,2,10]]},"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. Control."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Malik, M., Bashir, Z., Rashid, T., and Ali, J. (2018). Probabilistic hesitant intuitionistic linguistic term sets in multi-attribute group decision making. Symmetry, 10.","DOI":"10.3390\/sym10090392"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Bashir, Z., Bashir, Y., Rashid, T., Ali, J., and Gao, W. (2019). A Novel Multi-Attribute Group Decision-Making Approach in the Framework of Proportional Dual Hesitant Fuzzy Sets. Appl. 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