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Then the corresponding distance measure of HFLTSs is obtained according to the relationship between the similarity measure and the distance measure. Furthermore, we develop the TOPSIS method to the proposed distance measure in hesitant fuzzy linguistic decision environment and apply the closeness coefficients to rank the alternatives. The main advantage of the proposed method is that it not only considers the distance measure from the point view of algebra and geometry but also overcomes the disadvantage of the existing cosine similarity measure. Finally, an example is provided to illustrate the feasibility of the proposed method and some comparative analyses are given to show its efficiency.<\/jats:p>","DOI":"10.3233\/jifs-181886","type":"journal-article","created":{"date-parts":[[2019,6,18]],"date-time":"2019-06-18T12:22:42Z","timestamp":1560860562000},"page":"995-1006","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":5,"title":["The new similarity measure and distance measure between hesitant fuzzy linguistic term sets and their application in multi-criteria decision making"],"prefix":"10.1177","volume":"37","author":[{"given":"Liu","family":"Donghai","sequence":"first","affiliation":[{"name":"Department of Statistics, Hunan University of Science and Technology, Hunan, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Liu","family":"Yuanyuan","sequence":"additional","affiliation":[{"name":"Department of Statistics, Hunan University of Science and Technology, Hunan, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chen","family":"Xiaohong","sequence":"additional","affiliation":[{"name":"Mobile E-business Collaborative Innovation Center of Hunan Province, Hunan University of Commerce, Hunan, China"},{"name":"Business School, Central South university, Hunan, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2019,6,14]]},"reference":[{"key":"e_1_3_2_2_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0019-9958(65)90241-X"},{"key":"e_1_3_2_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/0031-3203(90)90054-O"},{"key":"e_1_3_2_4_2","doi-asserted-by":"publisher","DOI":"10.1109\/TSMC.1986.4308946"},{"key":"e_1_3_2_5_2","doi-asserted-by":"publisher","DOI":"10.1109\/91.366570"},{"key":"e_1_3_2_6_2","doi-asserted-by":"publisher","DOI":"10.3233\/IFS-151644"},{"issue":"6","key":"e_1_3_2_7_2","first-page":"529","article-title":"Hesitant fuzzy sets [J]","volume":"25","author":"Torra V.","year":"2010","unstructured":"TorraV., Hesitant fuzzy sets [J], International Journal of Intelligent Systems 25 (6) (2010)529\u2013539.","journal-title":"International Journal of Intelligent Systems"},{"key":"e_1_3_2_8_2","doi-asserted-by":"publisher","DOI":"10.1002\/int.20474"},{"key":"e_1_3_2_9_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2013.03.034"},{"issue":"2","key":"e_1_3_2_10_2","first-page":"1","article-title":"Some studies on properties of hesitant fuzzy sets [J]","volume":"8","author":"Xia M.","year":"2015","unstructured":"XiaM. and XuZ., Some studies on properties of hesitant fuzzy sets [J], International Journal of Machine Learning & Cybernetics 8 (2) (2015)1\u20137.","journal-title":"International Journal of Machine Learning & Cybernetics"},{"key":"e_1_3_2_11_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.eswa.2018.01.016"},{"key":"e_1_3_2_12_2","doi-asserted-by":"publisher","DOI":"10.1007\/s12652-019-01238-w"},{"key":"e_1_3_2_13_2","doi-asserted-by":"publisher","DOI":"10.1016\/0020-0255(75)90036-5"},{"key":"e_1_3_2_14_2","doi-asserted-by":"publisher","DOI":"10.1016\/0020-0255(75)90046-8"},{"key":"e_1_3_2_15_2","doi-asserted-by":"publisher","DOI":"10.1016\/0020-0255(75)90017-1"},{"key":"e_1_3_2_16_2","doi-asserted-by":"publisher","DOI":"10.1109\/TFUZZ.2011.2170076"},{"key":"e_1_3_2_17_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2014.11.011"},{"key":"e_1_3_2_18_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.cie.2017.10.029"},{"key":"e_1_3_2_19_2","doi-asserted-by":"publisher","DOI":"10.3390\/ijerph15040664"},{"key":"e_1_3_2_20_2","doi-asserted-by":"publisher","DOI":"10.1007\/s40815-018-0488-1"},{"key":"e_1_3_2_21_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.knosys.2015.06.011"},{"issue":"3","key":"e_1_3_2_22_2","article-title":"Distance and similarity measures for hesitant fuzzy linguistic term sets and their application in multi-criteria decision making [J]","volume":"271","author":"Liao H.","year":"2014","unstructured":"LiaoH., XuZ. and ZengX.J., Distance and similarity measures for hesitant fuzzy linguistic term sets and their application in multi-criteria decision making [J], Information Sciences 271 (3) (2014).","journal-title":"Information Sciences"},{"key":"e_1_3_2_23_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2014.09.061"},{"key":"e_1_3_2_24_2","doi-asserted-by":"crossref","unstructured":"HesamianG. and ShamsM. 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