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We first refine the axiomatic principles of hesitant fuzzy entropy based on the fuzzy factor and hesitant factor, and propose some distance-based entropy formulas of HFSs. Then, a novel hesitant fuzzy cross-entropy is defined to measure the discrimination of uncertain information of different HFSs. Meanwhile, the relationship between cross-entropy and entropy of HFSs is also discussed, and the hesitant fuzzy entropy may be divided into arithmetic average of fuzzy entropy and hesitant entropy. Moreover, some parameterized uncertainty measures are investigated, and two comparative examples are presented to demonstrate their reasonability. Finally, we apply these proposed measures in multiple attribute decision-making problem to illustrate their efficiency and applicability.<\/jats:p>","DOI":"10.3233\/ifs-151790","type":"journal-article","created":{"date-parts":[[2016,2,9]],"date-time":"2016-02-09T10:56:14Z","timestamp":1455015374000},"page":"691-703","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":4,"title":["Some novel uncertainty measures of hesitant fuzzy sets and their applications"],"prefix":"10.1177","volume":"30","author":[{"given":"Dengbao","family":"Yao","sequence":"first","affiliation":[{"name":"School of Economics and Management, Southeast University, Nanjing, Jiangsu, China"}]},{"given":"Xiaoxing","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Economics and Management, Southeast University, Nanjing, Jiangsu, China"}]},{"given":"Xu","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Economics and Management, Southeast University, Nanjing, Jiangsu, China"}]},{"given":"Cuicui","family":"Wang","sequence":"additional","affiliation":[{"name":"Foundation Department, Anhui Sanlian University, Hefei, Anhui, China"}]}],"member":"179","published-online":{"date-parts":[[2015,10,9]]},"reference":[{"key":"e_1_3_2_2_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-0114(86)80034-3"},{"key":"e_1_3_2_3_2","doi-asserted-by":"publisher","DOI":"10.1002\/int.21655"},{"key":"e_1_3_2_4_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.apm.2012.04.031"},{"key":"e_1_3_2_5_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2013.03.034"},{"key":"e_1_3_2_6_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2014.02.009"},{"key":"e_1_3_2_7_2","doi-asserted-by":"publisher","DOI":"10.1002\/int.20131"},{"key":"e_1_3_2_8_2","doi-asserted-by":"publisher","DOI":"10.3233\/IFS-130978"},{"key":"e_1_3_2_9_2","doi-asserted-by":"publisher","DOI":"10.3233\/IFS-130841"},{"key":"e_1_3_2_10_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00500-014-1422-6"},{"key":"e_1_3_2_11_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10700-013-9162-0"},{"key":"e_1_3_2_12_2","doi-asserted-by":"publisher","DOI":"10.1142\/S0218488514500275"},{"key":"e_1_3_2_13_2","doi-asserted-by":"publisher","DOI":"10.1142\/S0219622014500035"},{"key":"e_1_3_2_14_2","doi-asserted-by":"publisher","DOI":"10.1108\/K-11-2013-0246"},{"key":"e_1_3_2_15_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.knosys.2015.02.020"},{"key":"e_1_3_2_16_2","doi-asserted-by":"publisher","DOI":"10.1109\/TFUZZ.2015.2426315"},{"key":"e_1_3_2_17_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.engappai.2014.12.012"},{"key":"e_1_3_2_18_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.knosys.2013.04.011"},{"key":"e_1_3_2_19_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2012.11.016"},{"key":"e_1_3_2_20_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.knosys.2015.04.005"},{"key":"e_1_3_2_21_2","doi-asserted-by":"publisher","DOI":"10.1002\/int.21654"},{"key":"e_1_3_2_22_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2015.03.041"},{"key":"e_1_3_2_23_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-8655(97)00028-7"},{"key":"e_1_3_2_24_2","first-page":"529","article-title":"Hesitant fuzzy sets","volume":"25","author":"Torra V.","year":"2010","unstructured":"TorraV., Hesitant fuzzy sets, International Journal of Intelligent Systems 25 (2010), 529\u2013539.","journal-title":"International Journal of Intelligent Systems"},{"key":"e_1_3_2_25_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.patrec.2006.07.004"},{"key":"e_1_3_2_26_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijar.2010.09.002"},{"key":"e_1_3_2_27_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.inffus.2010.12.001"},{"key":"e_1_3_2_28_2","doi-asserted-by":"crossref","unstructured":"XuZ.S. 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