{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T06:36:44Z","timestamp":1777703804802,"version":"3.51.4"},"reference-count":37,"publisher":"SAGE Publications","issue":"6","license":[{"start":{"date-parts":[[2016,6,14]],"date-time":"2016-06-14T00:00:00Z","timestamp":1465862400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Journal of Intelligent &amp; Fuzzy Systems"],"published-print":{"date-parts":[[2017,5,23]]},"abstract":"<jats:p>Neutrosophic hesitant fuzzy set (NHFS) is an extension of neutrosophic set and the hesitant fuzzy set, which can easily express the uncertain, incomplete and inconsistent information, and the VIKOR (from Serbian: VIseKriterijumska Optimizacija I Kompromisno Resenje) method is an effective decision making tool which can select the optimal alternative by the maximizing \u201cgroup utility\u201d and minimizing \u201cindividual regret\u201d with cognitive computation. In this paper, we firstly introduced some operational laws, comparison rules and the Hamming distance measure of neutrosophic hesitant fuzzy set, and described the traditional VIKOR method which only processes the crisp numbers. Then we extended the VIKOR method to process the Neutrosophic hesitant fuzzy information (NHFI), and proposed an extended VIKOR method for the multiple criteria decision making (MCDM) problems with NHFI, and an illustrative example shows the effectiveness of the proposed approach.<\/jats:p>","DOI":"10.3233\/jifs-16136","type":"journal-article","created":{"date-parts":[[2017,5,26]],"date-time":"2017-05-26T14:42:25Z","timestamp":1495809745000},"page":"4403-4413","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":19,"title":["An extended multiple criteria decision making method based on neutrosophic hesitant fuzzy information"],"prefix":"10.1177","volume":"32","author":[{"given":"Peide","family":"Liu","sequence":"first","affiliation":[{"name":"School of Management Science and Engineering, Shandong University of Finance and Economics, Jinan Shandong, China"}]},{"given":"Lili","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Management Science and Engineering, Shandong University of Finance and Economics, Jinan Shandong, China"}]}],"member":"179","published-online":{"date-parts":[[2016,6,14]]},"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\/S0165-0114(86)80034-3"},{"key":"e_1_3_2_4_2","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(89)90215-7"},{"key":"e_1_3_2_5_2","volume-title":"Proc Of 10th 476 Int Conf on Fuzzy Theory and Technology","author":"Wang H.","year":"2005","unstructured":"WangH., SmarandacheF., ZhangY. and SunderramanR., Single valued neutrosophic sets, Proc Of 10th 476 Int Conf on Fuzzy Theory and Technology, Salt Lake City, 477 Utah, 2005."},{"key":"e_1_3_2_6_2","volume-title":"A unifying field in logics","author":"Smarandache F.","year":"1999","unstructured":"SmarandacheF., Neutrosophy: Neutrosophic probability, set and logic, A unifying field in logics, American Research Press, Rehoboth, 1999."},{"key":"e_1_3_2_7_2","first-page":"410","article-title":"Single valued neutrosophic sets","volume":"4","author":"Wang H.","year":"2010","unstructured":"WangH., SmarandacheF., ZhangY.Q. and SunderramanR., Single valued neutrosophic sets, Multispace and Multistructure 4 (2010), 410\u2013413.","journal-title":"Multispace and Multistructure"},{"key":"e_1_3_2_8_2","doi-asserted-by":"publisher","DOI":"10.1080\/03081079.2012.761609"},{"key":"e_1_3_2_9_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.apm.2013.07.020"},{"key":"e_1_3_2_10_2","first-page":"1378","volume-title":"In: The 18th IEEE International Conference on Fuzzy Systems","author":"Torra V.","year":"2009","unstructured":"TorraV. and NarukawaY., On hesitant fuzzy sets and decision, In: The 18th IEEE International Conference on Fuzzy Systems, Jeju Island, Korea, 2009, pp. 1378\u20131382."},{"key":"e_1_3_2_11_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_12_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.apm.2012.04.031"},{"key":"e_1_3_2_13_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.eswa.2013.07.104"},{"key":"e_1_3_2_14_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2014.02.012"},{"key":"e_1_3_2_15_2","doi-asserted-by":"publisher","DOI":"10.1002\/int.21633"},{"key":"e_1_3_2_16_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.apm.2013.07.010"},{"key":"e_1_3_2_17_2","doi-asserted-by":"publisher","DOI":"10.1155\/2014\/868515"},{"key":"e_1_3_2_18_2","doi-asserted-by":"publisher","DOI":"10.1515\/jisys-2014-0001"},{"issue":"4","key":"e_1_3_2_19_2","first-page":"766","article-title":"An extended VIKOR method for multiple attribute group decision making based on generalized interval-valued trapezoidal fuzzy numbers","volume":"6","author":"Liu P.D.","year":"2011","unstructured":"LiuP.D. and WangM.H., An extended VIKOR method for multiple attribute group decision making based on generalized interval-valued trapezoidal fuzzy numbers, Scientific Research and Essays 2011 6(4) (2011), 766\u2013776.","journal-title":"Scientific Research and Essays 2011"},{"key":"e_1_3_2_20_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.asoc.2016.02.007"},{"key":"e_1_3_2_21_2","doi-asserted-by":"publisher","DOI":"10.1109\/TFUZZ.2014.2360556"},{"key":"e_1_3_2_22_2","doi-asserted-by":"publisher","DOI":"10.1142\/S0219622015500212"},{"key":"e_1_3_2_23_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.apm.2012.10.002"},{"key":"e_1_3_2_24_2","doi-asserted-by":"publisher","DOI":"10.3846\/20294913.2012.753169"},{"issue":"2","key":"e_1_3_2_25_2","first-page":"527","article-title":"The research of enterprise credit risk evaluation based on hybrid decision-making index and VIKOR method","volume":"4","author":"Zhang X.","year":"2010","unstructured":"ZhangX., DuH.T. and LuP.D., The research of enterprise credit risk evaluation based on hybrid decision-making index and VIKOR method, ICIC-EL 4(2) (2010), 527\u2013532.","journal-title":"ICIC-EL"},{"issue":"8","key":"e_1_3_2_26_2","first-page":"2575","article-title":"Extended fuzzy VIKOR method with intuitionistic trapezoidal fuzzy numbers","volume":"14","author":"Du Y.","year":"2011","unstructured":"DuY. and LiuP.D., Extended fuzzy VIKOR method with intuitionistic trapezoidal fuzzy numbers, INFORMATION-An International Interdisciplinary Journal 14(8) (2011), 2575\u20132584.","journal-title":"INFORMATION-An International Interdisciplinary Journal"},{"key":"e_1_3_2_27_2","unstructured":"WangH. SmarandacheF. ZhangY.Q. and SunderramanR. Interval neutrosophic sets and logic: Theory and applications in computing Hexis Phoenix AZ 2005."},{"key":"e_1_3_2_28_2","doi-asserted-by":"publisher","DOI":"10.1109\/GRC.2011.6122666"},{"key":"e_1_3_2_29_2","doi-asserted-by":"publisher","DOI":"10.3233\/IFS-130916"},{"key":"e_1_3_2_30_2","doi-asserted-by":"publisher","DOI":"10.1002\/int.21654"},{"key":"e_1_3_2_31_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijar.2010.09.002"},{"key":"e_1_3_2_32_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejor.2006.01.020"},{"issue":"1","key":"e_1_3_2_33_2","first-page":"5","article-title":"Multi-criteria optimization of civil engineering systems","volume":"2","author":"Opricovic S.","year":"1998","unstructured":"OpricovicS., Multi-criteria optimization of civil engineering systems, Faculty of Civil Engineering, Belgrade 2(1) (1998), 5\u201321.","journal-title":"Faculty of Civil Engineering, Belgrade"},{"key":"e_1_3_2_34_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0377-2217(03)00020-1"},{"issue":"6","key":"e_1_3_2_35_2","first-page":"1139","article-title":"TODIM method with multi-valued neutrosophic sets","volume":"30","author":"Wang J.Q.","year":"2015","unstructured":"WangJ.Q. and LiX.E., TODIM method with multi-valued neutrosophic sets, Control and Decision 30(6) (2015), 1139\u20131143.","journal-title":"Control and Decision"},{"key":"e_1_3_2_36_2","first-page":"86","article-title":"Single valued neutrosophic graphs","author":"Broumi S.","year":"2016","unstructured":"BroumiS., TaleaM., BakaliA. and SmarandacheF., Single valued neutrosophic graphs, Journal of New Theory (10) (2016), 86\u2013101.","journal-title":"Journal of New Theory (10)"},{"key":"e_1_3_2_37_2","first-page":"84","article-title":"On bipolar single valued neutrosophic graphs","author":"Broumi S.","year":"2016","unstructured":"BroumiS., TaleaM., BakaliA. and SmarandacheF., On bipolar single valued neutrosophic graphs, Journal of New Theory (11) (2016), 84\u2013102.","journal-title":"Journal of New Theory (11)"},{"key":"e_1_3_2_38_2","doi-asserted-by":"publisher","DOI":"10.13189\/ms.2014.020202"}],"container-title":["Journal of Intelligent &amp; Fuzzy Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/JIFS-16136","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/full-xml\/10.3233\/JIFS-16136","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/JIFS-16136","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T09:39:39Z","timestamp":1777455579000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/JIFS-16136"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,6,14]]},"references-count":37,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2017,5,23]]}},"alternative-id":["10.3233\/JIFS-16136"],"URL":"https:\/\/doi.org\/10.3233\/jifs-16136","relation":{},"ISSN":["1064-1246","1875-8967"],"issn-type":[{"value":"1064-1246","type":"print"},{"value":"1875-8967","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,6,14]]}}}