{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T12:54:43Z","timestamp":1740142483628,"version":"3.37.3"},"reference-count":35,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2020,10,6]],"date-time":"2020-10-06T00:00:00Z","timestamp":1601942400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2020,10,6]],"date-time":"2020-10-06T00:00:00Z","timestamp":1601942400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Science Foundation of China","doi-asserted-by":"crossref","award":["11671244"],"award-info":[{"award-number":["11671244"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Comp. Appl. Math."],"published-print":{"date-parts":[[2020,12]]},"DOI":"10.1007\/s40314-020-01339-9","type":"journal-article","created":{"date-parts":[[2020,10,6]],"date-time":"2020-10-06T15:02:48Z","timestamp":1601996568000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["An (R,\u00a0S)-norm information measure for hesitant fuzzy sets and its application in decision-making"],"prefix":"10.1007","volume":"39","author":[{"given":"Chunfeng","family":"Suo","sequence":"first","affiliation":[]},{"given":"Yongming","family":"Li","sequence":"additional","affiliation":[]},{"given":"Zhihui","family":"Li","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2020,10,6]]},"reference":[{"issue":"1","key":"1339_CR1","doi-asserted-by":"publisher","first-page":"87","DOI":"10.1016\/S0165-0114(86)80034-3","volume":"20","author":"K Atanassov","year":"1986","unstructured":"Atanassov K (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20(1):87\u201396","journal-title":"Fuzzy Sets Syst"},{"issue":"3","key":"1339_CR2","doi-asserted-by":"publisher","first-page":"343","DOI":"10.1016\/0165-0114(89)90205-4","volume":"31","author":"KT Atanassov","year":"1989","unstructured":"Atanassov KT, Gargov G (1989) Interval valued intuitionistic fuzzy sets. Fuzzy Sets Syst 31(3):343\u2013349","journal-title":"Fuzzy Sets Syst"},{"issue":"7","key":"1339_CR3","doi-asserted-by":"publisher","first-page":"3323","DOI":"10.1109\/TAC.2016.2644871","volume":"62","author":"T Aviv","year":"2017","unstructured":"Aviv T, Yinlam C, Mohammad G, Shie M (2017) Sequential decision making with coherent risk. IEEE Trans Autom Control 62(7):3323\u20133338","journal-title":"IEEE Trans Autom Control"},{"issue":"8","key":"1339_CR4","doi-asserted-by":"publisher","first-page":"11363","DOI":"10.1016\/j.eswa.2009.03.039","volume":"36","author":"FE Boran","year":"2009","unstructured":"Boran FE, Genc S, Kurt M (2009) A multi-criteria intuitionistic fuzzy group decision making for supplier selection with TOPSIS method. Expert Syst Appl 36(8):11363\u201311368","journal-title":"Expert Syst Appl"},{"key":"1339_CR5","doi-asserted-by":"publisher","first-page":"175","DOI":"10.1016\/j.ins.2014.08.054","volume":"292","author":"N Chen","year":"2015","unstructured":"Chen N, Xu ZS (2015) Hesitant fuzzy ELECTRE II approach: a new way to handle multi-criteria decision making problems. Inf Sci 292:175\u2013197","journal-title":"Inf Sci"},{"issue":"8","key":"1339_CR6","doi-asserted-by":"publisher","first-page":"752","DOI":"10.1002\/int.21600","volume":"28","author":"B Farhadinia","year":"2013","unstructured":"Farhadinia B (2013a) A novel method of ranking hesitant fuzzy values for multiple attribute decision-making problems. Int J Intell Syst 28(8):752\u2013767","journal-title":"Int J Intell Syst"},{"key":"1339_CR7","doi-asserted-by":"publisher","first-page":"129","DOI":"10.1016\/j.ins.2013.03.034","volume":"240","author":"B Farhadinia","year":"2013","unstructured":"Farhadinia B (2013b) Information measures for hesitant fuzzy sets and interval-valued hesitant fuzzy sets. Inf Sci 240:129\u2013144","journal-title":"Inf Sci"},{"key":"1339_CR8","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-30690-2","volume-title":"Set functions, games and capacities in decision making","author":"M Grabisch","year":"2016","unstructured":"Grabisch M (2016) Set functions, games and capacities in decision making. Springer-Verlag, Berlin, Germany"},{"issue":"2","key":"1339_CR9","doi-asserted-by":"publisher","first-page":"319","DOI":"10.1016\/j.fss.2003.08.005","volume":"148","author":"P Grzegorzewski","year":"2004","unstructured":"Grzegorzewski P (2004) Distances between intuitionistic fuzzy sets and\/or interval-valued fuzzy sets based on the Hausdorff metric. Fuzzy Sets Syst 148(2):319\u2013328","journal-title":"Fuzzy Sets Syst"},{"key":"1339_CR10","doi-asserted-by":"crossref","unstructured":"Guleria A, Bajaj RK (2018) Pythagorean fuzzy $$(R,S)$$-norm information measure for multicriteria decision-making problem. Adv Fuzzy Syst Art. ID 8023013, p 11","DOI":"10.1155\/2018\/8023013"},{"issue":"8","key":"1339_CR11","doi-asserted-by":"publisher","first-page":"2517","DOI":"10.1007\/s40815-018-0523-2","volume":"20","author":"Z Hussain","year":"2018","unstructured":"Hussain Z, Yang MS (2018) Entropy for hesitant fuzzy sets based on Hausdorff metric with construction of hesitant fuzzy TOPSIS. Int J Fuzzy Syst 20(8):2517\u20132533","journal-title":"Int J Fuzzy Syst"},{"issue":"3","key":"1339_CR12","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1142\/S1230161216500153","volume":"23","author":"R Joshi","year":"2016","unstructured":"Joshi R, Kumar S (2016) $$(R, S)$$-norm information and a relation between coding and questionnaire theory. Open Syst Inf Dyn 23(3):1\u201312","journal-title":"Open Syst Inf Dyn"},{"issue":"2","key":"1339_CR13","doi-asserted-by":"crossref","first-page":"181","DOI":"10.1016\/j.fiae.2017.06.004","volume":"9","author":"R Joshi","year":"2017","unstructured":"Joshi R, Kumar S (2017) Parametric $$(R, S)$$-norm entropy on intuitionistic fuzzy sets with a new approach in multiple attribute decision making. Fuzzy Inf Eng 9(2):181\u2013203","journal-title":"Fuzzy Inf Eng"},{"issue":"37","key":"1339_CR14","doi-asserted-by":"crossref","first-page":"4518","DOI":"10.1007\/s40314-018-0582-x","volume":"4","author":"R Joshi","year":"2018","unstructured":"Joshi R, Kumar S (2018a) An ($$R^{^{\\prime }}, S^{^{\\prime }}$$)-norm fuzzy relative information measure and its application in strategic decision-making. Comput Appl Math 4(37):4518\u20134543","journal-title":"Comput Appl Math"},{"issue":"37","key":"1339_CR15","doi-asserted-by":"crossref","first-page":"2943","DOI":"10.1007\/s40314-017-0491-4","volume":"3","author":"R Joshi","year":"2018","unstructured":"Joshi R, Kumar S (2018b) An $$(R, S)$$-norm fuzzy information measure with its applications in multiple-attribute decision-making. Comput Appl Math 3(37):2943\u20132964","journal-title":"Comput Appl Math"},{"key":"1339_CR16","doi-asserted-by":"publisher","first-page":"1304","DOI":"10.1016\/j.eswa.2010.07.003","volume":"38","author":"MS Kuo","year":"2011","unstructured":"Kuo MS, Liang GS (2011) Combining VIKOR with GRA techniques to evaluate service quality of airports under fuzzy environment. Expert Syst Appl 38:1304\u20131312","journal-title":"Expert Syst Appl"},{"issue":"1","key":"1339_CR17","first-page":"221","volume":"23","author":"DF Li","year":"2002","unstructured":"Li DF, Cheng CT (2002) New similarity measures of intuitionistic fuzzy sets and application to pattern recognitions. Pattern Recogn Lett 23(1):221\u2013225","journal-title":"Pattern Recogn Lett"},{"issue":"5","key":"1339_CR18","doi-asserted-by":"publisher","first-page":"1343","DOI":"10.1109\/TFUZZ.2014.2360556","volume":"23","author":"HC Liao","year":"2015","unstructured":"Liao HC, Xu ZS, Zeng XJ (2015) Hesitant fuzzy linguistic VIKOR method and its application in qualitative multiple criteria decision making. IEEE Trans Fuzzy Syst 23(5):1343\u20131355","journal-title":"IEEE Trans Fuzzy Syst"},{"issue":"5","key":"1339_CR19","doi-asserted-by":"publisher","first-page":"2221","DOI":"10.3233\/IFS-141186","volume":"27","author":"QH Liu","year":"2014","unstructured":"Liu QH (2014) An extended TOPSIS method for multiple attribute decision making problems with unknown weight based on 2-dimension uncertain linguistic variables. J Intell Fuzzy Syst 27(5):2221\u20132230","journal-title":"J Intell Fuzzy Syst"},{"issue":"4","key":"1339_CR20","doi-asserted-by":"publisher","first-page":"301","DOI":"10.1016\/S0019-9958(72)90199-4","volume":"20","author":"AD De Luca","year":"1972","unstructured":"De Luca AD, Termini S (1972) A definition of a nonprobabilistic entropy in the setting of fuzzy sets theory. Inf Control 20(4):301\u2013312","journal-title":"Inf Control"},{"key":"1339_CR21","doi-asserted-by":"publisher","first-page":"521","DOI":"10.1016\/j.eswa.2017.09.048","volume":"92","author":"GS Sun","year":"2018","unstructured":"Sun GS, Guan X, Yi X, Zheng Z (2018) Grey relational analysis between hesitant fuzzy sets with applications to pattern recognition. Expert Syst Appl 92:521\u2013532","journal-title":"Expert Syst Appl"},{"issue":"6","key":"1339_CR22","first-page":"529","volume":"25","author":"V Torra","year":"2010","unstructured":"Torra V (2010) Hesitant fuzzy sets. Int J Intell Syst 25(6):529\u2013539","journal-title":"Int J Intell Syst"},{"issue":"2","key":"1339_CR23","doi-asserted-by":"publisher","first-page":"191","DOI":"10.1016\/0165-0114(86)90077-1","volume":"20","author":"IB Turksen","year":"1986","unstructured":"Turksen IB (1986) Interval valued fuzzy sets based on normal forms. Fuzzy Sets Syst 20(2):191\u2013210","journal-title":"Fuzzy Sets Syst"},{"issue":"4","key":"1339_CR24","doi-asserted-by":"publisher","first-page":"297","DOI":"10.1007\/BF00122574","volume":"5","author":"A Tversky","year":"1992","unstructured":"Tversky A, Kahneman D (1992) Advances in propect theory: cumulative representation of uncertainty. J Risk Uncertain 5(4):297\u2013323","journal-title":"J Risk Uncertain"},{"key":"1339_CR25","doi-asserted-by":"publisher","first-page":"155","DOI":"10.1016\/j.ins.2017.02.045","volume":"397\u2013398","author":"CY Wang","year":"2017","unstructured":"Wang CY, Chen SM (2017) Multiple attribute decision making based on interval-valued intuitionistic fuzzy sets, linear programming methodology, and the extended TOPSIS method. Inf Sci 397\u2013398:155\u2013167","journal-title":"Inf Sci"},{"issue":"5","key":"1339_CR26","first-page":"864","volume":"32","author":"YM Wang","year":"2017","unstructured":"Wang YM, Que CP, Lan YX (2017) Hesitant fuzzy TOPSIS multi-attribute decision method based on prospect theory. Control Decis (Chin) 32(5):864\u2013870","journal-title":"Control Decis (Chin)"},{"issue":"1","key":"1339_CR27","doi-asserted-by":"publisher","first-page":"673","DOI":"10.3233\/IFS-2180","volume":"31","author":"CP Wei","year":"2016","unstructured":"Wei CP, Yan FF, Rodriguez RM (2016) Entropy measures for hesitant fuzzy sets and their application relations and fuzzy in multi-criteria decision-making. J Intell Fuzzy Syst 31(1):673\u2013685","journal-title":"J Intell Fuzzy Syst"},{"issue":"3","key":"1339_CR28","doi-asserted-by":"publisher","first-page":"395","DOI":"10.1016\/j.ijar.2010.09.002","volume":"52","author":"MM Xia","year":"2011","unstructured":"Xia MM, Xu ZS (2011) Hesitant fuzzy information aggregation in decision making. Int J Approx Reasioning 52(3):395\u2013407","journal-title":"Int J Approx Reasioning"},{"key":"1339_CR29","doi-asserted-by":"publisher","first-page":"2128","DOI":"10.1016\/j.ins.2011.01.028","volume":"181","author":"ZS Xu","year":"2011","unstructured":"Xu ZS, Xia MM (2011) Distance and similarity fuzzy sets. Inf Sci 181:2128\u20132138","journal-title":"Inf Sci"},{"issue":"9","key":"1339_CR30","doi-asserted-by":"publisher","first-page":"799","DOI":"10.1002\/int.21548","volume":"27","author":"ZS Xu","year":"2012","unstructured":"Xu ZS, Xia MM (2012) Hesitant fuzzy entropy and cross-entropy and their use in multiattribute decision- making. Int J Intell Syst 27(9):799\u2013822","journal-title":"Int J Intell Syst"},{"issue":"6","key":"1339_CR31","doi-asserted-by":"publisher","first-page":"53","DOI":"10.1016\/j.knosys.2013.05.011","volume":"52","author":"ZS Xu","year":"2013","unstructured":"Xu ZS, Zhang XL (2013) Hesitant fuzzy multi-attribute decision making based on TOPSIS with incomplete weight information. Knowl Based Syst 52(6):53\u201364","journal-title":"Knowl Based Syst"},{"issue":"2","key":"1339_CR32","doi-asserted-by":"publisher","first-page":"351","DOI":"10.1016\/S0165-0114(99)00071-8","volume":"120","author":"JFF Yao","year":"2001","unstructured":"Yao JFF, Yao JS (2001) Fuzzy decision making for medical diagosis based on fuzzy number and compositional rule of inference. Fuzzy Sets Syst 120(2):351\u2013366","journal-title":"Fuzzy Sets Syst"},{"issue":"3","key":"1339_CR33","doi-asserted-by":"publisher","first-page":"338","DOI":"10.1016\/S0019-9958(65)90241-X","volume":"8","author":"LA Zadeh","year":"1965","unstructured":"Zadeh LA (1965) Fuzzy sets. Inf Control 8(3):338\u2013353","journal-title":"Inf Control"},{"issue":"2","key":"1339_CR34","doi-asserted-by":"publisher","first-page":"421","DOI":"10.1016\/0022-247X(68)90078-4","volume":"23","author":"LA Zadeh","year":"1968","unstructured":"Zadeh LA (1968) Probability measures of fuzzy events. J Math Anal Appl 23(2):421\u2013427","journal-title":"J Math Anal Appl"},{"issue":"1","key":"1339_CR35","doi-asserted-by":"publisher","first-page":"48","DOI":"10.1016\/j.knosys.2014.02.006","volume":"61","author":"XL Zhang","year":"2014","unstructured":"Zhang XL, Xu ZS (2014) The TODIM analysis approach based on novel measured functions under hesitant fuzzy environment. Knowl Based Syst 61(1):48\u201358","journal-title":"Knowl Based Syst"}],"container-title":["Computational and Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-020-01339-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s40314-020-01339-9\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-020-01339-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,10,6]],"date-time":"2021-10-06T06:26:08Z","timestamp":1633501568000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s40314-020-01339-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,10,6]]},"references-count":35,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2020,12]]}},"alternative-id":["1339"],"URL":"https:\/\/doi.org\/10.1007\/s40314-020-01339-9","relation":{},"ISSN":["2238-3603","1807-0302"],"issn-type":[{"type":"print","value":"2238-3603"},{"type":"electronic","value":"1807-0302"}],"subject":[],"published":{"date-parts":[[2020,10,6]]},"assertion":[{"value":"24 February 2020","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"11 August 2020","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"23 September 2020","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"6 October 2020","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Compliance with ethical standards"}},{"value":"All authors agree to contribute without conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"286"}}