{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,18]],"date-time":"2025-12-18T14:11:11Z","timestamp":1766067071373,"version":"3.37.3"},"reference-count":42,"publisher":"Springer Science and Business Media LLC","issue":"12","license":[{"start":{"date-parts":[[2019,11,9]],"date-time":"2019-11-09T00:00:00Z","timestamp":1573257600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2019,11,9]],"date-time":"2019-11-09T00:00:00Z","timestamp":1573257600000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"name":"Humanities and Social Sciences Foundation of Chinese Ministry of Education","award":["18YJC790211","17YJC630067"],"award-info":[{"award-number":["18YJC790211","17YJC630067"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["71671031","71701040","71803073"],"award-info":[{"award-number":["71671031","71701040","71803073"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Soft Comput"],"published-print":{"date-parts":[[2020,6]]},"DOI":"10.1007\/s00500-019-04447-9","type":"journal-article","created":{"date-parts":[[2019,11,9]],"date-time":"2019-11-09T06:03:20Z","timestamp":1573279400000},"page":"9205-9213","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["On possible outputs of group decision making with interval uncertainties based on simulation techniques"],"prefix":"10.1007","volume":"24","author":[{"given":"Pingtao","family":"Yi","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5186-5608","authenticated-orcid":false,"given":"Weiwei","family":"Li","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Danning","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2019,11,9]]},"reference":[{"issue":"7","key":"4447_CR1","doi-asserted-by":"crossref","first-page":"634","DOI":"10.1002\/int.21650","volume":"29","author":"I Beg","year":"2014","unstructured":"Beg I, Rashid T (2014) Aggregation operators of interval-valued 2-tuple linguistic information. Int J Intell Syst 29(7):634\u2013667","journal-title":"Int J Intell Syst"},{"key":"4447_CR2","volume-title":"Aggregation functions: a guide for practitioners","author":"G Beliakov","year":"2007","unstructured":"Beliakov G, Pradera A, Calvo T (2007) Aggregation functions: a guide for practitioners. Springer, Berlin"},{"issue":"1","key":"4447_CR3","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1016\/j.fss.2012.07.015","volume":"220","author":"H Bustince","year":"2013","unstructured":"Bustince H, Fernandez J, Koles\u00e1rov\u00e1 A, Mesiar R (2013) Generation of linear orders for intervals by means of aggregation functions. Fuzzy Sets Syst 220(1):69\u201377","journal-title":"Fuzzy Sets Syst"},{"key":"4447_CR4","doi-asserted-by":"crossref","first-page":"206","DOI":"10.1016\/j.ins.2017.02.046","volume":"397\u2013398","author":"SM Chen","year":"2017","unstructured":"Chen SM, Huang ZC (2017) Multiattribute decision making based on interval-valued intuitionistic fuzzy values and particle swarm optimization techniques. Inf Sci 397\u2013398:206\u2013218","journal-title":"Inf Sci"},{"key":"4447_CR5","doi-asserted-by":"crossref","first-page":"528","DOI":"10.1016\/j.knosys.2012.09.009","volume":"37","author":"N Chen","year":"2013","unstructured":"Chen N, Xu ZS, Xia MM (2013) Interval-valued hesitant preference relations and their applications to group decision making. Knowl Based Syst 37:528\u2013540","journal-title":"Knowl Based Syst"},{"key":"4447_CR6","doi-asserted-by":"crossref","first-page":"418","DOI":"10.1016\/j.ins.2016.05.041","volume":"367\u2013368","author":"SM Chen","year":"2016","unstructured":"Chen SM, Cheng SH, Tsai WH (2016) Multiple attribute group decision making based on interval-valued intuitionistic fuzzy aggregation operators and transformation techniques of interval-valued intuitionistic fuzzy values. Inf Sci 367\u2013368:418\u2013442","journal-title":"Inf Sci"},{"key":"4447_CR7","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1016\/j.ins.2013.03.034","volume":"240","author":"B Farhadinia","year":"2013","unstructured":"Farhadinia B (2013) Information measures for hesitant fuzzy sets and interval-valued hesitant fuzzy sets. Inf Sci 240:129\u2013144","journal-title":"Inf Sci"},{"issue":"2","key":"4447_CR8","doi-asserted-by":"crossref","first-page":"236","DOI":"10.1109\/91.388176","volume":"3","author":"J Fodor","year":"1995","unstructured":"Fodor J, Marichal JL, Roubens M (1995) Characterization of the ordered weighted averaging operators. IEEE Trans Fuzzy Syst 3(2):236\u2013240","journal-title":"IEEE Trans Fuzzy Syst"},{"issue":"2","key":"4447_CR9","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1007\/s10700-016-9243-y","volume":"16","author":"XJ Gou","year":"2017","unstructured":"Gou XJ, Xu ZS (2017) Exponential operations for intuitionistic fuzzy numbers and interval numbers in multi-attribute decision making. Fuzzy Optim Decis Mak 16(2):183\u2013204","journal-title":"Fuzzy Optim Decis Mak"},{"issue":"5","key":"4447_CR10","doi-asserted-by":"crossref","first-page":"1129","DOI":"10.1007\/s00500-015-1843-x","volume":"21","author":"YD He","year":"2017","unstructured":"He YD, He Z, Huang H (2017) Decision making with the generalized intuitionistic fuzzy power interaction averaging operators. Soft Comput 21(5):1129\u20131144","journal-title":"Soft Comput"},{"issue":"1","key":"4447_CR11","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1016\/j.ejor.2015.06.047","volume":"248","author":"D Joshi","year":"2016","unstructured":"Joshi D, Kumar S (2016) Interval-valued intuitionstic hesitant fuzzy Choquet integral based TOPSIS method for multi-criteria group decision making. Eur J Oper Res 248(1):183\u2013191","journal-title":"Eur J Oper Res"},{"issue":"1","key":"4447_CR12","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1016\/S0165-0114(02)00429-3","volume":"137","author":"C Labreuche","year":"2003","unstructured":"Labreuche C, Grabisch M (2003) The Choquet integral for the aggregation of interval scales in multicriteria decision making. Fuzzy Sets Syst 137(1):11\u201326","journal-title":"Fuzzy Sets Syst"},{"issue":"1","key":"4447_CR13","doi-asserted-by":"crossref","first-page":"1053","DOI":"10.1016\/j.eswa.2010.07.144","volume":"38","author":"PD Liu","year":"2011","unstructured":"Liu PD (2011) A weighted aggregation operators multi-attribute group decision-making method based on interval-valued trapezoidal fuzzy numbers. Expert Syst Appl 38(1):1053\u20131060","journal-title":"Expert Syst Appl"},{"issue":"6","key":"4447_CR14","doi-asserted-by":"crossref","first-page":"2498","DOI":"10.1016\/j.apm.2011.09.006","volume":"36","author":"PD Liu","year":"2012","unstructured":"Liu PD, Jin F (2012) A multi-attribute group decision-making method based on weighted geometric aggregation operators of interval-valued trapezoidal fuzzy numbers. Appl Math Model 36(6):2498\u20132509","journal-title":"Appl Math Model"},{"issue":"5","key":"4447_CR15","doi-asserted-by":"crossref","first-page":"1079","DOI":"10.1007\/s00521-015-2122-6","volume":"28","author":"PD Liu","year":"2017","unstructured":"Liu PD, Shi LL (2017) Some neutrosophic uncertain linguistic number Heronian mean operators and their application to multi-attribute group decision making. Neural Comput Appl 28(5):1079\u20131093","journal-title":"Neural Comput Appl"},{"issue":"1","key":"4447_CR16","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1016\/j.ejor.2015.02.025","volume":"245","author":"BS Liu","year":"2015","unstructured":"Liu BS, Shen YH, Zhang W, Chen XH, Wang XQ (2015) An interval-valued intuitionistic fuzzy principal component analysis model-based method for complex multi-attribute large-group decision-making. Eur J Oper Res 245(1):209\u2013225","journal-title":"Eur J Oper Res"},{"issue":"1","key":"4447_CR17","doi-asserted-by":"crossref","first-page":"86","DOI":"10.1007\/s40815-015-0130-4","volume":"19","author":"X Liu","year":"2017","unstructured":"Liu X, Tao ZF, Chen HY (2017) A new interval-valued 2-tuple linguistic bonferroni mean operator and its application to multiattribute group decision making. Int J Fuzzy Syst 19(1):86\u2013108","journal-title":"Int J Fuzzy Syst"},{"issue":"1","key":"4447_CR18","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1142\/S0219622016500498","volume":"16","author":"V Lopez-Morales","year":"2016","unstructured":"Lopez-Morales V, Suarez-Cansino J (2016) Reliable intervals method in decision-based support models for group decision-making. Int J Inf Technol Decis Mak 16(1):183\u2013204","journal-title":"Int J Inf Technol Decis Mak"},{"issue":"9\u201310","key":"4447_CR19","doi-asserted-by":"crossref","first-page":"2543","DOI":"10.1016\/j.apm.2013.11.003","volume":"38","author":"FY Meng","year":"2014","unstructured":"Meng FY, Chen XH, Zhang Q (2014) Some interval-valued intuitionistic uncertain linguistic Choquet operators and their application to multi-attribute group decision making. Appl Math Model 38(9\u201310):2543\u20132557","journal-title":"Appl Math Model"},{"issue":"1","key":"4447_CR20","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1002\/int.20444","volume":"26","author":"JM Merig\u00f3","year":"2011","unstructured":"Merig\u00f3 JM, Casanovas M (2011) The uncertain induced quasi-arithmetic OWA operator. Int J Intell Syst 26(1):1\u201324","journal-title":"Int J Intell Syst"},{"issue":"1","key":"4447_CR21","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1016\/j.ejor.2013.10.011","volume":"235","author":"JM Merig\u00f3","year":"2014","unstructured":"Merig\u00f3 JM, Casanovas M, Yang JB (2014) Group decision making with expertons and uncertain generalized probabilistic weighted aggregation operators. Eur J Oper Res 235(1):215\u2013224","journal-title":"Eur J Oper Res"},{"issue":"4","key":"4447_CR22","doi-asserted-by":"crossref","first-page":"1133","DOI":"10.1016\/j.ins.2007.09.023","volume":"178","author":"R Mesiar","year":"2008","unstructured":"Mesiar R, \u0160pirkov\u00e1 J, Vavr\u00edkov\u00e1 L (2008) Weighted aggregation operators based on minimization. Inf Sci 178(4):1133\u20131140","journal-title":"Inf Sci"},{"key":"4447_CR23","volume-title":"Interval analysis","author":"R Moore","year":"1966","unstructured":"Moore R (1966) Interval analysis. Prentice Hall, Englewood Cliffs"},{"issue":"5","key":"4447_CR24","doi-asserted-by":"crossref","first-page":"2544","DOI":"10.1016\/j.apm.2010.11.025","volume":"35","author":"JH Park","year":"2011","unstructured":"Park JH, Park Y, Kwun YC, Tan X (2011) Extension of TOPSIS method for decision making problems under interval-valued intuitionistic fuzzy environment. Appl Math Model 35(5):2544\u20132556","journal-title":"Appl Math Model"},{"key":"4447_CR25","first-page":"1","volume":"2014","author":"JJ Peng","year":"2014","unstructured":"Peng JJ, Wang JQ, Wang J, Chen XH (2014) Multicriteria decision making approach with hesitant interval-valued intuitionistic fuzzy sets. Sci World J 2014:1\u201322","journal-title":"Sci World J"},{"issue":"7","key":"4447_CR26","doi-asserted-by":"crossref","first-page":"2557","DOI":"10.1007\/s00500-015-1657-x","volume":"20","author":"R Sahin","year":"2016","unstructured":"Sahin R (2016) Fuzzy multicriteria decision making method based on the improved accuracy function for interval-valued intuitionistic fuzzy sets. Soft Comput 20(7):2557\u20132563","journal-title":"Soft Comput"},{"issue":"6","key":"4447_CR27","doi-asserted-by":"crossref","first-page":"631","DOI":"10.1002\/int.21861","volume":"32","author":"MX Song","year":"2017","unstructured":"Song MX, Jiang W, Xie CH, Zhou DY (2017) A new interval numbers power average operator in multiple attribute decision making. Int J Intell Syst 32(6):631\u2013644","journal-title":"Int J Intell Syst"},{"issue":"4","key":"4447_CR28","doi-asserted-by":"crossref","first-page":"3023","DOI":"10.1016\/j.eswa.2010.08.092","volume":"38","author":"CQ Tan","year":"2011","unstructured":"Tan CQ (2011) A multi-criteria interval-valued intuitionistic fuzzy group decision making with Choquet integral-based TOPSIS. Expert Syst Appl 38(4):3023\u20133033","journal-title":"Expert Syst Appl"},{"issue":"4","key":"4447_CR29","first-page":"703","volume":"23","author":"SF Wang","year":"2017","unstructured":"Wang SF (2017) Interval-valued intuitionistic fuzzy Choquet integral operators based on Archimedean t-norm and their calculations. J Comput Anal Appl 23(4):703\u2013712","journal-title":"J Comput Anal Appl"},{"issue":"6","key":"4447_CR30","doi-asserted-by":"crossref","first-page":"1093","DOI":"10.1007\/s13042-015-0433-7","volume":"7","author":"GW Wei","year":"2016","unstructured":"Wei GW (2016) Interval valued hesitant fuzzy uncertain linguistic aggregation operators in multiple attribute decision making. Int J Mach Learn Cybern 7(6):1093\u20131114","journal-title":"Int J Mach Learn Cybern"},{"key":"4447_CR31","first-page":"1","volume":"2015","author":"CP Wei","year":"2015","unstructured":"Wei CP, Zhang YZ (2015) Entropy measures for interval-valued intuitionistic fuzzy sets and their application in group decision-making. Math Probl Eng 2015:1\u201313","journal-title":"Math Probl Eng"},{"key":"4447_CR32","first-page":"45","volume":"46","author":"G Wei","year":"2013","unstructured":"Wei G, Zhao X, Lin R (2013) Some hesitant interval-valued fuzzy aggregation operators and their applications in multiple attribute decision making. Knowl Based Syst 46:45\u201353","journal-title":"Knowl Based Syst"},{"key":"4447_CR33","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1016\/j.knosys.2016.09.023","volume":"113","author":"YN Wu","year":"2016","unstructured":"Wu YN, Xu H, Xu CB, Chen KF (2016) Uncertain multi-attributes decision making method based on interval number with probability distribution weighted operators and stochastic dominance degree. Knowl Based Syst 113:199\u2013209","journal-title":"Knowl Based Syst"},{"issue":"6","key":"4447_CR34","doi-asserted-by":"crossref","first-page":"569","DOI":"10.1002\/int.10038","volume":"17","author":"ZS Xu","year":"2002","unstructured":"Xu ZS, Da QL (2002) The uncertain OWA operator. Int J Intell Syst 17(6):569\u2013575","journal-title":"Int J Intell Syst"},{"issue":"3","key":"4447_CR35","doi-asserted-by":"crossref","first-page":"1914","DOI":"10.1016\/j.ejor.2005.02.064","volume":"174","author":"DL Xu","year":"2006","unstructured":"Xu DL, Yang JB, Wang YM (2006) The evidential reasoning approach for multi-attribute decision analysis under interval uncertainties. Eur J Oper Res 174(3):1914\u20131943","journal-title":"Eur J Oper Res"},{"issue":"2","key":"4447_CR36","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1007\/s11518-015-5274-0","volume":"24","author":"XH Xu","year":"2015","unstructured":"Xu XH, Cai CG, Chen XH (2015) A multi-attribute large group emergency decision making method based on group preference consistency of generalized interval-valued trapezoidal fuzzy numbers. J Syst Sci Syst Eng 24(2):211\u2013228","journal-title":"J Syst Sci Syst Eng"},{"issue":"6","key":"4447_CR37","doi-asserted-by":"crossref","first-page":"724","DOI":"10.1109\/3468.983429","volume":"31","author":"RR Yager","year":"2001","unstructured":"Yager RR (2001) The power average operator. IEEE Trans Syst Man Cybern Part A Syst Hum 31(6):724\u2013731","journal-title":"IEEE Trans Syst Man Cybern Part A Syst Hum"},{"issue":"3","key":"4447_CR38","doi-asserted-by":"crossref","first-page":"837","DOI":"10.1007\/s13042-015-0382-1","volume":"8","author":"J Ye","year":"2017","unstructured":"Ye J (2017) Multiple attribute group decision making based on interval neutrosophic uncertain linguistic variables. Int J Mach Learn Cybern 8(3):837\u2013848","journal-title":"Int J Mach Learn Cybern"},{"issue":"4","key":"4447_CR39","doi-asserted-by":"crossref","first-page":"551","DOI":"10.1016\/j.inffus.2013.01.003","volume":"14","author":"ZL Yue","year":"2013","unstructured":"Yue ZL (2013) Group decision making with multi-attribute interval data. Inf Fusion 14(4):551\u2013561","journal-title":"Inf Fusion"},{"issue":"9","key":"4447_CR40","doi-asserted-by":"crossref","first-page":"2395","DOI":"10.1007\/s00500-015-1953-5","volume":"21","author":"ZL Yue","year":"2017","unstructured":"Yue ZL, Jia YY (2017) A direct projection-based group decision-making methodology with crisp values and interval data. Soft Comput 21(9):2395\u20132405","journal-title":"Soft Comput"},{"issue":"6","key":"4447_CR41","doi-asserted-by":"crossref","first-page":"4269","DOI":"10.1016\/j.apm.2012.09.033","volume":"37","author":"HM Zhang","year":"2013","unstructured":"Zhang HM (2013a) Some interval-valued 2-tuple linguistic aggregation operators and application in multiattribute group decision making. Appl Math Model 37(6):4269\u20134282","journal-title":"Appl Math Model"},{"key":"4447_CR42","first-page":"1","volume":"2013","author":"Z Zhang","year":"2013","unstructured":"Zhang Z (2013b) Interval-valued intuitionistic hesitant fuzzy aggregation operators and their application in group decision making. J Appl Math 2013:1\u201333","journal-title":"J Appl Math"}],"container-title":["Soft Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00500-019-04447-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00500-019-04447-9\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00500-019-04447-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,11,8]],"date-time":"2020-11-08T00:35:24Z","timestamp":1604795724000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00500-019-04447-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,11,9]]},"references-count":42,"journal-issue":{"issue":"12","published-print":{"date-parts":[[2020,6]]}},"alternative-id":["4447"],"URL":"https:\/\/doi.org\/10.1007\/s00500-019-04447-9","relation":{},"ISSN":["1432-7643","1433-7479"],"issn-type":[{"type":"print","value":"1432-7643"},{"type":"electronic","value":"1433-7479"}],"subject":[],"published":{"date-parts":[[2019,11,9]]},"assertion":[{"value":"9 November 2019","order":1,"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 declare that they have no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}},{"value":"This article does not contain any studies with human participants or animals performed by any of the authors.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethical approval"}}]}}