{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,6]],"date-time":"2026-03-06T05:59:32Z","timestamp":1772776772874,"version":"3.50.1"},"reference-count":45,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2016,2,11]],"date-time":"2016-02-11T00:00:00Z","timestamp":1455148800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China (CN)","doi-asserted-by":"publisher","award":["71471172, 71271124"],"award-info":[{"award-number":["71471172, 71271124"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Int. J. Mach. Learn. & Cyber."],"published-print":{"date-parts":[[2018,2]]},"DOI":"10.1007\/s13042-016-0508-0","type":"journal-article","created":{"date-parts":[[2016,2,11]],"date-time":"2016-02-11T17:10:15Z","timestamp":1455210615000},"page":"347-358","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":65,"title":["The neutrosophic number generalized weighted power averaging operator and its application in multiple attribute group decision making"],"prefix":"10.1007","volume":"9","author":[{"given":"Peide","family":"Liu","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xi","family":"Liu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2016,2,11]]},"reference":[{"key":"508_CR1","doi-asserted-by":"crossref","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 8:338\u2013356","journal-title":"Inf Control"},{"key":"508_CR2","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1016\/S0165-0114(86)80034-3","volume":"20","author":"KT Atanassov","year":"1986","unstructured":"Atanassov KT (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20:87\u201396","journal-title":"Fuzzy Sets Syst"},{"key":"508_CR3","volume-title":"A unifying field in logics. Neutrosophy: neutrosophic probability, setand logic","author":"F Smarandache","year":"1999","unstructured":"Smarandache F (1999) A unifying field in logics. Neutrosophy: neutrosophic probability, setand logic. American Research Press, Rehoboth"},{"key":"508_CR4","doi-asserted-by":"publisher","DOI":"10.1007\/s00521-015-1882-3","author":"HY Zhang","year":"2015","unstructured":"Zhang HY, Wang J, Chen XH (2015) An outranking approach for multi-criteria decision-making problems with interval-valued neutrosophic sets. Neural Comput Appl. doi:\n                        10.1007\/s00521-015-1882-3","journal-title":"Neural Comput Appl"},{"issue":"6","key":"508_CR5","doi-asserted-by":"crossref","first-page":"1027","DOI":"10.1080\/18756891.2015.1099917","volume":"8","author":"HY Zhang","year":"2015","unstructured":"Zhang HY, Ji P, Wang J, Chen XH (2015) An improved weighted correlation coefficient based on integrated weight for interval neutrosophic sets and its application in multi-criteria decision-making problems. Int J Comput Intell Syst 8(6):1027\u20131043","journal-title":"Int J Comput Intell Syst"},{"key":"508_CR6","doi-asserted-by":"publisher","DOI":"10.1080\/00207721.2015.1102359","author":"ZP Tian","year":"2015","unstructured":"Tian ZP, Zhang HY, Wang J, Wang JQ, Chen XH (2015) Multi-criteria decision-making method based on a cross-entropy with interval neutrosophic sets. Int J Syst Sci. doi:\n                        10.1080\/00207721.2015.1102359","journal-title":"Int J Syst Sci"},{"key":"508_CR7","doi-asserted-by":"publisher","DOI":"10.2298\/FIL1508576F","author":"ZP Tian","year":"2015","unstructured":"Tian ZP, Wang J, Zhang H, Chen X, Wang JQ (2015) Simplified neutrosophic linguistic normalized weighted Bonferroni mean operator and its application to multi-criteria decision-making problems. FILOMAT. doi:\n                        10.2298\/FIL1508576F","journal-title":"FILOMAT"},{"key":"508_CR8","doi-asserted-by":"publisher","DOI":"10.1080\/00207721.2014.994050","author":"JJ Peng","year":"2015","unstructured":"Peng JJ, Wang JQ, Wang J, Zhang HY, Chen XH (2015) Simplified neutrosophic sets and their applications in multi-criteria group decision-making problems. Int J Syst Sci. doi:\n                        10.1080\/00207721.2014.994050","journal-title":"Int J Syst Sci"},{"key":"508_CR9","doi-asserted-by":"crossref","first-page":"336","DOI":"10.1016\/j.asoc.2014.08.070","volume":"25","author":"J Peng","year":"2014","unstructured":"Peng J, Wang J, Zhang H, Chen X (2014) An outranking approach for multi-criteria decision-making problems with simplified neutrosophic sets. Appl Soft Comput 25:336\u2013346","journal-title":"Appl Soft Comput"},{"issue":"2","key":"508_CR10","first-page":"242","volume":"16","author":"PD Liu","year":"2014","unstructured":"Liu PD, Chu YC, Li YW (2014) Some generalized neutrosophic number Hamacher aggregation operators and their application to group decision making. Int J Fuzzy Syst 16(2):242\u2013255","journal-title":"Int J Fuzzy Syst"},{"issue":"7\u20138","key":"508_CR11","first-page":"2001","volume":"25","author":"PD Liu","year":"2014","unstructured":"Liu PD, Wang YM (2014) Multiple attribute decision making method based on single valued neutrosophic normalized weighted bonferroni mean. Neural Comput Appl 25(7\u20138):2001\u20132010","journal-title":"Neural Comput Appl"},{"issue":"2","key":"508_CR12","doi-asserted-by":"crossref","first-page":"457","DOI":"10.1007\/s00521-014-1736-4","volume":"26","author":"PD Liu","year":"2015","unstructured":"Liu PD, Shi LL (2015) The generalized hybrid weighted average operator based on interval neutrosophic hesitant set and its application to multiple attribute decision making. Neural Comput Appl 26(2):457\u2013471","journal-title":"Neural Comput Appl"},{"key":"508_CR13","doi-asserted-by":"publisher","DOI":"10.1007\/s11424-015-4010-7","author":"PD Li","year":"2015","unstructured":"Li PD, Wang YM (2015) Interval neutrosophic prioritized OWA operator and its application to multiple attribute decision making. J Syst Sci Complex. doi:\n                        10.1007\/s11424-015-4010-7","journal-title":"J Syst Sci Complex"},{"key":"508_CR14","doi-asserted-by":"publisher","DOI":"10.1007\/s00521-015-2048-z","author":"PD Liu","year":"2015","unstructured":"Liu PD, Li HG (2015) Multiple attribute decision making method based on some normal neutrosophic Bonferroni mean operators. Neural Comput Appl. doi:\n                        10.1007\/s00521-015-2048-z","journal-title":"Neural Comput Appl"},{"key":"508_CR15","volume-title":"Neutrosophy: neutrosophic probability, set, and logic","author":"F Smarandache","year":"1998","unstructured":"Smarandache F (1998) Neutrosophy: neutrosophic probability, set, and logic. American Research Press, Rehoboth"},{"key":"508_CR16","doi-asserted-by":"publisher","DOI":"10.1515\/jisys-2014-0149","author":"J Ye","year":"2015","unstructured":"Ye J (2015) Multiple attribute group decision making method under neutrosophic number environment. J Intell Syst. doi:\n                        10.1515\/jisys-2014-0149","journal-title":"J Intell Syst"},{"key":"508_CR17","volume-title":"Uncertain multiple attribute decision making: methods and applications","author":"ZS Xu","year":"2004","unstructured":"Xu ZS (2004) Uncertain multiple attribute decision making: methods and applications. Tsinghua University Press, Beijing"},{"key":"508_CR18","doi-asserted-by":"crossref","first-page":"310","DOI":"10.1016\/j.inffus.2006.10.008","volume":"9","author":"ZS Xu","year":"2008","unstructured":"Xu ZS (2008) Dependent uncertain ordered weighted aggregation operators. Inf Fusion 9:310\u2013316","journal-title":"Inf Fusion"},{"key":"508_CR19","doi-asserted-by":"crossref","first-page":"66","DOI":"10.1016\/j.cie.2010.09.017","volume":"60","author":"JM Merig\u00f3","year":"2011","unstructured":"Merig\u00f3 JM, Casanovas M (2011) Decision-making with distance measures and induced aggregation operators. Comput Ind Eng 60:66\u201376","journal-title":"Comput Ind Eng"},{"key":"508_CR20","doi-asserted-by":"crossref","first-page":"106","DOI":"10.1016\/j.cie.2010.10.005","volume":"60","author":"JM Merig\u00f3","year":"2011","unstructured":"Merig\u00f3 JM, Casanovas M (2011) Induced and uncertain heavy OWA operators. Comput Ind Eng 60:106\u2013116","journal-title":"Comput Ind Eng"},{"key":"508_CR21","doi-asserted-by":"crossref","first-page":"646","DOI":"10.1109\/3468.618263","volume":"27","author":"F Herrera","year":"1997","unstructured":"Herrera F, Herrera-Viedma E (1997) Aggregation operators for linguistic weighted information. IEEE Trans Syst Man Cybern Part B Cybern 27:646\u2013655","journal-title":"IEEE Trans Syst Man Cybern Part B Cybern"},{"key":"508_CR22","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1016\/j.jcss.2012.07.001","volume":"79","author":"PD Liu","year":"2013","unstructured":"Liu PD (2013) Some generalized dependent aggregation operators with intuitionistic linguistic numbers and their application to group decision making. J Comput Syst Sci 79:131\u2013143","journal-title":"J Comput Syst Sci"},{"issue":"3","key":"508_CR23","doi-asserted-by":"crossref","first-page":"287","DOI":"10.1142\/S0218488510006544","volume":"18","author":"JM Merig\u00f3","year":"2010","unstructured":"Merig\u00f3 JM, Casanovas M, Mart\u00ednez L (2010) Linguistic aggregation operators for linguistic decision making based on the Dempster\u2013Shafer theory of evidence. Int J Uncertain Fuzz Knowl Based Syst 18(3):287\u2013304","journal-title":"Int J Uncertain Fuzz Knowl Based Syst"},{"key":"508_CR24","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1016\/j.knosys.2010.04.010","volume":"24","author":"ZS Xu","year":"2011","unstructured":"Xu ZS, Xia MM (2011) Induced generalized intuitionistic fuzzy operators. Knowl Based Syst 24:197\u2013209","journal-title":"Knowl Based Syst"},{"issue":"4","key":"508_CR25","doi-asserted-by":"crossref","first-page":"126","DOI":"10.1016\/S1874-8651(08)60026-5","volume":"27","author":"ZS Xu","year":"2007","unstructured":"Xu ZS, Chen J (2007) Approach to group decision making based on interval-valued intuitionistic judgment matrices. Syst Eng Theory Pract 27(4):126\u2013133","journal-title":"Syst Eng Theory Pract"},{"key":"508_CR26","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1002\/int.20386","volume":"25","author":"H Zhao","year":"2010","unstructured":"Zhao H, Xu ZS, Ni MF, Liu SS (2010) Generalized aggregation operators for intuitionistic fuzzy sets. Int J Intell Syst 25:1\u201330","journal-title":"Int J Intell Syst"},{"issue":"6","key":"508_CR27","doi-asserted-by":"crossref","first-page":"724","DOI":"10.1109\/3468.983429","volume":"31","author":"R Yager","year":"2001","unstructured":"Yager R (2001) The power average operator. IEEE Trans Syst Man Cybern 31(6):724\u2013731","journal-title":"IEEE Trans Syst Man Cybern"},{"key":"508_CR28","doi-asserted-by":"crossref","first-page":"989","DOI":"10.1016\/j.cie.2011.12.025","volume":"62","author":"L Zhou","year":"2012","unstructured":"Zhou L, Chen H, Liu J (2012) Generalized power aggregation operators and their applications in group decision making. Comput Ind Eng 62:989\u2013999","journal-title":"Comput Ind Eng"},{"key":"508_CR29","doi-asserted-by":"crossref","first-page":"3988","DOI":"10.1016\/j.asoc.2011.02.027","volume":"11","author":"YJ Xu","year":"2011","unstructured":"Xu YJ, Wang HM (2011) Approaches based on 2-tuple linguistic power aggregation operators for multiple attribute group decision making under linguistic environment. Appl Soft Comput 11:3988\u20133997","journal-title":"Appl Soft Comput"},{"key":"508_CR30","doi-asserted-by":"crossref","first-page":"216","DOI":"10.1016\/j.knosys.2011.08.004","volume":"26","author":"LG Zhou","year":"2012","unstructured":"Zhou LG, Chen HY (2012) A generalization of the power aggregation operators for linguistic environment and its application in group decision making. Knowl Based Syst 26:216\u2013224","journal-title":"Knowl Based Syst"},{"issue":"4","key":"508_CR31","doi-asserted-by":"crossref","first-page":"345","DOI":"10.1080\/18756891.2015.1001957","volume":"8","author":"JJ Peng","year":"2015","unstructured":"Peng JJ, Wang JQ, Wu X-H, Wang J, Chen XH (2015) Multi-valued neutrosophic sets and power aggregation operators with their applications in multi-criteria group decision-making problems. Int J Comput Intell Syst 8(4):345\u2013363","journal-title":"Int J Comput Intell Syst"},{"issue":"1","key":"508_CR32","first-page":"69","volume":"57","author":"PD Liu","year":"2014","unstructured":"Liu PD, Yu XC (2014) 2-dimension uncertain linguistic power generalized weighted aggregation operator and its application for multiple attribute group decision making. Knowl Based Syst 57(1):69\u201380","journal-title":"Knowl Based Syst"},{"key":"508_CR33","doi-asserted-by":"crossref","first-page":"90","DOI":"10.1016\/j.asoc.2013.12.010","volume":"17","author":"PD Liu","year":"2014","unstructured":"Liu PD, Wang YM (2014) Multiple attribute group decision making methods based on intuitionistic linguistic power generalized aggregation operators. Appl Soft Comput 17:90\u2013104","journal-title":"Appl Soft Comput"},{"issue":"2","key":"508_CR34","doi-asserted-by":"crossref","first-page":"291","DOI":"10.1080\/18756891.2013.862357","volume":"7","author":"PD Liu","year":"2014","unstructured":"Liu PD, Liu Y (2014) An approach to multiple attribute group decision making based on intuitionistic trapezoidal fuzzy power generalized aggregation operator. Int J Comput Intell Syst 7(2):291\u2013304","journal-title":"Int J Comput Intell Syst"},{"issue":"4","key":"508_CR35","first-page":"534","volume":"5","author":"PD Liu","year":"2015","unstructured":"Liu PD, Shi LL (2015) Intuitionistic uncertain linguistic powered einstein aggregation operators and their application to multi-attribute group decision making. J Appl Anal Comput 5(4):534\u2013561","journal-title":"J Appl Anal Comput"},{"key":"508_CR36","doi-asserted-by":"crossref","first-page":"2235","DOI":"10.3233\/IFS-151699","volume":"29","author":"X Zhang","year":"2015","unstructured":"Zhang X, Liu PD, Wang YM (2015) Multiple attribute group decision making methods based on intuitionistic fuzzy frank power aggregation operators. J Intell Fuzzy Syst 29:2235\u20132246","journal-title":"J Intell Fuzzy Syst"},{"key":"508_CR37","doi-asserted-by":"publisher","DOI":"10.1007\/s00500-015-1668-7","author":"Y Li","year":"2015","unstructured":"Li Y, Liu PD, Wang YM (2015) Multiple attribute group decision making methods based on trapezoidal fuzzy two-dimension linguistic power generalized aggregation operators. Soft Comput. doi:\n                        10.1007\/s00500-015-1668-7","journal-title":"Soft Comput"},{"key":"508_CR38","doi-asserted-by":"publisher","DOI":"10.1007\/s13042-015-0385-y","author":"PD Liu","year":"2015","unstructured":"Liu PD, Teng F (2015) Multiple attribute decision making method based on normal neutrosophic generalized weighted power averaging operator. Int J Mach Learn Cybernet. doi:\n                        10.1007\/s13042-015-0385-y","journal-title":"Int J Mach Learn Cybernet"},{"key":"508_CR39","doi-asserted-by":"publisher","DOI":"10.3233\/IFS-151782","author":"PD Liu","year":"2015","unstructured":"Liu PD, Tang GL (2015) Some power generalized aggregation operators based on the interval neutrosophic numbers and their application to decision making. J Intell Fuzzy Syst. doi:\n                        10.3233\/IFS-151782","journal-title":"J Intell Fuzzy Syst"},{"key":"508_CR40","first-page":"1","volume":"9","author":"F Smarandache","year":"2015","unstructured":"Smarandache F (2015) Refined Literal Indeterminacy and the Multiplication Law of Sub-Indeterminacies. Neutrosophic Sets Syst 9:1\u20135","journal-title":"Neutrosophic Sets Syst"},{"key":"508_CR41","first-page":"143","volume":"4","author":"F Smarandache","year":"2013","unstructured":"Smarandache F (2013) n-Valued refined neutrosophic logic and its applications in physics. Prog Phys 4:143\u2013146","journal-title":"Prog Phys"},{"issue":"3","key":"508_CR42","doi-asserted-by":"crossref","first-page":"556","DOI":"10.1109\/TFUZZ.2008.924342","volume":"17","author":"XZ Wang","year":"2009","unstructured":"Wang XZ, Dong CR (2009) Improving generalization of fuzzy if\u2013then rules by maximizing fuzzy entropy. IEEE Trans Fuzzy Syst 17(3):556\u2013567","journal-title":"IEEE Trans Fuzzy Syst"},{"issue":"5","key":"508_CR43","doi-asserted-by":"crossref","first-page":"1638","DOI":"10.1109\/TFUZZ.2014.2371479","volume":"23","author":"XZ Wang","year":"2015","unstructured":"Wang XZ, Xing HJ, Li Y, Hua Q, Dong CR, Pedrycz W (2015) A study on relationship between generalization abilities and fuzziness of base classifiers in ensemble learning. IEEE Trans Fuzzy Syst 23(5):1638\u20131654","journal-title":"IEEE Trans Fuzzy Syst"},{"issue":"3","key":"508_CR44","doi-asserted-by":"crossref","first-page":"1185","DOI":"10.3233\/IFS-151729","volume":"29","author":"XZ Wang","year":"2015","unstructured":"Wang XZ, Ashfaq RAR, Fu AM (2015) Fuzziness based sample categorization for classifier performance improvement. J Intell Fuzzy Syst 29(3):1185\u20131196","journal-title":"J Intell Fuzzy Syst"},{"issue":"5","key":"508_CR45","doi-asserted-by":"crossref","first-page":"2329","DOI":"10.3233\/IFS-141516","volume":"28","author":"XZ Wang","year":"2015","unstructured":"Wang XZ (2015) Uncertainty in learning from big data-editorial. J Intell Fuzzy Syst 28(5):2329\u20132330","journal-title":"J Intell Fuzzy Syst"}],"container-title":["International Journal of Machine Learning and Cybernetics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s13042-016-0508-0\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s13042-016-0508-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s13042-016-0508-0","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s13042-016-0508-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,2]],"date-time":"2019-06-02T10:31:22Z","timestamp":1559471482000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s13042-016-0508-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,2,11]]},"references-count":45,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2018,2]]}},"alternative-id":["508"],"URL":"https:\/\/doi.org\/10.1007\/s13042-016-0508-0","relation":{},"ISSN":["1868-8071","1868-808X"],"issn-type":[{"value":"1868-8071","type":"print"},{"value":"1868-808X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,2,11]]}}}