{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,16]],"date-time":"2026-06-16T15:10:17Z","timestamp":1781622617938,"version":"3.54.5"},"reference-count":29,"publisher":"Springer Science and Business Media LLC","issue":"6","license":[{"start":{"date-parts":[[2015,10,3]],"date-time":"2015-10-03T00:00:00Z","timestamp":1443830400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Int. J. Mach. Learn. &amp; Cyber."],"published-print":{"date-parts":[[2016,12]]},"DOI":"10.1007\/s13042-015-0432-8","type":"journal-article","created":{"date-parts":[[2015,10,3]],"date-time":"2015-10-03T06:33:52Z","timestamp":1443854032000},"page":"1075-1092","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":71,"title":["Generalized intuitionistic fuzzy multiplicative interactive geometric operators and their application to multiple criteria decision making"],"prefix":"10.1007","volume":"7","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9099-8422","authenticated-orcid":false,"given":"Harish","family":"Garg","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2015,10,3]]},"reference":[{"key":"432_CR1","doi-asserted-by":"crossref","first-page":"343","DOI":"10.1016\/0165-0114(89)90205-4","volume":"31","author":"K Atanassov","year":"1989","unstructured":"Atanassov K, Gargov G (1989) Interval-valued intuitionistic fuzzy sets. Fuzzy Sets Syst 31:343\u2013349","journal-title":"Fuzzy Sets Syst"},{"key":"432_CR2","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1016\/S0165-0114(86)80034-3","volume":"20","author":"KT Attanassov","year":"1986","unstructured":"Attanassov KT (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20:87\u201396","journal-title":"Fuzzy Sets Syst"},{"issue":"1","key":"432_CR3","first-page":"19","volume":"8","author":"G Deshrijver","year":"2002","unstructured":"Deshrijver G, Kerre E (2002) A generalizationof opertors on intuitionistic fuzzy sets using triangular fuzzy t-norms and t-conorms. IEEE Trans Fuzzy Syst 8(1):19\u201327","journal-title":"IEEE Trans Fuzzy Syst"},{"key":"432_CR4","first-page":"13","volume":"6","author":"H Garg","year":"2015","unstructured":"Garg H, Agarwal N, Tripathi A (2015) Entropy based multi-criteria decision making method under fuzzy environment and unknown attribute weights. Glob J Technol Optim 6:13\u201320","journal-title":"Glob J Technol Optim"},{"key":"432_CR5","doi-asserted-by":"crossref","first-page":"2484","DOI":"10.1016\/j.eswa.2013.09.048","volume":"41","author":"Y He","year":"2014","unstructured":"He Y, Chen H, Zhou L, Han B, Zhao Q, Liu J (2014) Generalized intuitionistic fuzzy geometric interaction operators and their application to decision making. Expert Syst Appl 41:2484\u20132495","journal-title":"Expert Syst Appl"},{"issue":"6","key":"432_CR6","doi-asserted-by":"crossref","first-page":"1669","DOI":"10.1109\/TFUZZ.2014.2302495","volume":"22","author":"H Liao","year":"2014","unstructured":"Liao H, Xu Z (2014) Priorities of intuitionistic fuzzy preference relation based on multiplicative consistency. IEEE Trans Fuzzy Syst 22(6):1669\u20131681","journal-title":"IEEE Trans Fuzzy Syst"},{"issue":"1","key":"432_CR7","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1109\/TFUZZ.2013.2248736","volume":"22","author":"P Liu","year":"2014","unstructured":"Liu P (2014) Some hamacher aggregation operators based on the interval-valued intuitionistic fuzzy numbers and their application to group decision making. IEEE Trans Fuzzy Syst 22(1):83\u201397","journal-title":"IEEE Trans Fuzzy Syst"},{"key":"432_CR8","doi-asserted-by":"crossref","first-page":"570","DOI":"10.1016\/j.amc.2013.12.133","volume":"230","author":"P Liu","year":"2014","unstructured":"Liu P, Liu Z, Zhang X (2014) Some intuitionistic uncertain linguistic heronian mean operators and their application to group decision making. Appl Math Comput 230:570\u2013586","journal-title":"Appl Math Comput"},{"issue":"6","key":"432_CR9","doi-asserted-by":"crossref","first-page":"1395","DOI":"10.1007\/s00521-014-1814-7","volume":"26","author":"P Liu","year":"2015","unstructured":"Liu P, Yanchang C, Yanwei L (2015) The multi-attribute group decision-making method based on the interval grey uncertain linguistic variable generalized hybrid averaging operator. Neural Comput Appl 26(6):1395\u20131405","journal-title":"Neural Comput Appl"},{"issue":"1","key":"432_CR10","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1016\/j.knosys.2013.12.009","volume":"57","author":"P Liu","year":"2014","unstructured":"Liu P, Yu X (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":"432_CR11","doi-asserted-by":"crossref","first-page":"155","DOI":"10.1016\/0165-0114(78)90001-5","volume":"1","author":"SA Orlovsky","year":"1978","unstructured":"Orlovsky SA (1978) Decision-making with a fuzzy preference relation. Fuzzy Sets Syst 1:155\u2013167","journal-title":"Fuzzy Sets Syst"},{"issue":"7","key":"432_CR12","doi-asserted-by":"crossref","first-page":"841","DOI":"10.1287\/mnsc.32.7.841","volume":"32","author":"TL Saaty","year":"1986","unstructured":"Saaty TL (1986) Axiomatic foundation of the analytic hierarchy process. Manag Sci 32(7):841\u2013845","journal-title":"Manag Sci"},{"issue":"5","key":"432_CR13","doi-asserted-by":"crossref","first-page":"923","DOI":"10.1109\/TFUZZ.2012.2189405","volume":"20","author":"W Wang","year":"2012","unstructured":"Wang W, Liu X (2012) Intuitionistic fuzzy information aggregation using einstein operations. IEEE Trans Fuzzy Syst 20(5):923\u2013938","journal-title":"IEEE Trans Fuzzy Syst"},{"key":"432_CR14","doi-asserted-by":"crossref","first-page":"1049","DOI":"10.1002\/int.20498","volume":"26","author":"WZ Wang","year":"2011","unstructured":"Wang WZ, Liu XW (2011) Intuitionistic fuzzy geometric aggregation operators based on Einstein operations. Int J Intel Syst 26:1049\u20131075","journal-title":"Int J Intel Syst"},{"issue":"3","key":"432_CR15","doi-asserted-by":"crossref","first-page":"556","DOI":"10.1109\/TFUZZ.2008.924342","volume":"17","author":"X Wang","year":"2009","unstructured":"Wang X, Dong C (2009) Improving generalization of fuzzy if-then rules by maximizing fuzzy entropy. IEEE Trans Fuzzy Syst 17(3):556\u2013567","journal-title":"IEEE Trans Fuzzy Syst"},{"issue":"8","key":"432_CR16","doi-asserted-by":"crossref","first-page":"1491","DOI":"10.1109\/TKDE.2011.67","volume":"24","author":"X Wang","year":"2012","unstructured":"Wang X, Dong L, Yan J (2012) Maximum ambiguity based sample selection in fuzzy decision tree induction. IEEE Trans Knowl Data Eng 24(8):1491\u20131505","journal-title":"IEEE Trans Knowl Data Eng"},{"key":"432_CR17","doi-asserted-by":"publisher","unstructured":"Wang X, Xing H, Li Y, Hua Q, Dong CR, Pedrycz W (2014) A study on relationship between generalization abilities and fuzziness of base classifiers in ensemble learning. IEEE Trans Fuzzy Syst. doi: 10.1109\/TFUZZ.2014.2371479","DOI":"10.1109\/TFUZZ.2014.2371479"},{"key":"432_CR18","doi-asserted-by":"crossref","first-page":"423","DOI":"10.1016\/j.asoc.2009.08.009","volume":"10","author":"G Wei","year":"2010","unstructured":"Wei G (2010) Some induced geometric aggregation operators with intuitionistic fuzzy information and their application to group decision making. Appl Soft Comput 10:423\u2013431","journal-title":"Appl Soft Comput"},{"issue":"2","key":"432_CR19","doi-asserted-by":"crossref","first-page":"2026","DOI":"10.1016\/j.eswa.2011.08.031","volume":"39","author":"GW Wei","year":"2012","unstructured":"Wei GW, Zhao XF (2012) Some induced correlated aggregating operators with intuitionistic fuzzy information and their application to multiple attribute group decision making. Expert Syst Appl 39(2):2026\u20132034","journal-title":"Expert Syst Appl"},{"issue":"1","key":"432_CR20","doi-asserted-by":"crossref","first-page":"113","DOI":"10.1109\/TFUZZ.2012.2202907","volume":"21","author":"M Xia","year":"2013","unstructured":"Xia M, Xu Z, Liao H (2013) Preference relations based on intuitionistic multiplicative information. IEEE Trans Fuzzy Syst 21(1):113\u2013132","journal-title":"IEEE Trans Fuzzy Syst"},{"issue":"2","key":"432_CR21","first-page":"197","volume":"24","author":"ZA Xu","year":"2003","unstructured":"Xu ZA, Xia M (2003) Induced generalized intuitionistic fuzzy operators. Knowl Based Syst 24(2):197\u2013209","journal-title":"Knowl Based Syst"},{"key":"432_CR22","doi-asserted-by":"crossref","first-page":"1179","DOI":"10.1109\/TFUZZ.2006.890678","volume":"15","author":"ZS Xu","year":"2007","unstructured":"Xu ZS (2007) Intuitionistic fuzzy aggregation operators. IEEE Trans Fuzzy Syst 15:1179\u20131187","journal-title":"IEEE Trans Fuzzy Syst"},{"key":"432_CR23","doi-asserted-by":"crossref","first-page":"2363","DOI":"10.1016\/j.ins.2006.12.019","volume":"177","author":"ZS Xu","year":"2007","unstructured":"Xu ZS (2007) Intuitionistic preference relations and their application in group decision making. Inf Sci 177:2363\u20132379","journal-title":"Inf Sci"},{"key":"432_CR24","doi-asserted-by":"crossref","first-page":"179","DOI":"10.1080\/03081070600913726","volume":"36","author":"ZS Xu","year":"2007","unstructured":"Xu ZS (2007) A survey of preference relations. Int J Gen Syst 36:179\u2013203","journal-title":"Int J Gen Syst"},{"key":"432_CR25","doi-asserted-by":"crossref","first-page":"417","DOI":"10.1080\/03081070600574353","volume":"35","author":"ZS Xu","year":"2006","unstructured":"Xu ZS, Yager RR (2006) Some geometric aggregation operators based on intuitionistic fuzzy sets. Int J Gen Syst 35:417\u2013433","journal-title":"Int J Gen Syst"},{"issue":"3","key":"432_CR26","doi-asserted-by":"crossref","first-page":"2559","DOI":"10.1007\/s11069-014-1450-7","volume":"75","author":"D Yu","year":"2015","unstructured":"Yu D (2015) Intuitionistic fuzzy theory based typhoon disaster evaluation in Zhejiang province, China: a comparative perspective. Nat Hazards 75(3):2559\u20132576","journal-title":"Nat Hazards"},{"issue":"4","key":"432_CR27","first-page":"412","volume":"15","author":"D Yu","year":"2013","unstructured":"Yu D, Merigo JM, Zhou L (2013) Interval-valued multiplicative intuitionistic fuzzy preference relations. Int J Fuzzy Syst 15(4):412\u2013422","journal-title":"Int J Fuzzy Syst"},{"key":"432_CR28","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\u2013353","journal-title":"Inf Control"},{"issue":"1","key":"432_CR29","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1002\/int.20386","volume":"25","author":"H Zhao","year":"2010","unstructured":"Zhao H, Xu Z, Ni M, Liu S (2010) Generalized aggregation operators for intuitionistic fuzzy sets. Int J Intel Syst 25(1):1\u201330","journal-title":"Int J Intel Syst"}],"container-title":["International Journal of Machine Learning and Cybernetics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s13042-015-0432-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s13042-015-0432-8\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s13042-015-0432-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s13042-015-0432-8","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,5,22]],"date-time":"2022-05-22T16:45:36Z","timestamp":1653237936000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s13042-015-0432-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,10,3]]},"references-count":29,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2016,12]]}},"alternative-id":["432"],"URL":"https:\/\/doi.org\/10.1007\/s13042-015-0432-8","relation":{},"ISSN":["1868-8071","1868-808X"],"issn-type":[{"value":"1868-8071","type":"print"},{"value":"1868-808X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,10,3]]}}}