{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,16]],"date-time":"2026-03-16T18:56:18Z","timestamp":1773687378543,"version":"3.50.1"},"reference-count":43,"publisher":"Springer Science and Business Media LLC","issue":"3","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"}],"funder":[{"DOI":"10.13039\/501100001809","name":"the National Natural Science Foundation of China","doi-asserted-by":"crossref","award":["No. 61273209"],"award-info":[{"award-number":["No. 61273209"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"name":"the Central University Basic Scientific Research Business Expenses Project","award":["No. skgt201501"],"award-info":[{"award-number":["No. skgt201501"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Int. J. Mach. Learn. &amp; Cyber."],"published-print":{"date-parts":[[2016,6]]},"DOI":"10.1007\/s13042-015-0434-6","type":"journal-article","created":{"date-parts":[[2015,10,3]],"date-time":"2015-10-03T03:54:16Z","timestamp":1443844456000},"page":"501-518","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":32,"title":["Exponential operations of interval-valued intuitionistic fuzzy numbers"],"prefix":"10.1007","volume":"7","author":[{"given":"Xunjie","family":"Gou","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zeshui","family":"Xu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Huchang","family":"Liao","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2015,10,3]]},"reference":[{"key":"434_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":"434_CR2","doi-asserted-by":"crossref","first-page":"859","DOI":"10.1080\/00207720500382365","volume":"36","author":"KT Atanassov","year":"2005","unstructured":"Atanassov KT, Pasi G, Yager RR (2005) Intuitionistic fuzzy interpretations of multi-criteria multi-person and multi-measurement tool decision making. Int J Syst Sci 36:859\u2013868","journal-title":"Int J Syst Sci"},{"key":"434_CR3","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1016\/j.patrec.2006.07.004","volume":"28","author":"KI Vlachos","year":"2007","unstructured":"Vlachos KI, Sergiadis GD (2007) Intuitionistic fuzzy information-applications to pattern recognition. Pattern Recogn Lett 28:197\u2013206","journal-title":"Pattern Recogn Lett"},{"key":"434_CR4","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1016\/j.artmed.2009.03.002","volume":"47","author":"V Khatibi","year":"2009","unstructured":"Khatibi V, Montazer GA (2009) Intuitionistic fuzzy set vs. fuzzy set application in medical pattern recognition. Artif Intell Med 47:43\u201352","journal-title":"Artif Intell Med"},{"key":"434_CR5","author":"XZ Wang","year":"2014","unstructured":"Wang XZ, Xing HJ, Li Y (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","journal-title":"IEEE Trans Fuzzy Syst"},{"issue":"8","key":"434_CR6","doi-asserted-by":"crossref","first-page":"1491","DOI":"10.1109\/TKDE.2011.67","volume":"24","author":"XZ Wang","year":"2012","unstructured":"Wang XZ, Dong LC, Yan JH (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"},{"issue":"3","key":"434_CR7","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"},{"key":"434_CR8","doi-asserted-by":"crossref","first-page":"388","DOI":"10.1007\/978-3-540-24844-6_56","volume":"3070","author":"E Szmidt","year":"2004","unstructured":"Szmidt E, Kacprzyk J (2004) A similarity measure for intuitionistic fuzzy sets and its application in supporting medical diagnostic reasoning. Lect Notes Comput Sci 3070:388\u2013393","journal-title":"Lect Notes Comput Sci"},{"key":"434_CR9","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 set. Fuzzy Sets Syst 20:87\u201396","journal-title":"Fuzzy Sets Syst"},{"issue":"3","key":"434_CR10","doi-asserted-by":"crossref","first-page":"1168","DOI":"10.1016\/j.asoc.2011.11.003","volume":"12","author":"YJ Xu","year":"2012","unstructured":"Xu YJ, Wang HM (2012) The induced generalized aggregation operators for intuitionistic fuzzy sets and their application in group decision making. Appl Soft Comput 12(3):1168\u20131179","journal-title":"Appl Soft Comput"},{"issue":"7","key":"434_CR11","doi-asserted-by":"crossref","first-page":"2029","DOI":"10.1007\/s11269-013-0271-x","volume":"27","author":"H Hashemi","year":"2013","unstructured":"Hashemi H, Bazargan J, Mousavi SM (2013) A compromise ratio method with an application to water resources management: an intuitionistic fuzzy set. Water Resour Manage 27(7):2029\u20132051","journal-title":"Water Resour Manage"},{"issue":"5","key":"434_CR12","doi-asserted-by":"crossref","first-page":"411","DOI":"10.1002\/int.21583","volume":"28","author":"DJ Yu","year":"2013","unstructured":"Yu DJ (2013) Prioritized information fusion method for triangular intuitionistic fuzzy set and its application to teaching quality evaluation. Int J Intell Syst 28(5):411\u2013435","journal-title":"Int J Intell Syst"},{"key":"434_CR13","doi-asserted-by":"crossref","first-page":"2354","DOI":"10.1016\/j.cnsns.2013.11.003","volume":"19","author":"M Mazandarani","year":"2014","unstructured":"Mazandarani M, Najariyan M (2014) Type-2 fuzzy fractional derivatives. Commun Nonlinear Sci Numer Simul 19:2354\u20132372","journal-title":"Commun Nonlinear Sci Numer Simul"},{"key":"434_CR14","doi-asserted-by":"crossref","first-page":"710","DOI":"10.1016\/j.cnsns.2013.07.002","volume":"19","author":"M Mazandarani","year":"2014","unstructured":"Mazandarani M, Najariyan M (2014) Differentiability of type-2 fuzzy number-valued functions. Commun Nonlinear Sci Numer Simul 19:710\u2013725","journal-title":"Commun Nonlinear Sci Numer Simul"},{"key":"434_CR15","doi-asserted-by":"crossref","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 31:343\u2013349","journal-title":"Fuzzy Sets Syst"},{"key":"434_CR16","doi-asserted-by":"crossref","unstructured":"Xu ZS, Chen J (2007) On geometric aggregation over interval-valued intuitionistic fuzzy information. In: The 4th international conference on fuzzy systems and knowledge discovery (FSKD\u201807), Haikou, China, vol 2, pp 466\u2013471","DOI":"10.1109\/FSKD.2007.427"},{"key":"434_CR17","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1007\/s10726-014-9386-6","volume":"24","author":"ZS Xu","year":"2015","unstructured":"Xu ZS, Cai XQ (2015) Group decision making with incomplete interval-valued intuitionistic preference relations. Group Decis Negot 24:193\u2013215","journal-title":"Group Decis Negot"},{"key":"434_CR18","doi-asserted-by":"crossref","first-page":"52","DOI":"10.1016\/j.cie.2014.10.017","volume":"79","author":"XW Qi","year":"2015","unstructured":"Qi XW, Liang CY, Zhang JL (2015) Generalized cross-entropy based group decision making with unknown expert and attribute weights under interval-valued intuitionistic fuzzy environment. Comput Ind Eng 79:52\u201364","journal-title":"Comput Ind Eng"},{"key":"434_CR19","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1016\/j.asoc.2014.09.015","volume":"26","author":"TY Chen","year":"2015","unstructured":"Chen TY (2015) The inclusion-based TOPSIS method with interval-valued intuitionistic fuzzy sets for multiple criteria group decision making. Appl Soft Comput 26:57\u201373","journal-title":"Appl Soft Comput"},{"key":"434_CR20","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. doi: 10.1155\/2015\/563745","journal-title":"Math Probl Eng"},{"key":"434_CR21","first-page":"357","volume":"18","author":"JH Park","year":"2015","unstructured":"Park JH, Lim KM, Lee BY (2015) Relationship between subsethood measure and entropy of interval-valued intuitionistic fuzzy sets. J Comput Anal Appl 18:357\u2013370","journal-title":"J Comput Anal Appl"},{"key":"434_CR22","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1016\/j.knosys.2014.06.023","volume":"70","author":"JP Xu","year":"2014","unstructured":"Xu JP, Shen F (2014) A new outranking choice method for group decision making under Atanassov\u2019s interval-valued intuitionistic fuzzy environment. Knowl-Based Syst 70:177\u2013188","journal-title":"Knowl-Based Syst"},{"key":"434_CR23","doi-asserted-by":"crossref","first-page":"1325","DOI":"10.1142\/S0219622014500722","volume":"13","author":"TY Chen","year":"2014","unstructured":"Chen TY (2014) The inclusion-based LINMAP method for multiple criteria decision analysis within an interval-valued Atanassov\u2019s intuitionistic fuzzy environment. Int J Inf Technol Dec Mak 13:1325\u20131360","journal-title":"Int J Inf Technol Dec Mak"},{"key":"434_CR24","doi-asserted-by":"crossref","first-page":"272","DOI":"10.1016\/j.asoc.2014.05.005","volume":"22","author":"J Wu","year":"2014","unstructured":"Wu J, Chiclana F (2014) A risk attitudinal ranking method for interval-valued intuitionistic fuzzynumbers based on novel attitudinal expected score and accuracy functions. Appl Soft Comput 22:272\u2013286","journal-title":"Appl Soft Comput"},{"key":"434_CR25","first-page":"268","volume":"2","author":"R Parvathi","year":"2012","unstructured":"Parvathi R, Malathi C (2012) Arithmetic operations on symmetric trapezoidal intuitionistic fuzzy numbers. Int J Soft Comput Eng 2:268\u2013273","journal-title":"Int J Soft Comput Eng"},{"key":"434_CR26","doi-asserted-by":"crossref","first-page":"4112","DOI":"10.1016\/j.apm.2012.09.017","volume":"37","author":"SP Wan","year":"2013","unstructured":"Wan SP (2013) Power average operators of trapezoidal intuitionistic fuzzy numbers and application to multi-attribute group decision making. Appl Math Model 37:4112\u20134126","journal-title":"Appl Math Model"},{"key":"434_CR27","doi-asserted-by":"crossref","first-page":"477","DOI":"10.1016\/S0165-0114(98)00191-2","volume":"114","author":"SK De","year":"2000","unstructured":"De SK, Biswas R, Roy AR (2000) Some operations on intuitionistic fuzzy sets. Fuzzy Sets Syst 114:477\u2013484","journal-title":"Fuzzy Sets Syst"},{"key":"434_CR28","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"},{"key":"434_CR29","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 operations. IEEE Trans Fuzzy Syst 15:1179\u20131187","journal-title":"IEEE Trans Fuzzy Syst"},{"key":"434_CR30","first-page":"145","volume":"2","author":"KT Atanassov","year":"2006","unstructured":"Atanassov KT, Ri\u011bcan B (2006) On two operations over intuitionistic fuzzy sets. J Appl Math Stat Informat 2:145\u2013148","journal-title":"J Appl Math Stat Informat"},{"key":"434_CR31","author":"XJ Gou","year":"2015","unstructured":"Gou XJ, Xu ZS, Lei Q (2015) New operational laws and aggregation method of intuitionistic fuzzy information. J Intell Fuzzy Syst. doi: 10.3233\/IFS-151739","journal-title":"J Intell Fuzzy Syst"},{"key":"434_CR32","doi-asserted-by":"crossref","unstructured":"Xu ZS, Cai XQ (2012) Intuitionistic fuzzy information aggregation: theory and applications. Science Press, Beijing; Springer, Berlin","DOI":"10.1007\/978-3-642-29584-3"},{"key":"434_CR33","doi-asserted-by":"crossref","first-page":"359","DOI":"10.1007\/s10700-010-9090-1","volume":"9","author":"ZS Xu","year":"2010","unstructured":"Xu ZS, Cai XQ (2010) Recent advances in intuitionistic fuzzy information aggregation. Fuzzy Optim Decis Making 9:359\u2013381","journal-title":"Fuzzy Optim Decis Making"},{"key":"434_CR34","doi-asserted-by":"crossref","first-page":"971","DOI":"10.1002\/int.21672","volume":"29","author":"HC Liao","year":"2014","unstructured":"Liao HC, Xu ZS (2014) Intuitionistic fuzzy hybrid weighted aggregation operators. Int J Intell Syst 29:971\u2013993","journal-title":"Int J Intell Syst"},{"key":"434_CR35","doi-asserted-by":"crossref","first-page":"251","DOI":"10.1016\/0165-0114(92)90236-W","volume":"52","author":"RN Xu","year":"1992","unstructured":"Xu RN, Zhai XY (1992) Extensions of the analytic hierarchy process in fuzzy environment. Fuzzy Sets Syst 52:251\u2013257","journal-title":"Fuzzy Sets Syst"},{"key":"434_CR36","first-page":"215","volume":"22","author":"ZS Xu","year":"2007","unstructured":"Xu ZS (2007) The aggregation method of interval-valued intuitionistic fuzzy information and appliation in decision making. Control Dec 22:215\u2013219","journal-title":"Control Dec"},{"key":"434_CR37","doi-asserted-by":"crossref","first-page":"3026","DOI":"10.1016\/j.ins.2009.05.001","volume":"179","author":"ZJ Wang","year":"2009","unstructured":"Wang ZJ, Li KW, Wang WZ (2009) An approach to multiattribute decision making with interval-valued intuitionistic fuzzy assessments and incomplete weights. Inf Sci 179:3026\u20133040","journal-title":"Inf Sci"},{"key":"434_CR38","doi-asserted-by":"crossref","first-page":"221","DOI":"10.1007\/s12665-013-2948-0","volume":"72","author":"I Masoumi","year":"2014","unstructured":"Masoumi I, Naraghi F, Rashidi-nejad F, Masoumi S (2014) Application of fuzzy multi-attribute decision making to select and to rank the post-mining land-use. Environ Earth Sci 72:221\u2013231","journal-title":"Environ Earth Sci"},{"key":"434_CR39","first-page":"3","volume":"19","author":"QL Da","year":"1999","unstructured":"Da QL, Liu XW (1999) Interval number linear programming and the satisfactory solution. Syst Eng Theory Pract 19:3\u20137","journal-title":"Syst Eng Theory Pract"},{"key":"434_CR40","first-page":"311","volume":"16","author":"ZS Xu","year":"2001","unstructured":"Xu ZS (2001) An algorithm of the ranking of fuzzy complementary judgment matrix. J Syst Eng 16:311\u2013314","journal-title":"J Syst Eng"},{"key":"434_CR41","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1007\/s10700-012-9118-9","volume":"11","author":"XM Zhang","year":"2012","unstructured":"Zhang XM, Xu ZS (2012) A new method for ranking intuitionistic fuzzy values and its application in multi-attribute decision making. Fuzzy Optim Dec Making 11:135\u2013146","journal-title":"Fuzzy Optim Dec Making"},{"key":"434_CR42","volume-title":"Selecting proper type of shield supports","author":"TM Barczak","year":"1990","unstructured":"Barczak TM (1990) Selecting proper type of shield supports. Information Circular, Bureau of Mines"},{"key":"434_CR43","unstructured":"Wiklund B, Kizil MS, Canbulat I (2011) Development of a cavity prediction model for longwall mining. In: Aziz N (ed) Proceedings of the 11th underground coal operators\u2019 conference, Wollongong, NSW, Australia, University of Wollongong, pp 48\u201359"}],"container-title":["International Journal of Machine Learning and Cybernetics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s13042-015-0434-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s13042-015-0434-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s13042-015-0434-6","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,2]],"date-time":"2019-06-02T10:31:20Z","timestamp":1559471480000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s13042-015-0434-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,10,3]]},"references-count":43,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2016,6]]}},"alternative-id":["434"],"URL":"https:\/\/doi.org\/10.1007\/s13042-015-0434-6","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]]}}}