{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,20]],"date-time":"2026-05-20T17:02:05Z","timestamp":1779296525574,"version":"3.51.4"},"reference-count":44,"publisher":"Springer Science and Business Media LLC","issue":"6","license":[{"start":{"date-parts":[[2020,6,22]],"date-time":"2020-06-22T00:00:00Z","timestamp":1592784000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2020,6,22]],"date-time":"2020-06-22T00:00:00Z","timestamp":1592784000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61866011"],"award-info":[{"award-number":["61866011"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Neural Comput &amp; Applic"],"published-print":{"date-parts":[[2021,3]]},"DOI":"10.1007\/s00521-020-05100-5","type":"journal-article","created":{"date-parts":[[2020,6,22]],"date-time":"2020-06-22T05:02:46Z","timestamp":1592802166000},"page":"2085-2105","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":78,"title":["Group decision-making framework using complex Pythagorean fuzzy information"],"prefix":"10.1007","volume":"33","author":[{"given":"Xueling","family":"Ma","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Muhammad","family":"Akram","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kiran","family":"Zahid","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4533-9281","authenticated-orcid":false,"given":"Jos\u00e9 Carlos R.","family":"Alcantud","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2020,6,22]]},"reference":[{"key":"5100_CR1","doi-asserted-by":"publisher","DOI":"10.22111\/ijfs.2020.5363","author":"M Akram","year":"2020","unstructured":"Akram M, Garg H, Zahid K (2020) Extensions of ELECTRE-I and TOPSIS methods for group decision-making under complex Pythagorean fuzzy environment. Iran J Fuzzy Syst. https:\/\/doi.org\/10.22111\/ijfs.2020.5363","journal-title":"Iran J Fuzzy Syst"},{"issue":"3","key":"5100_CR2","first-page":"73","volume":"24","author":"M Akram","year":"2019","unstructured":"Akram M, Naz S (2019) A novel decision-making approach under complex Pythagorean fuzzy environment. Math Comput Appl 24(3):73","journal-title":"Math Comput Appl"},{"key":"5100_CR3","doi-asserted-by":"publisher","first-page":"106","DOI":"10.1016\/j.ins.2019.12.008","volume":"514","author":"JCR Alcantud","year":"2020","unstructured":"Alcantud JCR, Khameneh AZ, Kilicman A (2020) Aggregation of infinite chains of intuitionistic fuzzy sets and their application to choices with temporal intuitionistic fuzzy information. Inf Sci 514:106\u2013117","journal-title":"Inf Sci"},{"key":"5100_CR4","doi-asserted-by":"crossref","unstructured":"Alkouri AM, Salleh AR (2012) Complex intuitionistic fuzzy sets. In: AIP conference proceedings. vol 1482(1)","DOI":"10.1063\/1.4757515"},{"key":"5100_CR5","doi-asserted-by":"publisher","first-page":"46324","DOI":"10.1109\/ACCESS.2020.2979141","volume":"8","author":"G Aquino","year":"2020","unstructured":"Aquino G, Rubio JDJ, Pacheco J, Gutierrez GJ, Ochoa G, Balcazar R, Cruz DR, Garcia E, Novoa JF, Zacarias A (2020) Novel nonlinear hypothesis for the delta parallel robot modeling IEEE. Access 8:46324\u201346334","journal-title":"Access"},{"issue":"1","key":"5100_CR6","doi-asserted-by":"publisher","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(1):87\u201396","journal-title":"Fuzzy Sets Syst"},{"issue":"3","key":"5100_CR7","doi-asserted-by":"publisher","first-page":"2550","DOI":"10.1016\/j.eswa.2010.08.043","volume":"38","author":"AA Bazzazi","year":"2011","unstructured":"Bazzazi AA, Osanloo M, Karimi B (2011) Deriving preference order of open pit mines equipment through MADM methods: application of modified VIKOR method. Expert Syst Appl 38(3):2550\u20132556","journal-title":"Expert Syst Appl"},{"issue":"5","key":"5100_CR8","doi-asserted-by":"publisher","first-page":"567","DOI":"10.1002\/int.20214","volume":"22","author":"G Buyukozkan","year":"2007","unstructured":"Buyukozkan G, Ruan D, Feyzioglu O (2007) Evaluating e-learning web site quality in a fuzzy environment. Int J Intell Syst 22(5):567\u2013586","journal-title":"Int J Intell Syst"},{"issue":"7","key":"5100_CR9","doi-asserted-by":"publisher","first-page":"722","DOI":"10.1002\/int.21873","volume":"32","author":"B Ceballos","year":"2017","unstructured":"Ceballos B, Lamata MT, Pelta DA (2017) Fuzzy multicriteria decision-making methods: a comparative analysis. Int J Intell Syst 32(7):722\u2013738","journal-title":"Int J Intell Syst"},{"key":"5100_CR10","doi-asserted-by":"publisher","first-page":"196","DOI":"10.1016\/j.ins.2014.02.118","volume":"271","author":"TH Chang","year":"2014","unstructured":"Chang TH (2014) Fuzzy VIKOR method: a case study of the hospital service evaluation in Taiwan. Inf Sci 271:196\u2013212","journal-title":"Inf Sci"},{"key":"5100_CR11","doi-asserted-by":"publisher","DOI":"10.1007\/s00521-019-04554-6","author":"PA Ejegwa","year":"2019","unstructured":"Ejegwa PA (2019) Modified Zhang and Xu\u2019s distance measure for Pythagorean fuzzy sets and its application to pattern recognition problems. Neural Comput Appl. https:\/\/doi.org\/10.1007\/s00521-019-04554-6","journal-title":"Neural Comput Appl"},{"issue":"3","key":"5100_CR12","doi-asserted-by":"publisher","first-page":"474","DOI":"10.1109\/TFUZZ.2018.2860967","volume":"27","author":"F Feng","year":"2019","unstructured":"Feng F, Fujita H, Ali MI, Yager RR, Liu X (2019) Another view on generalized intuitionistic fuzzy soft sets and related multiattribute decision making methods. IEEE Trans Fuzzy Syst 27(3):474\u2013488","journal-title":"IEEE Trans Fuzzy Syst"},{"key":"5100_CR13","doi-asserted-by":"publisher","first-page":"135","DOI":"10.1016\/j.jsr.2019.03.005","volume":"69","author":"M Gul","year":"2019","unstructured":"Gul M, Ak MF, Guneri AF (2019) Pythagorean fuzzy VIKOR-based approach for safety risk assessment in mine industry. J Saf Res 69:135\u2013153","journal-title":"J Saf Res"},{"key":"5100_CR14","doi-asserted-by":"publisher","first-page":"184","DOI":"10.1016\/j.ins.2016.07.058","volume":"370","author":"P Gupta","year":"2016","unstructured":"Gupta P, Mehlawat MK, Grover N (2016) Intuitionistic fuzzy multi-attribute group decision-making with an application to plant location selection based on a new extended VIKOR method. Inf Sci 370:184\u2013203","journal-title":"Inf Sci"},{"key":"5100_CR15","doi-asserted-by":"publisher","DOI":"10.1007\/s00521-019-04014-1","author":"Y Han","year":"2019","unstructured":"Han Y, Deng Y, Cao Z et al (2019) An interval-valued Pythagorean prioritized operator-based game theoretical framework with its applications in multicriteria group decision making. Neural Comput Appl. https:\/\/doi.org\/10.1007\/s00521-019-04014-1","journal-title":"Neural Comput Appl"},{"issue":"2","key":"5100_CR16","doi-asserted-by":"publisher","first-page":"1236","DOI":"10.1111\/itor.12569","volume":"27","author":"J Hu","year":"2020","unstructured":"Hu J, Zhang X, Yang Y, Liu Y, Chen X (2020) New doctors ranking system based on VIKOR method. Int Trans Oper Res 27(2):1236\u20131261","journal-title":"Int Trans Oper Res"},{"issue":"5","key":"5100_CR17","doi-asserted-by":"publisher","first-page":"3112","DOI":"10.1016\/j.apm.2012.07.035","volume":"37","author":"Y Ju","year":"2013","unstructured":"Ju Y, Wang A (2013) Extension of VIKOR method for multi-criteria group decision making problem with linguistic information. Appl Math Model 37(5):3112\u20133125","journal-title":"Appl Math Model"},{"key":"5100_CR18","doi-asserted-by":"publisher","DOI":"10.1007\/s00521-020-04802-0","author":"R Krishankumar","year":"2020","unstructured":"Krishankumar R, Ravichandran KS, Shyam V, Sneha SV, Kar S, Garg H (2020) Multi-attribute group decision-making using double hierarchy hesitant fuzzy linguistic preference information. Neural Comput Appl. https:\/\/doi.org\/10.1007\/s00521-020-04802-0","journal-title":"Neural Comput Appl"},{"key":"5100_CR19","doi-asserted-by":"publisher","first-page":"579","DOI":"10.1016\/j.asoc.2014.11.036","volume":"28","author":"HC Liu","year":"2015","unstructured":"Liu HC, You JX, You XY, Shan MM (2015) A novel approach for failure mode and effects analysis using combination weighting and fuzzy VIKOR method. Appl Soft Comput 28:579\u2013588","journal-title":"Appl Soft Comput"},{"issue":"11","key":"5100_CR20","doi-asserted-by":"publisher","first-page":"1381","DOI":"10.3390\/sym11111381","volume":"11","author":"A Luqman","year":"2019","unstructured":"Luqman A, Akram M, Al-Kenani AN, Alcantud JCR (2019) A study on hypergraph representations of complex fuzzy information. Symmetry 11(11):1381","journal-title":"Symmetry"},{"key":"5100_CR21","doi-asserted-by":"publisher","first-page":"31968","DOI":"10.1109\/ACCESS.2018.2846483","volume":"6","author":"JA Meda-Campana","year":"2018","unstructured":"Meda-Campana JA (2018) On the estimation and control of nonlinear systems with parametric uncertainties and noisy outputs. IEEE Access 6:31968\u201331973","journal-title":"IEEE Access"},{"issue":"1","key":"5100_CR22","first-page":"67","volume":"12","author":"S Mishra","year":"2012","unstructured":"Mishra S, Samantra C, Datta S, Mahapatra SS (2012) Multi-attribute group decision-making (MAGDM) for supplier selection using fuzzy linguistic modelling integrated with VIKOR method. Int J Serv Oper Manag 12(1):67\u201389","journal-title":"Int J Serv Oper Manag"},{"issue":"1","key":"5100_CR23","first-page":"45","volume":"13","author":"SM Mousavi","year":"2016","unstructured":"Mousavi SM, Vahdani B, Behzadi SS (2016) Designing a model of intuitionistic fuzzy VIKOR in multi-attribute group decision-making problems. Iran J Fuzzy Syst 13(1):45\u201365","journal-title":"Iran J Fuzzy Syst"},{"issue":"1","key":"5100_CR24","first-page":"5","volume":"2","author":"S Opricovic","year":"1998","unstructured":"Opricovic S (1998) Multicriteria optimization of civil engineering systems. Fac Civ Eng Belg 2(1):5\u201321","journal-title":"Fac Civ Eng Belg"},{"issue":"10","key":"5100_CR25","doi-asserted-by":"publisher","first-page":"12983","DOI":"10.1016\/j.eswa.2011.04.097","volume":"38","author":"S Opricovic","year":"2011","unstructured":"Opricovic S (2011) Fuzzy VIKOR with an application to water resources planning. Expert Syst Appl 38(10):12983\u201312990","journal-title":"Expert Syst Appl"},{"issue":"2","key":"5100_CR26","doi-asserted-by":"publisher","first-page":"514","DOI":"10.1016\/j.ejor.2006.01.020","volume":"178","author":"S Opricovic","year":"2007","unstructured":"Opricovic S, Tzeng GH (2007) Extended VIKOR method in comparison with outranking methods. Eur J Oper Res 178(2):514\u2013529","journal-title":"Eur J Oper Res"},{"issue":"2","key":"5100_CR27","doi-asserted-by":"publisher","first-page":"171","DOI":"10.1109\/91.995119","volume":"10","author":"D Ramot","year":"2002","unstructured":"Ramot D, Milo R, Friedman M, Kandel A (2002) Complex fuzzy sets. IEEE Trans Fuzzy Syst 10(2):171\u2013186","journal-title":"IEEE Trans Fuzzy Syst"},{"issue":"6","key":"5100_CR28","doi-asserted-by":"publisher","first-page":"1296","DOI":"10.1109\/TFUZZ.2009.2029569","volume":"17","author":"JDJ Rubio","year":"2009","unstructured":"Rubio JDJ (2009) SOFMLS: online self-organizing fuzzy modified least-squares network. IEEE Trans Fuzzy Syst 17(6):1296\u20131309","journal-title":"IEEE Trans Fuzzy Syst"},{"issue":"5","key":"5100_CR29","doi-asserted-by":"publisher","first-page":"6731","DOI":"10.3233\/JIFS-190216","volume":"37","author":"JDJ Rubio","year":"2019","unstructured":"Rubio JDJ, Garc\u00eda E, Ochoa G, El\u00edas I, Cruz DR, Balcazar R, L\u00f3pez J, Novoa JF (2019) Unscented Kalman filter for learning of a solar dryer and a greenhouse. J Intell Fuzzy Syst 37(5):6731\u20136741","journal-title":"J Intell Fuzzy Syst"},{"issue":"2","key":"5100_CR30","doi-asserted-by":"publisher","first-page":"498","DOI":"10.1016\/j.renene.2010.07.031","volume":"36","author":"JR San Crist\u00f3bal","year":"2011","unstructured":"San Crist\u00f3bal JR (2011) Multi-criteria decision-making in the selection of a renewable energy project in Spain: the VIKOR method. Renew Energy 36(2):498\u2013502","journal-title":"Renew Energy"},{"issue":"1","key":"5100_CR31","doi-asserted-by":"publisher","first-page":"24","DOI":"10.1016\/j.eswa.2009.04.063","volume":"37","author":"A Sanayei","year":"2010","unstructured":"Sanayei A, Mousavi SF, Yazdankhah A (2010) Group decision making process for supplier selection with VIKOR under fuzzy environment. Expert Syst Appl 37(1):24\u201330","journal-title":"Expert Syst Appl"},{"issue":"10","key":"5100_CR32","doi-asserted-by":"publisher","first-page":"12160","DOI":"10.1016\/j.eswa.2011.03.027","volume":"38","author":"A Shemshadi","year":"2011","unstructured":"Shemshadi A, Shirazi H, Toreihi M, Tarokh MJ (2011) A fuzzy VIKOR method for supplier selection based on entropy measure for objective weighting. Expert Syst Appl 38(10):12160\u201312167","journal-title":"Expert Syst Appl"},{"issue":"10","key":"5100_CR33","doi-asserted-by":"publisher","first-page":"1313","DOI":"10.3390\/sym11101313","volume":"11","author":"MA Shumaiza","year":"2019","unstructured":"Shumaiza MA, Al-Kenani AN, Alcantud JCR (2019) Group decision-making based on the VIKOR method with trapezoidal bipolar fuzzy information. Symmetry 11(10):1313","journal-title":"Symmetry"},{"issue":"18","key":"5100_CR34","doi-asserted-by":"publisher","first-page":"8112","DOI":"10.1016\/j.eswa.2014.07.021","volume":"41","author":"S Tadi\u0107","year":"2014","unstructured":"Tadi\u0107 S, Ze\u010devi\u0107 S, Krsti\u0107 M (2014) A novel hybrid MCDM model based on fuzzy DEMATEL, fuzzy ANP and fuzzy VIKOR for city logistics concept selection. Expert Syst Appl 41(18):8112\u20138128","journal-title":"Expert Syst Appl"},{"issue":"4","key":"5100_CR35","doi-asserted-by":"publisher","first-page":"285","DOI":"10.1002\/int.20454","volume":"26","author":"DE Tamir","year":"2011","unstructured":"Tamir DE, Jin L, Kandel A (2011) A new interpretation of complex membership grade. Int J Intell Syst 26(4):285\u2013312","journal-title":"Int J Intell Syst"},{"key":"5100_CR36","doi-asserted-by":"publisher","first-page":"15","DOI":"10.1007\/s40747-019-0103-6","volume":"6","author":"K Ullah","year":"2020","unstructured":"Ullah K, Mahmood T, Ali Z, Jan N (2020) On some distance measures of complex Pythagorean fuzzy sets and their applications in pattern recognition. Complex Intell Syst 6:15\u201327","journal-title":"Complex Intell Syst"},{"key":"5100_CR37","doi-asserted-by":"publisher","first-page":"65","DOI":"10.1016\/j.knosys.2013.06.019","volume":"52","author":"SP Wan","year":"2013","unstructured":"Wan SP, Wang QY, Dong JY (2013) The extended VIKOR method for multi-attribute group decision making with triangular intuitionistic fuzzy numbers. Knowl Based Syst 52:65\u201377","journal-title":"Knowl Based Syst"},{"key":"5100_CR38","unstructured":"Wang TC, chang TH (2005) Fuzzy VIKOR as a resolution for multicriteria group decision-making. In: The 11th international conference on industrial engineering and engineering management. pp 352\u2013356"},{"key":"5100_CR39","doi-asserted-by":"crossref","unstructured":"Wang TC, Liang JL, Ho CY (2006) Multi-criteria decision analysis by using fuzzy VIKOR. In: 2006 International conference on service systems and service management. vol 2, pp 901\u2013906","DOI":"10.1109\/ICSSSM.2006.320751"},{"issue":"4","key":"5100_CR40","doi-asserted-by":"publisher","first-page":"958","DOI":"10.1109\/TFUZZ.2013.2278989","volume":"22","author":"RR Yager","year":"2013","unstructured":"Yager RR (2013) Pythagorean membership grades in multicriteria decision making. IEEE Trans Fuzzy Syst 22(4):958\u2013965","journal-title":"IEEE Trans Fuzzy Syst"},{"issue":"5","key":"5100_CR41","doi-asserted-by":"publisher","first-page":"754","DOI":"10.1002\/int.22075","volume":"34","author":"W Yang","year":"2019","unstructured":"Yang W, Pang Y (2019) Hesitant interval-valued Pythagorean fuzzy VIKOR method. Int J Intell Syst 34(5):754\u2013789","journal-title":"Int J Intell Syst"},{"key":"5100_CR42","first-page":"293","volume":"23","author":"Y Yildirim","year":"2014","unstructured":"Yildirim Y, \u00d6nder E (2014) VIKOR method for ranking logistic villages in Turkey. J Manag Econ Res 23:293\u2013314","journal-title":"J Manag Econ Res"},{"issue":"3","key":"5100_CR43","doi-asserted-by":"publisher","first-page":"3702","DOI":"10.1016\/j.eswa.2011.09.065","volume":"39","author":"GN Y\u00fccenur","year":"2012","unstructured":"Y\u00fccenur GN, Demirel N\u00c7 (2012) Group decision making process for insurance company selection problem with extended VIKOR method under fuzzy environment. Expert Syst Appl 39(3):3702\u20133707","journal-title":"Expert Syst Appl"},{"issue":"3","key":"5100_CR44","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"}],"container-title":["Neural Computing and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00521-020-05100-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00521-020-05100-5\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00521-020-05100-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,6,21]],"date-time":"2021-06-21T23:58:43Z","timestamp":1624319923000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00521-020-05100-5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,6,22]]},"references-count":44,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2021,3]]}},"alternative-id":["5100"],"URL":"https:\/\/doi.org\/10.1007\/s00521-020-05100-5","relation":{},"ISSN":["0941-0643","1433-3058"],"issn-type":[{"value":"0941-0643","type":"print"},{"value":"1433-3058","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,6,22]]},"assertion":[{"value":"6 March 2020","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"4 June 2020","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"22 June 2020","order":3,"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":"The authors declare no conflicts of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflicts of interest"}},{"value":"Not applicable","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Availability of data and material"}},{"value":"Not applicable","order":4,"name":"Ethics","group":{"name":"EthicsHeading","label":"Code availability"}}]}}