{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T20:18:14Z","timestamp":1776802694443,"version":"3.51.2"},"reference-count":64,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2023,9,12]],"date-time":"2023-09-12T00:00:00Z","timestamp":1694476800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2023,9,12]],"date-time":"2023-09-12T00:00:00Z","timestamp":1694476800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100001809","name":"Natural Science Foundation of China","doi-asserted-by":"crossref","award":["62162055"],"award-info":[{"award-number":["62162055"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100004775","name":"Gansu Provincial Natural Science Foundation of China","doi-asserted-by":"crossref","award":["21JR7RA115"],"award-info":[{"award-number":["21JR7RA115"]}],"id":[{"id":"10.13039\/501100004775","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Complex Intell. Syst."],"published-print":{"date-parts":[[2024,2]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Hesitant Fermatean fuzzy sets (HFFS) can characterize the membership degree (MD) and non-membership degree (NMD) of hesitant fuzzy elements in a broader range, which offers superior fuzzy data processing capabilities for addressing complex uncertainty issues. In this research, first, we present the definition of the hesitant Fermatean fuzzy Bonferroni mean operator (HFFBM). Further, with the basic operations of HFFS in Einstein t-norms, the definition and derivation process of the hesitant Fermatean fuzzy Einstein Bonferroni mean operator (HFFEBM) are given. In addition, considering how weights affect decision-making outcomes, the hesitant Fermatean fuzzy weighted Bonferroni mean (HFFWBM) operator and the hesitant Fermatean fuzzy Einstein weighted Bonferroni mean operator (HFFEWBM) are developed. Then, the properties of the operators are discussed. Based on HFFWBM and HFFEWBM operator, a new multi-attribute decision-making (MADM) approach is provided. Finally, we apply the proposed decision-making approach to the case of a depression diagnostic evaluation for three depressed patients. The three patients' diagnosis results confirmed the proposed method's validity and rationality. Through a series of comparative experiments and analyses, the proposed MADM method is an efficient solution\u00a0for decision-making issues\u00a0in the hesitant Fermatean fuzzy environment.<\/jats:p>","DOI":"10.1007\/s40747-023-01203-3","type":"journal-article","created":{"date-parts":[[2023,9,12]],"date-time":"2023-09-12T07:02:12Z","timestamp":1694502132000},"page":"1425-1457","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["Hesitant Fermatean fuzzy Bonferroni mean operators for multi-attribute decision-making"],"prefix":"10.1007","volume":"10","author":[{"given":"Yibo","family":"Wang","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1569-460X","authenticated-orcid":false,"given":"Xiuqin","family":"Ma","sequence":"additional","affiliation":[]},{"given":"Hongwu","family":"Qin","sequence":"additional","affiliation":[]},{"given":"Huanling","family":"Sun","sequence":"additional","affiliation":[]},{"given":"Weiyi","family":"Wei","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2023,9,12]]},"reference":[{"key":"1203_CR1","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 8:338\u2013353. https:\/\/doi.org\/10.1016\/s0019-9958(65)90241-x","journal-title":"Inf Control"},{"key":"1203_CR2","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 20:87\u201396. https:\/\/doi.org\/10.1016\/s0165-0114(86)80034-3","journal-title":"Fuzzy Sets Syst"},{"key":"1203_CR3","doi-asserted-by":"publisher","first-page":"357","DOI":"10.1109\/tfuzz.2020.3039335","volume":"30","author":"X Ma","year":"2020","unstructured":"Ma X, Qin H, Abawajy JH (2020) Interval-valued intuitionistic fuzzy soft sets based decision-making and parameter reduction. IEEE Trans Fuzzy Syst 30:357\u2013369. https:\/\/doi.org\/10.1109\/tfuzz.2020.3039335","journal-title":"IEEE Trans Fuzzy Syst"},{"key":"1203_CR4","doi-asserted-by":"publisher","first-page":"35499","DOI":"10.1109\/access.2019.2905140","volume":"7","author":"X Ma","year":"2019","unstructured":"Ma X, Qin H (2019) Soft set based parameter value reduction for decision making application. IEEE Access 7:35499\u201335511. https:\/\/doi.org\/10.1109\/access.2019.2905140","journal-title":"IEEE Access"},{"key":"1203_CR5","doi-asserted-by":"publisher","first-page":"3718","DOI":"10.1007\/s10489-020-01708-1","volume":"50","author":"X Ma","year":"2020","unstructured":"Ma X, Qin H (2020) A new parameter reduction algorithm for interval-valued fuzzy soft sets based on Pearson\u2019s product moment coefficient. Appl Intell 50:3718\u20133730. https:\/\/doi.org\/10.1007\/s10489-020-01708-1","journal-title":"Appl Intell"},{"key":"1203_CR6","doi-asserted-by":"publisher","first-page":"3226","DOI":"10.1007\/s10489-020-01915-w","volume":"51","author":"X Ma","year":"2021","unstructured":"Ma X, Fei Q, Qin H et al (2021) A new efficient decision making algorithm based on interval-valued fuzzy soft set. Appl Intell 51:3226\u20133240. https:\/\/doi.org\/10.1007\/s10489-020-01915-w","journal-title":"Appl Intell"},{"key":"1203_CR7","doi-asserted-by":"publisher","first-page":"341","DOI":"10.1016\/j.eswa.2019.01.054","volume":"124","author":"F Alali","year":"2019","unstructured":"Alali F, Tolga AC (2019) Portfolio allocation with the TODIM method. Expert Syst Appl 124:341\u2013348. https:\/\/doi.org\/10.1016\/j.eswa.2019.01.054","journal-title":"Expert Syst Appl"},{"key":"1203_CR8","doi-asserted-by":"publisher","first-page":"103352","DOI":"10.1016\/j.engappai.2019.103352","volume":"87","author":"AC Tolga","year":"2020","unstructured":"Tolga AC, Parlak IB, Castillo O (2020) Finite-interval-valued Type-2 Gaussian fuzzy numbers applied to fuzzy TODIM in a healthcare problem. Eng Appl Artif Intell 87:103352. https:\/\/doi.org\/10.1016\/j.engappai.2019.103352","journal-title":"Eng Appl Artif Intell"},{"key":"1203_CR9","doi-asserted-by":"publisher","first-page":"1","DOI":"10.3233\/jifs-219170","volume":"42","author":"AC Tolga","year":"2021","unstructured":"Tolga AC, Basar M (2021) The assessment of a smart system in hydroponic vertical farming via fuzzy MCDM methods. J Intell Fuzzy Syst 42:1\u201312. https:\/\/doi.org\/10.3233\/jifs-219170","journal-title":"J Intell Fuzzy Syst"},{"key":"1203_CR10","doi-asserted-by":"publisher","first-page":"108773","DOI":"10.1016\/j.cie.2022.108773","volume":"174","author":"M Deveci","year":"2022","unstructured":"Deveci M, Gokasar I, Castillo O, Daim T (2022) Evaluation of Metaverse integration of freight fluidity measurement alternatives using fuzzy Dombi EDAS model. Comput Ind Eng 174:108773. https:\/\/doi.org\/10.1016\/j.cie.2022.108773","journal-title":"Comput Ind Eng"},{"key":"1203_CR11","doi-asserted-by":"publisher","first-page":"1378","DOI":"10.1109\/fuzzy.2009.5276884","volume":"2009","author":"V Torra","year":"2009","unstructured":"Torra V, Narukawa Y (2009) On hesitant fuzzy sets and decision. IEEE Int Conf Fuzzy Syst 2009:1378\u20131382. https:\/\/doi.org\/10.1109\/fuzzy.2009.5276884","journal-title":"IEEE Int Conf Fuzzy Syst"},{"key":"1203_CR12","doi-asserted-by":"publisher","first-page":"102","DOI":"10.1016\/j.ins.2014.02.009","volume":"277","author":"B Farhadinia","year":"2014","unstructured":"Farhadinia B (2014) A series of score functions for hesitant fuzzy sets. Inf Sci 277:102\u2013110. https:\/\/doi.org\/10.1016\/j.ins.2014.02.009","journal-title":"Inf Sci"},{"key":"1203_CR13","doi-asserted-by":"publisher","first-page":"2128","DOI":"10.1016\/j.ins.2011.01.028","volume":"181","author":"Z Xu","year":"2011","unstructured":"Xu Z, Xia M (2011) Distance and similarity measures for hesitant fuzzy sets. Inf Sci 181:2128\u20132138. https:\/\/doi.org\/10.1016\/j.ins.2011.01.028","journal-title":"Inf Sci"},{"key":"1203_CR14","doi-asserted-by":"publisher","first-page":"395","DOI":"10.1016\/j.ijar.2010.09.002","volume":"52","author":"M Xia","year":"2011","unstructured":"Xia M, Xu Z (2011) Hesitant fuzzy information aggregation in decision making. Int J Approx Reason 52:395\u2013407. https:\/\/doi.org\/10.1016\/j.ijar.2010.09.002","journal-title":"Int J Approx Reason"},{"key":"1203_CR15","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1155\/2012\/879629","volume":"2012","author":"B Zhu","year":"2012","unstructured":"Zhu B, Xu Z, Xia M (2012) Dual hesitant fuzzy sets. J Appl Math 2012:1\u201313. https:\/\/doi.org\/10.1155\/2012\/879629","journal-title":"J Appl Math"},{"key":"1203_CR16","doi-asserted-by":"publisher","first-page":"2547","DOI":"10.3233\/ifs-130926","volume":"26","author":"Y Chen","year":"2014","unstructured":"Chen Y, Peng X, Guan G, Jiang H (2014) Approaches to multiple attribute decision making based on the correlation coefficient with dual hesitant fuzzy information. J Intell Fuzzy Syst 26:2547\u20132556. https:\/\/doi.org\/10.3233\/ifs-130926","journal-title":"J Intell Fuzzy Syst"},{"key":"1203_CR17","doi-asserted-by":"publisher","first-page":"819","DOI":"10.1007\/s13042-015-0400-3","volume":"7","author":"D Yu","year":"2016","unstructured":"Yu D, Li D-F, Merig\u00f3 JM (2016) Dual hesitant fuzzy group decision making method and its application to supplier selection. Int J Mach Learn Cybern 7:819\u2013831. https:\/\/doi.org\/10.1007\/s13042-015-0400-3","journal-title":"Int J Mach Learn Cybern"},{"key":"1203_CR18","doi-asserted-by":"publisher","first-page":"111","DOI":"10.1007\/s40314-015-0219-2","volume":"36","author":"P Singh","year":"2017","unstructured":"Singh P (2017) Distance and similarity measures for multiple-attribute decision making with dual hesitant fuzzy sets. Comput Appl Math 36:111\u2013126. https:\/\/doi.org\/10.1007\/s40314-015-0219-2","journal-title":"Comput Appl Math"},{"key":"1203_CR19","doi-asserted-by":"publisher","first-page":"167","DOI":"10.1016\/j.asoc.2017.06.034","volume":"60","author":"D Liang","year":"2017","unstructured":"Liang D, Xu Z (2017) The new extension of TOPSIS method for multiple criteria decision making with hesitant Pythagorean fuzzy sets. Appl Soft Comput 60:167\u2013179. https:\/\/doi.org\/10.1016\/j.asoc.2017.06.034","journal-title":"Appl Soft Comput"},{"key":"1203_CR20","doi-asserted-by":"publisher","first-page":"365","DOI":"10.1515\/acsc-2017-0024","volume":"27","author":"G Wei","year":"2017","unstructured":"Wei G, Lu M (2017) Dual hesitant pythagorean fuzzy Hamacher aggregation operators in multiple attribute decision making. Arch Control Sci 27:365\u2013395. https:\/\/doi.org\/10.1515\/acsc-2017-0024","journal-title":"Arch Control Sci"},{"key":"1203_CR21","doi-asserted-by":"publisher","first-page":"958","DOI":"10.1109\/tfuzz.2013.2278989","volume":"22","author":"RR Yager","year":"2014","unstructured":"Yager RR (2014) Pythagorean membership grades in multicriteria decision making. IEEE Trans Fuzzy Syst 22:958\u2013965. https:\/\/doi.org\/10.1109\/tfuzz.2013.2278989","journal-title":"IEEE Trans Fuzzy Syst"},{"key":"1203_CR22","doi-asserted-by":"publisher","DOI":"10.1109\/ifsa-nafips.2013.6608375","author":"RR Yager","year":"2013","unstructured":"Yager RR (2013) Pythagorean fuzzy subsets. Jt IFSA World Congr NAFIPS Annu Meet (IFSA\/NAFIPS). https:\/\/doi.org\/10.1109\/ifsa-nafips.2013.6608375","journal-title":"Jt IFSA World Congr NAFIPS Annu Meet (IFSA\/NAFIPS)"},{"key":"1203_CR23","doi-asserted-by":"publisher","first-page":"954","DOI":"10.1016\/j.cie.2018.11.029","volume":"127","author":"Q Wu","year":"2019","unstructured":"Wu Q, Lin W, Zhou L et al (2019) Enhancing multiple attribute group decision making flexibility based on information fusion technique and hesitant Pythagorean fuzzy sets. Comput Ind Eng 127:954\u2013970. https:\/\/doi.org\/10.1016\/j.cie.2018.11.029","journal-title":"Comput Ind Eng"},{"key":"1203_CR24","doi-asserted-by":"publisher","first-page":"1145","DOI":"10.1016\/j.eswa.2022.116945","volume":"200","author":"M Akram","year":"2022","unstructured":"Akram M, Luqman A, Alcantud JCR (2022) An integrated ELECTRE-I approach for risk evaluation with hesitant Pythagorean fuzzy information. Expert Syst Appl 200:1145. https:\/\/doi.org\/10.1016\/j.eswa.2022.116945","journal-title":"Expert Syst Appl"},{"key":"1203_CR25","doi-asserted-by":"publisher","first-page":"125281","DOI":"10.1016\/j.jclepro.2020.125281","volume":"291","author":"S Geetha","year":"2021","unstructured":"Geetha S, Narayanamoorthy S, Kureethara JV et al (2021) The hesitant Pythagorean fuzzy ELECTRE III: an adaptable recycling method for plastic materials. J Clean Prod 291:125281. https:\/\/doi.org\/10.1016\/j.jclepro.2020.125281","journal-title":"J Clean Prod"},{"key":"1203_CR26","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-015-9540-7","volume-title":"Triangular norms","author":"EP Klement","year":"2000","unstructured":"Klement EP, Mesiar R, Pap E (2000) Triangular norms. Springer, Dordrecht. https:\/\/doi.org\/10.1007\/978-94-015-9540-7"},{"key":"1203_CR27","doi-asserted-by":"publisher","first-page":"17","DOI":"10.1016\/b978-044451814-9\/50002-1","volume-title":"Triangular norms: Basic notions and properties. Logical, algebraic analytic and probabilistic aspects of triangular norms","author":"EP Klement","year":"2005","unstructured":"Klement EP, Mesiar R, Pap E (2005) Triangular norms: Basic notions and properties. Logical, algebraic analytic and probabilistic aspects of triangular norms. Springer, pp 17\u201360. https:\/\/doi.org\/10.1016\/b978-044451814-9\/50002-1"},{"key":"1203_CR28","doi-asserted-by":"publisher","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 20:923\u2013938. https:\/\/doi.org\/10.1109\/tfuzz.2012.2189405","journal-title":"IEEE Trans Fuzzy Syst"},{"key":"1203_CR29","doi-asserted-by":"publisher","first-page":"5","DOI":"10.1016\/j.fss.2003.06.007","volume":"143","author":"EP Klement","year":"2004","unstructured":"Klement EP, Mesiar R, Pap E (2004) Triangular norms. Position paper I: basic analytical and algebraic properties. Fuzzy Sets Syst 143:5\u201326. https:\/\/doi.org\/10.1016\/j.fss.2003.06.007","journal-title":"Fuzzy Sets Syst"},{"key":"1203_CR30","doi-asserted-by":"publisher","first-page":"317","DOI":"10.1002\/wics.82","volume":"2","author":"H-J Zimmermann","year":"2010","unstructured":"Zimmermann H-J (2010) Fuzzy set theory. WIREs Comput Stat 2:317\u2013332. https:\/\/doi.org\/10.1002\/wics.82","journal-title":"WIREs Comput Stat"},{"key":"1203_CR31","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1155\/2014\/745617","volume":"2014","author":"X Zhou","year":"2014","unstructured":"Zhou X, Li Q (2014) Multiple attribute decision making based on hesitant fuzzy Einstein geometric aggregation operators. J Appl Math 2014:1\u201314. https:\/\/doi.org\/10.1155\/2014\/745617","journal-title":"J Appl Math"},{"key":"1203_CR32","doi-asserted-by":"publisher","first-page":"240","DOI":"10.1007\/s11518-015-5289-6","volume":"26","author":"H Zhao","year":"2017","unstructured":"Zhao H, Xu Z, Liu S (2017) Dual hesitant fuzzy information aggregation with Einstein t-conorm and t-norm. J Syst Sci Syst Eng 26:240\u2013264. https:\/\/doi.org\/10.1007\/s11518-015-5289-6","journal-title":"J Syst Sci Syst Eng"},{"key":"1203_CR33","doi-asserted-by":"publisher","first-page":"7239","DOI":"10.1002\/int.22587","volume":"36","author":"HMA Farid","year":"2021","unstructured":"Farid HMA, Riaz M (2021) Some generalized q-rung orthopair fuzzy Einstein interactive geometric aggregation operators with improved operational laws. Int J Intell Syst 36:7239\u20137273. https:\/\/doi.org\/10.1002\/int.22587","journal-title":"Int J Intell Syst"},{"key":"1203_CR34","doi-asserted-by":"publisher","first-page":"69","DOI":"10.1007\/s40314-022-01769-7","volume":"41","author":"V Anusha","year":"2022","unstructured":"Anusha V, Sireesha V (2022) Einstein Heronian mean aggregation operator and its application in decision making problems. Comput Appl Math 41:69. https:\/\/doi.org\/10.1007\/s40314-022-01769-7","journal-title":"Comput Appl Math"},{"key":"1203_CR35","doi-asserted-by":"publisher","first-page":"18","DOI":"10.1038\/162018f0","volume":"162","author":"Bonferroni","year":"1948","unstructured":"Bonferroni (1948) Sulle medie multiple di potenze. Nature 162:18\u201319. https:\/\/doi.org\/10.1038\/162018f0","journal-title":"Nature"},{"key":"1203_CR36","doi-asserted-by":"publisher","first-page":"1279","DOI":"10.1016\/j.ijar.2009.06.004","volume":"50","author":"RR Yager","year":"2009","unstructured":"Yager RR (2009) On generalized Bonferroni mean operators for multi-criteria aggregation. Int J Approx Reason 50:1279\u20131286. https:\/\/doi.org\/10.1016\/j.ijar.2009.06.004","journal-title":"Int J Approx Reason"},{"key":"1203_CR37","doi-asserted-by":"publisher","first-page":"2227","DOI":"10.1016\/j.fss.2010.04.004","volume":"161","author":"G Beliakov","year":"2010","unstructured":"Beliakov G, James S, Mordelov\u00e1 J et al (2010) Generalized Bonferroni mean operators in multi-criteria aggregation. Fuzzy Sets Syst 161:2227\u20132242. https:\/\/doi.org\/10.1016\/j.fss.2010.04.004","journal-title":"Fuzzy Sets Syst"},{"key":"1203_CR38","doi-asserted-by":"publisher","first-page":"1831","DOI":"10.1057\/jors.2013.7","volume":"64","author":"B Zhu","year":"2013","unstructured":"Zhu B, Xu ZS (2013) Hesitant fuzzy Bonferroni means for multi-criteria decision making. J Oper Res Soc 64:1831\u20131840. https:\/\/doi.org\/10.1057\/jors.2013.7","journal-title":"J Oper Res Soc"},{"key":"1203_CR39","doi-asserted-by":"publisher","DOI":"10.21203\/rs.3.rs-1151389\/v2","author":"M Kiri\u015fci","year":"2022","unstructured":"Kiri\u015fci M (2022) Fermatean hesitant fuzzy sets with medical decision making application. Res Sq. https:\/\/doi.org\/10.21203\/rs.3.rs-1151389\/v2","journal-title":"Res Sq"},{"key":"1203_CR40","doi-asserted-by":"publisher","first-page":"1532","DOI":"10.1016\/j.ins.2022.06.037","volume":"607","author":"AR Mishra","year":"2022","unstructured":"Mishra AR, Chen S-M, Rani P (2022) Multiattribute decision making based on Fermatean hesitant fuzzy sets and modified VIKOR method. Inf Sci 607:1532\u20131549. https:\/\/doi.org\/10.1016\/j.ins.2022.06.037","journal-title":"Inf Sci"},{"key":"1203_CR41","doi-asserted-by":"publisher","first-page":"2643","DOI":"10.1007\/s40815-022-01319-7","volume":"24","author":"H Lai","year":"2022","unstructured":"Lai H, Liao H, Long Y, Zavadskas EK (2022) A Hesitant Fermatean fuzzy CoCoSo method for group decision-making and an application to blockchain platform evaluation. Int J Fuzzy Syst 24:2643\u20132661. https:\/\/doi.org\/10.1007\/s40815-022-01319-7","journal-title":"Int J Fuzzy Syst"},{"key":"1203_CR42","doi-asserted-by":"publisher","first-page":"663","DOI":"10.1007\/s12652-019-01377-0","volume":"11","author":"T Senapati","year":"2020","unstructured":"Senapati T, Yager RR (2020) Fermatean fuzzy sets. J Ambient Intell Humaniz Comput 11:663\u2013674. https:\/\/doi.org\/10.1007\/s12652-019-01377-0","journal-title":"J Ambient Intell Humaniz Comput"},{"key":"1203_CR43","volume-title":"Fuzzy sets and fuzzy logic: theory and applications","author":"K Geogre","year":"1995","unstructured":"Geogre K, Bo Y (1995) Fuzzy sets and fuzzy logic: theory and applications. Prentice Hall"},{"key":"1203_CR44","volume-title":"Logical, algebraic, analytic and probabilistic aspects of triangular norms","author":"EP Klement","year":"2005","unstructured":"Klement EP, Radko M (2005) Logical, algebraic, analytic and probabilistic aspects of triangular norms. Elsevier"},{"key":"1203_CR45","doi-asserted-by":"publisher","first-page":"1116","DOI":"10.1016\/j.ins.2010.11.024","volume":"181","author":"G Beliakov","year":"2011","unstructured":"Beliakov G, Bustince H, Goswami DP et al (2011) On averaging operators for Atanassov\u2019s intuitionistic fuzzy sets. Inf Sci 181:1116\u20131124. https:\/\/doi.org\/10.1016\/j.ins.2010.11.024","journal-title":"Inf Sci"},{"key":"1203_CR46","doi-asserted-by":"publisher","first-page":"23","DOI":"10.1016\/j.asoc.2015.09.012","volume":"38","author":"L Wang","year":"2016","unstructured":"Wang L, Shen Q, Zhu L (2016) Dual hesitant fuzzy power aggregation operators based on Archimedean t-conorm and t-norm and their application to multiple attribute group decision making. Appl Soft Comput 38:23\u201350. https:\/\/doi.org\/10.1016\/j.asoc.2015.09.012","journal-title":"Appl Soft Comput"},{"key":"1203_CR47","doi-asserted-by":"publisher","first-page":"23","DOI":"10.1002\/int.20515","volume":"27","author":"M Xia","year":"2012","unstructured":"Xia M, Xu Z, Zhu B (2012) Generalized intuitionistic fuzzy Bonferroni means. Int J Intell Syst 27:23\u201347. https:\/\/doi.org\/10.1002\/int.20515","journal-title":"Int J Intell Syst"},{"key":"1203_CR48","doi-asserted-by":"publisher","first-page":"568","DOI":"10.1109\/tsmcb.2010.2072918","volume":"41","author":"Z Xu","year":"2011","unstructured":"Xu Z, Yager RR (2011) Intuitionistic Fuzzy Bonferroni means. IEEE Trans Syst Man Cybern Part B 41:568\u2013578. https:\/\/doi.org\/10.1109\/tsmcb.2010.2072918","journal-title":"IEEE Trans Syst Man Cybern Part B"},{"key":"1203_CR49","doi-asserted-by":"publisher","first-page":"2548","DOI":"10.1016\/s0140-6736(15)61146-1","volume":"385","author":"T Lancet","year":"2015","unstructured":"Lancet T (2015) Mental health in China: what will be achieved by 2020? Lancet 385:2548. https:\/\/doi.org\/10.1016\/s0140-6736(15)61146-1","journal-title":"Lancet"},{"key":"1203_CR50","doi-asserted-by":"publisher","first-page":"95","DOI":"10.1016\/j.jad.2020.03.011","volume":"268","author":"X Ren","year":"2020","unstructured":"Ren X, Yu S, Dong W et al (2020) Burden of depression in China, 1990\u20132017: findings from the global burden of disease study 2017. J Affect Disord 268:95\u2013101. https:\/\/doi.org\/10.1016\/j.jad.2020.03.011","journal-title":"J Affect Disord"},{"key":"1203_CR51","doi-asserted-by":"publisher","first-page":"93","DOI":"10.1186\/s12888-016-0802-0","volume":"16","author":"Y Yu","year":"2016","unstructured":"Yu Y, Hu M, Liu Z et al (2016) Recognition of depression, anxiety, and alcohol abuse in a Chinese rural sample: a cross-sectional study. BMC Psychiatry 16:93. https:\/\/doi.org\/10.1186\/s12888-016-0802-0","journal-title":"BMC Psychiatry"},{"key":"1203_CR52","doi-asserted-by":"publisher","DOI":"10.1176\/appi.books.9780890425596","volume-title":"Diagnostic and statistical manual of mental disorders, DSM-5","author":"Association AP","year":"2013","unstructured":"Association AP (2013) Diagnostic and statistical manual of mental disorders, DSM-5. Association AP. https:\/\/doi.org\/10.1176\/appi.books.9780890425596"},{"key":"1203_CR53","doi-asserted-by":"publisher","first-page":"171","DOI":"10.1159\/000065140","volume":"35","author":"Y-F Chen","year":"2002","unstructured":"Chen Y-F (2002) Chinese Classification of Mental Disorders (CCMD-3): towards integration in international classification. Psychopathology 35:171\u2013175. https:\/\/doi.org\/10.1159\/000065140","journal-title":"Psychopathology"},{"key":"1203_CR54","doi-asserted-by":"publisher","first-page":"271","DOI":"10.31887\/dcns.2008.10.3\/shkennedy","volume":"10","author":"SH Kennedy","year":"2008","unstructured":"Kennedy SH (2008) Core symptoms of major depressive disorder: relevance to diagnosis and treatment. Dialog Clin Neurosci 10:271\u2013277. https:\/\/doi.org\/10.31887\/dcns.2008.10.3\/shkennedy","journal-title":"Dialog Clin Neurosci"},{"key":"1203_CR55","doi-asserted-by":"publisher","first-page":"340","DOI":"10.1093\/occmed\/kqv043","volume":"65","author":"R Sharp","year":"2015","unstructured":"Sharp R (2015) The Hamilton Rating Scale for depression. Occup Med 65:340\u2013340. https:\/\/doi.org\/10.1093\/occmed\/kqv043","journal-title":"Occup Med"},{"key":"1203_CR56","doi-asserted-by":"publisher","first-page":"2163","DOI":"10.1176\/appi.ajp.161.12.2163","volume":"161","author":"RM Bagby","year":"2004","unstructured":"Bagby RM, Ryder AG, Schuller DR, Marshall MB (2004) The Hamilton Depression Rating Scale: has the gold standard become a lead weight? Am J Psychiatry 161:2163\u20132177. https:\/\/doi.org\/10.1176\/appi.ajp.161.12.2163","journal-title":"Am J Psychiatry"},{"key":"1203_CR57","doi-asserted-by":"publisher","first-page":"594","DOI":"10.1192\/bjp.168.5.594","volume":"168","author":"RP Snaith","year":"1996","unstructured":"Snaith RP (1996) Present use of the Hamilton Depression Rating Scale: observations on method of assessment in research of depressive disorders. Br J Psychiatry 168:594\u2013597. https:\/\/doi.org\/10.1192\/bjp.168.5.594","journal-title":"Br J Psychiatry"},{"key":"1203_CR58","doi-asserted-by":"publisher","first-page":"606","DOI":"10.1046\/j.1525-1497.2001.016009606.x","volume":"16","author":"K Kroenke","year":"2001","unstructured":"Kroenke K, Spitzer RL, Williams JBW (2001) The PHQ-9. J Gen Intern Med 16:606\u2013613. https:\/\/doi.org\/10.1046\/j.1525-1497.2001.016009606.x","journal-title":"J Gen Intern Med"},{"key":"1203_CR59","doi-asserted-by":"publisher","first-page":"601","DOI":"10.1002\/int.22067","volume":"34","author":"H Garg","year":"2019","unstructured":"Garg H (2019) Hesitant Pythagorean fuzzy Maclaurin symmetric mean operators and its applications to multiattribute decision-making process. Int J Intell Syst 34:601\u2013626. https:\/\/doi.org\/10.1002\/int.22067","journal-title":"Int J Intell Syst"},{"key":"1203_CR60","doi-asserted-by":"publisher","first-page":"3464","DOI":"10.1002\/int.22423","volume":"36","author":"A Hadi","year":"2021","unstructured":"Hadi A, Khan W, Khan A (2021) A novel approach to MADM problems using Fermatean fuzzy Hamacher aggregation operators. Int J Intell Syst 36:3464\u20133499. https:\/\/doi.org\/10.1002\/int.22423","journal-title":"Int J Intell Syst"},{"key":"1203_CR61","doi-asserted-by":"publisher","first-page":"419","DOI":"10.1016\/s0888-613x(98)10018-x","volume":"19","author":"S Roychowdhury","year":"1998","unstructured":"Roychowdhury S, Wang B-H (1998) On generalized Hamacher families of triangular operators. Int J Approx Reason 19:419\u2013439. https:\/\/doi.org\/10.1016\/s0888-613x(98)10018-x","journal-title":"Int J Approx Reason"},{"key":"1203_CR62","doi-asserted-by":"publisher","first-page":"2104","DOI":"10.1002\/int.22133","volume":"34","author":"D Liu","year":"2019","unstructured":"Liu D, Peng D, Liu Z (2019) The distance measures between q-rung orthopair hesitant fuzzy sets and their application in multiple criteria decision making. Int J Intell Syst 34:2104\u20132121. https:\/\/doi.org\/10.1002\/int.22133","journal-title":"Int J Intell Syst"},{"key":"1203_CR63","doi-asserted-by":"publisher","first-page":"1167","DOI":"10.1007\/s40747-021-00551-2","volume":"8","author":"P Liu","year":"2022","unstructured":"Liu P, Mahmood T, Ali Z (2022) The cross-entropy and improved distance measures for complex q-rung orthopair hesitant fuzzy sets and their applications in multi-criteria decision-making. Complex Intell Syst 8:1167\u20131186. https:\/\/doi.org\/10.1007\/s40747-021-00551-2","journal-title":"Complex Intell Syst"},{"key":"1203_CR64","doi-asserted-by":"publisher","first-page":"3275","DOI":"10.1002\/int.22194","volume":"34","author":"D Liang","year":"2019","unstructured":"Liang D, Zhang Y, Cao W (2019) q-Rung orthopair fuzzy Choquet integral aggregation and its application in heterogeneous multicriteria two-sided matching decision making. Int J Intell Syst 34:3275\u20133301. https:\/\/doi.org\/10.1002\/int.22194","journal-title":"Int J Intell Syst"}],"container-title":["Complex &amp; Intelligent Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40747-023-01203-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s40747-023-01203-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40747-023-01203-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,2,10]],"date-time":"2024-02-10T22:35:43Z","timestamp":1707604543000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s40747-023-01203-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,9,12]]},"references-count":64,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2024,2]]}},"alternative-id":["1203"],"URL":"https:\/\/doi.org\/10.1007\/s40747-023-01203-3","relation":{},"ISSN":["2199-4536","2198-6053"],"issn-type":[{"value":"2199-4536","type":"print"},{"value":"2198-6053","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,9,12]]},"assertion":[{"value":"28 February 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"3 August 2023","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"12 September 2023","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that they have no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}