{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,24]],"date-time":"2026-02-24T04:31:45Z","timestamp":1771907505733,"version":"3.50.1"},"reference-count":69,"publisher":"Springer Science and Business Media LLC","issue":"16","license":[{"start":{"date-parts":[[2020,1,20]],"date-time":"2020-01-20T00:00:00Z","timestamp":1579478400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2020,1,20]],"date-time":"2020-01-20T00:00:00Z","timestamp":1579478400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"name":"EPSRC UKRI Innovation Fellowship","award":["EP\/S001328\/1"],"award-info":[{"award-number":["EP\/S001328\/1"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Soft Comput"],"published-print":{"date-parts":[[2020,8]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>In this paper, a multiple criteria decision making (MCDM) method based on weighted Archimedean power partitioned Bonferroni aggregation operators of generalised orthopair membership grades (GOMGs) is proposed. Bonferroni mean operator, geometric Bonferroni mean operator, power average operator, partitioned average operator, and Archimedean <jats:italic>T<\/jats:italic>-norm and <jats:italic>T<\/jats:italic>-conorm operations are introduced into generalised orthopair fuzzy sets to develop the Bonferroni aggregation operators. Their formal definitions are provided, and generalised and specific expressions are constructed. On the basis of the specific operators, a method for solving the MCDM problems based on GOMGs is designed. The working process, characteristics, and feasibility of the method are, respectively, demonstrated via a numerical example, a qualitative comparison at the aspect of characteristics, and a quantitative comparison using the example as benchmark. The demonstration results show that the proposed method is feasible that has desirable generality and flexibility in the aggregation of criterion values and concurrently has the capabilities to deal with the heterogeneous interrelationships of criteria, reduce the negative influence of biased criterion values, and capture the risk attitudes of decision makers.<\/jats:p>","DOI":"10.1007\/s00500-020-04676-3","type":"journal-article","created":{"date-parts":[[2020,1,20]],"date-time":"2020-01-20T17:02:49Z","timestamp":1579539769000},"page":"12329-12355","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":28,"title":["Multiple criteria decision making based on weighted Archimedean power partitioned Bonferroni aggregation operators of generalised orthopair membership grades"],"prefix":"10.1007","volume":"24","author":[{"given":"Yuchu","family":"Qin","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5936-1714","authenticated-orcid":false,"given":"Qunfen","family":"Qi","sequence":"additional","affiliation":[]},{"given":"Paul J.","family":"Scott","sequence":"additional","affiliation":[]},{"given":"Xiangqian","family":"Jiang","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2020,1,20]]},"reference":[{"key":"4676_CR1","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-030-10674-4","volume-title":"Feature selection and enhanced krill herd algorithm for text document clustering","author":"LMQ Abualigah","year":"2019","unstructured":"Abualigah LMQ (2019) Feature selection and enhanced krill herd algorithm for text document clustering. Springer, Cham"},{"issue":"1","key":"4676_CR2","first-page":"19","volume":"5","author":"LMQ Abualigah","year":"2015","unstructured":"Abualigah LMQ, Hanandeh ES (2015) Applying genetic algorithms to information retrieval using vector space model. Int J Comput Sci Eng Appl 5(1):19\u201328","journal-title":"Int J Comput Sci Eng Appl"},{"issue":"11","key":"4676_CR3","doi-asserted-by":"crossref","first-page":"4773","DOI":"10.1007\/s11227-017-2046-2","volume":"73","author":"LM Abualigah","year":"2017","unstructured":"Abualigah LM, Khader AT (2017) Unsupervised text feature selection technique based on hybrid particle swarm optimization algorithm with genetic operators for the text clustering. J Supercomput 73(11):4773\u20134795","journal-title":"J Supercomput"},{"key":"4676_CR4","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1016\/j.engappai.2018.05.003","volume":"73","author":"LM Abualigah","year":"2018","unstructured":"Abualigah LM, Khader AT, Hanandeh ES (2018a) A combination of objective functions and hybrid Krill herd algorithm for text document clustering analysis. Eng Appl Artif Intell 73:111\u2013125","journal-title":"Eng Appl Artif Intell"},{"key":"4676_CR5","doi-asserted-by":"crossref","first-page":"456","DOI":"10.1016\/j.jocs.2017.07.018","volume":"25","author":"LM Abualigah","year":"2018","unstructured":"Abualigah LM, Khader AT, Hanandeh ES (2018b) A new feature selection method to improve the document clustering using particle swarm optimization algorithm. J Comput Sci 25:456\u2013466","journal-title":"J Comput Sci"},{"issue":"11","key":"4676_CR6","doi-asserted-by":"crossref","first-page":"4047","DOI":"10.1007\/s10489-018-1190-6","volume":"48","author":"LM Abualigah","year":"2018","unstructured":"Abualigah LM, Khader AT, Hanandeh ES (2018c) Hybrid clustering analysis using improved krill herd algorithm. Appl Intell 48(11):4047\u20134071","journal-title":"Appl Intell"},{"issue":"2","key":"4676_CR7","doi-asserted-by":"crossref","first-page":"670","DOI":"10.1109\/TFUZZ.2017.2687885","volume":"26","author":"Z Ai","year":"2018","unstructured":"Ai Z, Xu Z (2018) Multiple definite integrals of intuitionistic fuzzy calculus and isomorphic mappings. IEEE Trans Fuzzy Syst 26(2):670\u2013680","journal-title":"IEEE Trans Fuzzy Syst"},{"issue":"1","key":"4676_CR8","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(1):87\u201396","journal-title":"Fuzzy Sets Syst"},{"issue":"9","key":"4676_CR9","doi-asserted-by":"crossref","first-page":"383","DOI":"10.3390\/sym10090383","volume":"10","author":"K Bai","year":"2018","unstructured":"Bai K, Zhu X, Wang J, Zhang R (2018) Some partitioned Maclaurin symmetric mean based on q-Rung orthopair fuzzy information for dealing with multi-attribute group decision making. Symmetry 10(9):383","journal-title":"Symmetry"},{"issue":"3\u20134","key":"4676_CR10","first-page":"267","volume":"5","author":"C Bonferroni","year":"1950","unstructured":"Bonferroni C (1950) Sulle medie multiple di potenze. Bollettino dell\u2019Unione Matematica Italiana 5(3\u20134):267\u2013270","journal-title":"Bollettino dell\u2019Unione Matematica Italiana"},{"issue":"1","key":"4676_CR11","doi-asserted-by":"crossref","first-page":"179","DOI":"10.1109\/TFUZZ.2015.2451692","volume":"24","author":"H Bustince","year":"2016","unstructured":"Bustince H, Barrenechea E, Pagola M, Fernandez J, Xu Z, Bedregal B, Montero J, Hagras H, Herrera F, De Baets B (2016) A historical account of types of fuzzy sets and their relationships. IEEE Trans Fuzzy Syst 24(1):179\u2013194","journal-title":"IEEE Trans Fuzzy Syst"},{"key":"4676_CR12","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1016\/j.inffus.2017.09.003","volume":"41","author":"TY Chen","year":"2018","unstructured":"Chen TY (2018) Remoteness index-based Pythagorean fuzzy VIKOR methods with a generalized distance measure for multiple criteria decision analysis. Inf Fus 41:129\u2013150","journal-title":"Inf Fus"},{"issue":"3","key":"4676_CR13","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(3):477\u2013484","journal-title":"Fuzzy Sets Syst"},{"issue":"1","key":"4676_CR14","first-page":"19","volume":"8","author":"G Deschrijver","year":"2002","unstructured":"Deschrijver G, Kerre EE (2002) A generalization of operators on intuitionistic fuzzy sets using T-norms and conorms. Notes IFS 8(1):19\u201327","journal-title":"Notes IFS"},{"issue":"5","key":"4676_CR15","doi-asserted-by":"crossref","first-page":"1009","DOI":"10.1109\/TFUZZ.2015.2500273","volume":"24","author":"S Dick","year":"2016","unstructured":"Dick S, Yager RR, Yazdanbakhsh O (2016) On pythagorean and complex fuzzy set operations. IEEE Trans Fuzzy Syst 24(5):1009\u20131021","journal-title":"IEEE Trans Fuzzy Syst"},{"issue":"4","key":"4676_CR16","doi-asserted-by":"crossref","first-page":"802","DOI":"10.1002\/int.21968","volume":"33","author":"WS Du","year":"2018","unstructured":"Du WS (2018) Minkowski-type distance measures for generalized orthopair fuzzy sets. Int J Intell Syst 33(4):802\u2013817","journal-title":"Int J Intell Syst"},{"issue":"4","key":"4676_CR17","doi-asserted-by":"crossref","first-page":"564","DOI":"10.1002\/int.22065","volume":"34","author":"WS Du","year":"2019","unstructured":"Du WS (2019) Correlation and correlation coefficient of generalized orthopair fuzzy sets. Int J Intell Syst 34(4):564\u2013583","journal-title":"Int J Intell Syst"},{"key":"4676_CR18","doi-asserted-by":"crossref","first-page":"166","DOI":"10.1016\/j.asoc.2015.08.017","volume":"37","author":"B Dutta","year":"2015","unstructured":"Dutta B, Guha D (2015) Partitioned Bonferroni mean based on linguistic 2-tuple for dealing with multi-attribute group decision making. Appl Soft Comput 37:166\u2013179","journal-title":"Appl Soft Comput"},{"issue":"9","key":"4676_CR19","doi-asserted-by":"crossref","first-page":"886","DOI":"10.1002\/int.21809","volume":"31","author":"H Garg","year":"2016","unstructured":"Garg H (2016) A new generalized Pythagorean fuzzy information aggregation using Einstein operations and its application to decision making. Int J Intell Syst 31(9):886\u2013920","journal-title":"Int J Intell Syst"},{"key":"4676_CR20","doi-asserted-by":"crossref","first-page":"164","DOI":"10.1016\/j.engappai.2017.02.008","volume":"60","author":"H Garg","year":"2017","unstructured":"Garg H (2017) Novel intuitionistic fuzzy decision making method based on an improved operation laws and its application. Eng Appl Artif Intell 60:164\u2013174","journal-title":"Eng Appl Artif Intell"},{"key":"4676_CR21","volume-title":"Aggregation functions, encyclopedia of mathematics and its applications 127","author":"M Grabisch","year":"2009","unstructured":"Grabisch M, Marichal JL, Mesiar R, Pap E (2009) Aggregation functions, encyclopedia of mathematics and its applications 127. Cambridge University Press, Cambridge"},{"issue":"1","key":"4676_CR22","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.ins.2010.08.043","volume":"181","author":"M Grabisch","year":"2011","unstructured":"Grabisch M, Marichal JL, Mesiar R, Pap E (2011) Aggregation functions: means. Inf Sci 181(1):1\u201322","journal-title":"Inf Sci"},{"key":"4676_CR23","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4939-3094-4","volume-title":"Multiple criteria decision analysis: state of the art surveys","author":"S Greco","year":"2016","unstructured":"Greco S, Figueira J, Ehrgott M (2016) Multiple criteria decision analysis: state of the art surveys. Springer, New York"},{"issue":"5","key":"4676_CR24","doi-asserted-by":"crossref","first-page":"1129","DOI":"10.1007\/s00500-015-1843-x","volume":"21","author":"Y He","year":"2017","unstructured":"He Y, He Z, Huang H (2017) Decision making with the generalized intuitionistic fuzzy power interaction averaging operators. Soft Comput 21(5):1129\u20131144","journal-title":"Soft Comput"},{"issue":"2","key":"4676_CR25","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1007\/s41066-017-0059-0","volume":"3","author":"EB Jamkhaneh","year":"2018","unstructured":"Jamkhaneh EB, Garg H (2018) Some new operations over the generalized intuitionistic fuzzy sets and their application to decision-making process. Granul Comput 3(2):111\u2013122","journal-title":"Granul Comput"},{"issue":"1","key":"4676_CR26","doi-asserted-by":"crossref","first-page":"251","DOI":"10.1007\/s00500-018-3592-0","volume":"23","author":"MSA Khan","year":"2019","unstructured":"Khan MSA, Abdullah S, Ali A, Amin F, Hussain F (2019) Pythagorean hesitant fuzzy Choquet integral aggregation operators and their application to multi-attribute decision-making. Soft Comput 23(1):251\u2013267","journal-title":"Soft Comput"},{"key":"4676_CR27","doi-asserted-by":"crossref","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"},{"issue":"10","key":"4676_CR28","doi-asserted-by":"crossref","first-page":"755","DOI":"10.1016\/j.crma.2005.04.012","volume":"340","author":"EP Klement","year":"2005","unstructured":"Klement EP, Mesiar R, Pap E (2005) Archimax copulas and invariance under transformations. C R Math Acad Sci Paris Math 340(10):755\u2013758","journal-title":"C R Math Acad Sci Paris Math"},{"key":"4676_CR29","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.knosys.2014.11.019","volume":"76","author":"Q Lei","year":"2015","unstructured":"Lei Q, Xu Z (2015) Fundamental properties of intuitionistic fuzzy calculus. Knowl Based Syst 76:1\u201316","journal-title":"Knowl Based Syst"},{"issue":"3","key":"4676_CR30","doi-asserted-by":"crossref","first-page":"519","DOI":"10.1109\/TFUZZ.2015.2450832","volume":"24","author":"Q Lei","year":"2016","unstructured":"Lei Q, Xu Z (2016) Chain and substitution rules of intuitionistic fuzzy calculus. IEEE Trans Fuzzy Syst 24(3):519\u2013529","journal-title":"IEEE Trans Fuzzy Syst"},{"key":"4676_CR31","doi-asserted-by":"crossref","first-page":"282","DOI":"10.1016\/j.ins.2018.01.015","volume":"435","author":"D Liang","year":"2018","unstructured":"Liang D, Xu Z, Liu D, Wu Y (2018) Method for three-way decisions using ideal TOPSIS solutions at Pythagorean fuzzy information. Inf Sci 435:282\u2013295","journal-title":"Inf Sci"},{"issue":"6","key":"4676_CR32","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 (2014a) 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":"4","key":"4676_CR33","doi-asserted-by":"crossref","first-page":"1703","DOI":"10.3233\/IFS-141137","volume":"27","author":"H Liao","year":"2014","unstructured":"Liao H, Xu Z (2014b) Multi-criteria decision making with intuitionistic fuzzy PROMETHEE. J Intell Fuzzy Syst 27(4):1703\u20131717","journal-title":"J Intell Fuzzy Syst"},{"issue":"9","key":"4676_CR34","doi-asserted-by":"crossref","first-page":"2514","DOI":"10.1109\/TCYB.2016.2634599","volume":"47","author":"P Liu","year":"2017","unstructured":"Liu P, Chen SM (2017) Group decision making based on Heronian aggregation operators of intuitionistic fuzzy numbers. IEEE Trans Cybern 47(9):2514\u20132530","journal-title":"IEEE Trans Cybern"},{"issue":"2","key":"4676_CR35","doi-asserted-by":"crossref","first-page":"315","DOI":"10.1002\/int.21933","volume":"33","author":"P Liu","year":"2018","unstructured":"Liu P, Liu J (2018) Some q-Rung orthopair fuzzy Bonferroni mean operators and their application to multi attribute group decision making. Int J Intell Syst 33(2):315\u2013347","journal-title":"Int J Intell Syst"},{"issue":"2","key":"4676_CR36","doi-asserted-by":"crossref","first-page":"259","DOI":"10.1002\/int.21927","volume":"33","author":"P Liu","year":"2018","unstructured":"Liu P, Wang P (2018a) Some q-Rung orthopair fuzzy aggregation operators and their applications to multiple attribute decision making. Int J Intell Syst 33(2):259\u2013280","journal-title":"Int J Intell Syst"},{"key":"4676_CR37","doi-asserted-by":"publisher","DOI":"10.1109\/TFUZZ.2018.2826452","author":"P Liu","year":"2018","unstructured":"Liu P, Wang P (2018b) Multiple-attribute decision making based on Archimedean Bonferroni operators of q-Rung orthopair fuzzy numbers. IEEE Trans Fuzzy Syst. https:\/\/doi.org\/10.1109\/TFUZZ.2018.2826452","journal-title":"IEEE Trans Fuzzy Syst"},{"issue":"3","key":"4676_CR38","doi-asserted-by":"crossref","first-page":"637","DOI":"10.1080\/00207540903490171","volume":"49","author":"P Liu","year":"2011","unstructured":"Liu P, Zhang X (2011) Research on the supplier selection of a supply chain based on entropy weight and improved ELECTRE-III method. Int J Prod Res 49(3):637\u2013646","journal-title":"Int J Prod Res"},{"key":"4676_CR39","doi-asserted-by":"publisher","DOI":"10.1109\/TSMC.2018.2852948","author":"P Liu","year":"2018","unstructured":"Liu P, Chen SM, Wang P (2018a) Multiple-attribute group decision-making based on q-Rung orthopair fuzzy power Maclaurin symmetric mean operators. IEEE Trans Syst Man Cybern Syst. https:\/\/doi.org\/10.1109\/TSMC.2018.2852948","journal-title":"IEEE Trans Syst Man Cybern Syst"},{"issue":"1","key":"4676_CR40","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1057\/s41274-017-0190-y","volume":"69","author":"P Liu","year":"2018","unstructured":"Liu P, Liu J, Chen SM (2018b) Some intuitionistic fuzzy Dombi Bonferroni mean operators and their application to multi-attribute group decision making. J Oper Res Soc 69(1):1\u201324","journal-title":"J Oper Res Soc"},{"issue":"9","key":"4676_CR41","doi-asserted-by":"crossref","first-page":"1900","DOI":"10.1002\/int.22001","volume":"33","author":"Z Liu","year":"2018","unstructured":"Liu Z, Liu P, Liang X (2018c) Multiple attribute decision-making method for dealing with heterogeneous relationship among attributes and unknown attribute weight information under q-Rung orthopair fuzzy environment. Int J Intell Syst 33(9):1900\u20131928","journal-title":"Int J Intell Syst"},{"issue":"12","key":"4676_CR42","doi-asserted-by":"crossref","first-page":"2341","DOI":"10.1002\/int.22032","volume":"33","author":"Z Liu","year":"2018","unstructured":"Liu Z, Wang S, Liu P (2018d) Multiple attribute group decision making based on q-Rung orthopair fuzzy Heronian mean operators. Int J Intell Syst 33(12):2341\u20132363","journal-title":"Int J Intell Syst"},{"issue":"2","key":"4676_CR43","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1007\/s005000050007","volume":"1","author":"E Pap","year":"1997","unstructured":"Pap E (1997) Pseudo-analysis as a mathematical base for soft computing. Soft Comput 1(2):61\u201368","journal-title":"Soft Comput"},{"issue":"3","key":"4676_CR44","doi-asserted-by":"crossref","first-page":"368","DOI":"10.1016\/j.ijar.2007.05.015","volume":"47","author":"E Pap","year":"2008","unstructured":"Pap E (2008) Generalized real analysis and its applications. Int J Approx Reason 47(3):368\u2013386","journal-title":"Int J Approx Reason"},{"issue":"11","key":"4676_CR45","doi-asserted-by":"crossref","first-page":"1133","DOI":"10.1002\/int.21738","volume":"30","author":"X Peng","year":"2015","unstructured":"Peng X, Yang Y (2015) Some results for Pythagorean fuzzy sets. Int J Intell Syst 30(11):1133\u20131160","journal-title":"Int J Intell Syst"},{"issue":"11","key":"4676_CR46","doi-asserted-by":"crossref","first-page":"2255","DOI":"10.1002\/int.22028","volume":"33","author":"X Peng","year":"2018","unstructured":"Peng X, Dai J, Garg H (2018) Exponential operation and aggregation operator for q-Rung orthopair fuzzy set and their decision-making method with a new score function. Int J Intell Syst 33(11):2255\u20132282","journal-title":"Int J Intell Syst"},{"issue":"12","key":"4676_CR47","doi-asserted-by":"crossref","first-page":"687","DOI":"10.3390\/sym10120687","volume":"10","author":"R Wang","year":"2018","unstructured":"Wang R, Li Y (2018) A novel approach for green supplier selection under a q-Rung orthopair fuzzy environment. Symmetry 10(12):687","journal-title":"Symmetry"},{"issue":"5","key":"4676_CR48","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"},{"issue":"2","key":"4676_CR49","doi-asserted-by":"crossref","first-page":"1599","DOI":"10.3233\/JIFS-18607","volume":"36","author":"J Wang","year":"2019","unstructured":"Wang J, Zhang R, Zhu X, Zhou Z, Shang X, Li W (2019) Some q-Rung orthopair fuzzy Muirhead means with their application to multi-attribute group decision making. J Intell Fuzzy Syst 36(2):1599\u20131614","journal-title":"J Intell Fuzzy Syst"},{"issue":"3","key":"4676_CR50","doi-asserted-by":"crossref","first-page":"243","DOI":"10.1016\/j.knosys.2010.01.003","volume":"23","author":"G Wei","year":"2010","unstructured":"Wei G (2010) GRA method for multiple attribute decision making with incomplete weight information in intuitionistic fuzzy setting. Knowl Based Syst 23(3):243\u2013247","journal-title":"Knowl Based Syst"},{"issue":"1","key":"4676_CR51","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1002\/int.21946","volume":"33","author":"G Wei","year":"2018","unstructured":"Wei G, Lu M (2018) Pythagorean fuzzy power aggregation operators in multiple attribute decision making. Int J Intell Syst 33(1):169\u2013186","journal-title":"Int J Intell Syst"},{"issue":"7","key":"4676_CR52","doi-asserted-by":"crossref","first-page":"1426","DOI":"10.1002\/int.21985","volume":"33","author":"G Wei","year":"2018","unstructured":"Wei G, Gao H, Wei Y (2018) Some q-Rung orthopair fuzzy Heronian mean operators in multiple attribute decision making. Int J Intell Syst 33(7):1426\u20131458","journal-title":"Int J Intell Syst"},{"issue":"1","key":"4676_CR53","doi-asserted-by":"crossref","first-page":"50","DOI":"10.1002\/int.22042","volume":"34","author":"G Wei","year":"2019","unstructured":"Wei G, Wei C, Wang J, Gao H, Wei Y (2019) Some q-Rung orthopair fuzzy Maclaurin symmetric mean operators and their applications to potential evaluation of emerging technology commercialization. Int J Intell Syst 34(1):50\u201381","journal-title":"Int J Intell Syst"},{"issue":"7","key":"4676_CR54","doi-asserted-by":"crossref","first-page":"78","DOI":"10.1016\/j.knosys.2012.02.004","volume":"31","author":"M Xia","year":"2012","unstructured":"Xia M, Xu Z, Zhu B (2012) Some issues on intuitionistic fuzzy aggregation operators based on Archimedean t-conorm and t-norm. Knowl Based Syst 31(7):78\u201388","journal-title":"Knowl Based Syst"},{"issue":"3","key":"4676_CR55","doi-asserted-by":"crossref","first-page":"88","DOI":"10.1016\/j.knosys.2012.11.013","volume":"40","author":"M Xia","year":"2013","unstructured":"Xia M, Xu Z, Zhu B (2013) Geometric Bonferroni means with their application in multi-criteria decision making. Knowl Based Syst 40(3):88\u2013100","journal-title":"Knowl Based Syst"},{"key":"4676_CR56","doi-asserted-by":"publisher","DOI":"10.1007\/s00500-018-03712-7","author":"Y Xing","year":"2019","unstructured":"Xing Y, Zhang R, Zhou Z, Wang J (2019) Some q-Rung orthopair fuzzy point weighted aggregation operators for multi-attribute decision making. Soft Comput. https:\/\/doi.org\/10.1007\/s00500-018-03712-7","journal-title":"Soft Comput"},{"issue":"11","key":"4676_CR57","doi-asserted-by":"crossref","first-page":"2363","DOI":"10.1016\/j.ins.2006.12.019","volume":"177","author":"Z Xu","year":"2007","unstructured":"Xu Z (2007) Intuitionistic preference relations and their application in group decision making. Inf Sci 177(11):2363\u20132379","journal-title":"Inf Sci"},{"issue":"2","key":"4676_CR58","doi-asserted-by":"crossref","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 B Cybern 41(2):568\u2013578","journal-title":"IEEE Trans Syst Man Cybern B Cybern"},{"issue":"4","key":"4676_CR59","doi-asserted-by":"crossref","first-page":"589","DOI":"10.1111\/j.1540-5915.1981.tb00111.x","volume":"12","author":"RR Yager","year":"1981","unstructured":"Yager RR (1981) Concepts, theory, and techniques a new methodology for ordinal multiobjective decisions based on fuzzy sets. Decis Sci 12(4):589\u2013600","journal-title":"Decis Sci"},{"issue":"6","key":"4676_CR60","doi-asserted-by":"crossref","first-page":"724","DOI":"10.1109\/3468.983429","volume":"31","author":"RR Yager","year":"2001","unstructured":"Yager RR (2001) The power average operator. IEEE Trans Syst Man Cybern A Syst Hum 31(6):724\u2013731","journal-title":"IEEE Trans Syst Man Cybern A Syst Hum"},{"issue":"4","key":"4676_CR61","doi-asserted-by":"crossref","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(4):958\u2013965","journal-title":"IEEE Trans Fuzzy Syst"},{"issue":"5","key":"4676_CR62","doi-asserted-by":"crossref","first-page":"1222","DOI":"10.1109\/TFUZZ.2016.2604005","volume":"25","author":"RR Yager","year":"2017","unstructured":"Yager RR (2017) Generalized orthopair fuzzy sets. IEEE Trans Fuzzy Syst 25(5):1222\u20131230","journal-title":"IEEE Trans Fuzzy Syst"},{"issue":"5","key":"4676_CR63","doi-asserted-by":"crossref","first-page":"436","DOI":"10.1002\/int.21584","volume":"28","author":"RR Yager","year":"2013","unstructured":"Yager RR, Abbasov AM (2013) Pythagorean membership grades, complex numbers, and decision making. Int J Intell Syst 28(5):436\u2013452","journal-title":"Int J Intell Syst"},{"key":"4676_CR64","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1016\/j.inffus.2017.02.005","volume":"38","author":"RR Yager","year":"2017","unstructured":"Yager RR, Alajlan N (2017) Approximate reasoning with generalized orthopair fuzzy sets. Inf Fus 38:65\u201373","journal-title":"Inf Fus"},{"issue":"11","key":"4676_CR65","doi-asserted-by":"crossref","first-page":"2154","DOI":"10.1002\/int.22008","volume":"33","author":"RR Yager","year":"2018","unstructured":"Yager RR, Alajlan N, Bazi Y (2018) Aspects of generalized orthopair fuzzy sets. Int J Intell Syst 33(11):2154\u20132174","journal-title":"Int J Intell Syst"},{"issue":"3","key":"4676_CR66","doi-asserted-by":"crossref","first-page":"439","DOI":"10.1002\/int.22060","volume":"34","author":"W Yang","year":"2019","unstructured":"Yang W, Pang Y (2019) New q-Rung orthopair fuzzy partitioned Bonferroni mean operators and their application in multiple attribute decision making. Int J Intell Syst 34(3):439\u2013476","journal-title":"Int J Intell Syst"},{"issue":"3","key":"4676_CR67","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(3):338\u2013353","journal-title":"Inf Control"},{"issue":"4","key":"4676_CR68","doi-asserted-by":"crossref","first-page":"945","DOI":"10.1109\/TFUZZ.2016.2587326","volume":"25","author":"Z Zhang","year":"2017","unstructured":"Zhang Z, Pedrycz W (2017) Models of mathematical programming for intuitionistic multiplicative preference relations. IEEE Trans Fuzzy Syst 25(4):945\u2013957","journal-title":"IEEE Trans Fuzzy Syst"},{"issue":"12","key":"4676_CR69","doi-asserted-by":"crossref","first-page":"1061","DOI":"10.1002\/int.21676","volume":"29","author":"X Zhang","year":"2014","unstructured":"Zhang X, Xu Z (2014) Extension of TOPSIS to multiple criteria decision making with Pythagorean fuzzy sets. Int J Intell Syst 29(12):1061\u20131078","journal-title":"Int J Intell Syst"}],"container-title":["Soft Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00500-020-04676-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00500-020-04676-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00500-020-04676-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,1,19]],"date-time":"2021-01-19T00:19:20Z","timestamp":1611015560000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00500-020-04676-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,1,20]]},"references-count":69,"journal-issue":{"issue":"16","published-print":{"date-parts":[[2020,8]]}},"alternative-id":["4676"],"URL":"https:\/\/doi.org\/10.1007\/s00500-020-04676-3","relation":{},"ISSN":["1432-7643","1433-7479"],"issn-type":[{"value":"1432-7643","type":"print"},{"value":"1433-7479","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,1,20]]},"assertion":[{"value":"20 January 2020","order":1,"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":"Yuchu Qin declares that he has no conflict of interest. Qunfen Qi declares that she has no conflict of interest. Paul J. Scott declares that he has no conflict of interest. Xiangqian Jiang declares that she has no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}},{"value":"This article does not contain any studies with human participants or animals performed by any of the authors.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethical approval"}}]}}