{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T03:18:07Z","timestamp":1740107887297,"version":"3.37.3"},"reference-count":47,"publisher":"Springer Science and Business Media LLC","issue":"17","license":[{"start":{"date-parts":[[2022,7,18]],"date-time":"2022-07-18T00:00:00Z","timestamp":1658102400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2022,7,18]],"date-time":"2022-07-18T00:00:00Z","timestamp":1658102400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"name":"Shanxi \u201c1331 Project\u201d Key Innovative Research Team"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Soft Comput"],"published-print":{"date-parts":[[2022,9]]},"DOI":"10.1007\/s00500-022-07239-w","type":"journal-article","created":{"date-parts":[[2022,7,18]],"date-time":"2022-07-18T16:20:37Z","timestamp":1658161237000},"page":"8459-8477","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Multi-attribute group decision-making method based on weighted partitioned Maclaurin symmetric mean operator and a novel score function under neutrosophic cubic environment"],"prefix":"10.1007","volume":"26","author":[{"given":"Jianping","family":"Fan","sequence":"first","affiliation":[]},{"given":"Shanshan","family":"Zhai","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6126-1122","authenticated-orcid":false,"given":"\u00b7Meiqin","family":"Wu","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2022,7,18]]},"reference":[{"issue":"4","key":"7239_CR1","doi-asserted-by":"publisher","first-page":"346","DOI":"10.3390\/math7040346","volume":"7","author":"K Alhazaymeh","year":"2019","unstructured":"Alhazaymeh K, Gulistan M, Khan M et al (2019) Neutrosophic cubic einstein hybrid geometric aggregation operators with application in prioritization using multiple attribute decision-making method. Mathematics 7(4):346","journal-title":"Mathematics"},{"issue":"4","key":"7239_CR2","doi-asserted-by":"publisher","first-page":"1957","DOI":"10.3233\/IFS-151906","volume":"30","author":"M Ali","year":"2016","unstructured":"Ali M, Deli I, Smarandache F (2016) The theory of neutrosophic cubic sets and their applications in pattern recognition. J Intell Fuzzy Syst 30(4):1957\u20131963","journal-title":"J Intell Fuzzy Syst"},{"key":"7239_CR3","doi-asserted-by":"publisher","first-page":"11511","DOI":"10.1007\/s00500-019-04614-y","volume":"24","author":"F Amin","year":"2020","unstructured":"Amin F, Fahmi A, Aslam M (2020) Approaches to multiple attribute group decision making based on triangular cubic linguistic uncertain fuzzy aggregation operators. Soft Comput 24:11511\u201311533","journal-title":"Soft Comput"},{"key":"7239_CR4","doi-asserted-by":"publisher","first-page":"3331","DOI":"10.1007\/s00500-019-04096-y","volume":"24","author":"M Aslam","year":"2020","unstructured":"Aslam M, Fahmi A (2020) New work of trapezoidal cubic linguistic uncertain fuzzy Einstein hybrid weighted averaging operator and decision making. Soft Comput 24:3331\u20133354","journal-title":"Soft Comput"},{"issue":"1","key":"7239_CR5","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":"1","key":"7239_CR6","doi-asserted-by":"publisher","first-page":"33","DOI":"10.1016\/0165-0114(89)90215-7","volume":"33","author":"KT Atanassov","year":"1989","unstructured":"Atanassov KT (1989) More on intuitionistic fuzzy sets. Fuzzy Sets Syst 33(1):33\u201337","journal-title":"Fuzzy Sets Syst"},{"issue":"3","key":"7239_CR7","doi-asserted-by":"publisher","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(3):343\u2013349","journal-title":"Fuzzy Sets Syst"},{"issue":"9","key":"7239_CR8","doi-asserted-by":"publisher","first-page":"383","DOI":"10.3390\/sym10090383","volume":"10","author":"KY Bai","year":"2018","unstructured":"Bai KY, Zhu XM, Wang J, Zhang RT (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"},{"key":"7239_CR9","doi-asserted-by":"publisher","first-page":"198","DOI":"10.1016\/j.compind.2019.06.008","volume":"111","author":"WH Cui","year":"2019","unstructured":"Cui WH, Ye J (2019) Logarithmic similarity measure of dynamic neutrosophic cubic sets and its application in medical diagnosis. Comput Ind 111:198\u2013206","journal-title":"Comput Ind"},{"issue":"3","key":"7239_CR10","doi-asserted-by":"publisher","first-page":"2089","DOI":"10.1002\/int.22767","volume":"37","author":"H Garg","year":"2022","unstructured":"Garg H (2022) SVNMPR: A new single-valued neutrosophic multiplicative preference relation and their application to decision-making process. Int J Intell Syst 37(3):2089\u20132130","journal-title":"Int J Intell Syst"},{"issue":"1","key":"7239_CR11","first-page":"396","volume":"27","author":"H Garg","year":"2020","unstructured":"Garg H, Kaur G (2020) Extended TOPSIS method for multi-criteria group decision-making problems under cubic intuitionistic fuzzy environment. Sci Iran 27(1):396\u2013410","journal-title":"Sci Iran"},{"issue":"1","key":"7239_CR12","doi-asserted-by":"publisher","first-page":"179","DOI":"10.1007\/s40747-021-00339-4","volume":"8","author":"H Garg","year":"2022","unstructured":"Garg H, Kaur G (2022) Algorithm for solving the decision-making problems based on correlation coefficients under cubic intuitionistic fuzzy information: a case study in watershed hydrological system. Complex Intell Syst 8(1):179\u2013198","journal-title":"Complex Intell Syst"},{"issue":"6","key":"7239_CR13","first-page":"507","volume":"33","author":"H Garg","year":"2019","unstructured":"Garg H, Kaur G (2019) Cubic intuitionistic fuzzy sets and its fundamental properties. J Mult-Valued Log Soft Comput 33(6):507\u2013537","journal-title":"J Mult-Valued Log Soft Comput"},{"key":"7239_CR14","doi-asserted-by":"crossref","unstructured":"Gulistan M, Beg I, Yaqoob N (2018) Decision making problems under the environment of neutrosophic cubic soft matrices. J Intell Fuzzy Syst 1\u201313","DOI":"10.3233\/JIFS-181296"},{"key":"7239_CR15","doi-asserted-by":"crossref","unstructured":"Gulistan M, Mohammad M, Karaaslan F et al (2019) Neutrosophic cubic Heronian mean operators with applications in multiple attribute group decision-making using cosine similarity functions. Int J Distrib Sens N 15(9)","DOI":"10.1177\/1550147719877613"},{"issue":"2","key":"7239_CR16","doi-asserted-by":"publisher","first-page":"309","DOI":"10.1007\/s40747-019-00120-8","volume":"6","author":"M Gulistan","year":"2019","unstructured":"Gulistan M, Khan S (2019) Extentions of neutrosophic cubic sets via complex fuzzy sets with application. Complex Intell Syst 6(2):309\u2013320","journal-title":"Complex Intell Syst"},{"issue":"2","key":"7239_CR17","doi-asserted-by":"publisher","first-page":"371","DOI":"10.1007\/s10726-020-09658-2","volume":"29","author":"FF Jin","year":"2020","unstructured":"Jin FF, Ni ZW, Langari R et al (2020) Consistency improvement-driven decision-making methods with probabilistic multiplicative preference relations. Group Decis Negot 29(2):371\u2013397","journal-title":"Group Decis Negot"},{"issue":"4","key":"7239_CR18","doi-asserted-by":"publisher","first-page":"813","DOI":"10.1007\/s10726-021-09736-z","volume":"30","author":"FF Jin","year":"2021","unstructured":"Jin FF, Liu JP, Zhou LG et al (2021a) Consensus-based linguistic distribution large-scale group decision making using statistical inference and regret theory. Group Decis Negot 30(4):813\u2013845","journal-title":"Group Decis Negot"},{"key":"7239_CR19","doi-asserted-by":"publisher","DOI":"10.1016\/j.asoc.2021.107170","volume":"103","author":"FF Jin","year":"2021","unstructured":"Jin FF, Cao M, Liu JP et al (2021b) Consistency and trust relationship-driven social network group decision-making method with probabilistic linguistic information. Appl Soft Comput 103:107170","journal-title":"Appl Soft Comput"},{"issue":"1","key":"7239_CR20","first-page":"83","volume":"4","author":"YB Jun","year":"2011","unstructured":"Jun YB, Kim CS, Yang KO (2011) Cubic sets. Ann Fuzzy Math Inf 4(1):83\u201398","journal-title":"Ann Fuzzy Math Inf"},{"issue":"1","key":"7239_CR21","doi-asserted-by":"publisher","first-page":"41","DOI":"10.1142\/S1793005717500041","volume":"13","author":"YB Jun","year":"2017","unstructured":"Jun YB, Smarandache F, Kim CS (2017) Neutrosophic cubic sets. New Math Nat Comput 13(1):41\u201354","journal-title":"New Math Nat Comput"},{"key":"7239_CR22","first-page":"234","volume":"33","author":"H Kamaci","year":"2020","unstructured":"Kamaci H (2020) Neutrosophic cubic Hamacher aggregation operators and their applications in decision making. Neutrosophic Sets SyST 33:234\u2013255","journal-title":"Neutrosophic Sets SyST"},{"issue":"2","key":"7239_CR23","doi-asserted-by":"publisher","first-page":"247","DOI":"10.3390\/sym11020247","volume":"11","author":"M Khan","year":"2019","unstructured":"Khan M, Gulistan M, Yaqoob N et al (2019) Neutrosophic cubic einstein geometric aggregation operators with application to multi-criteria decision making method. Symmetry 11(2):247","journal-title":"Symmetry"},{"issue":"4","key":"7239_CR24","doi-asserted-by":"publisher","first-page":"496","DOI":"10.3390\/sym12040496","volume":"12","author":"M Khan","year":"2020","unstructured":"Khan M, Gulistan M, Ali M et al (2020) The generalized neutrosophic cubic aggregation operators and their application to multi-expert decision-making method. Symmetry 12(4):496","journal-title":"Symmetry"},{"issue":"1","key":"7239_CR25","first-page":"459","volume":"20","author":"W Li","year":"2016","unstructured":"Li W, Zhou XQ, Guo GQ (2016) Hesitant fuzzy Maclaurin symmetric mean operators and their application in multiple attribute decision making. J Comput Anal Appl 20(1):459\u2013469","journal-title":"J Comput Anal Appl"},{"key":"7239_CR26","doi-asserted-by":"publisher","first-page":"209","DOI":"10.1016\/j.ins.2020.05.131","volume":"538","author":"PD Liu","year":"2020","unstructured":"Liu PD, Li Y (2020) Multiattribute decision method for comprehensive logistics distribution center location selection based on 2-dimensional linguistic information. Inf Sci 538:209\u2013244","journal-title":"Inf Sci"},{"issue":"3","key":"7239_CR27","doi-asserted-by":"publisher","first-page":"2131","DOI":"10.1007\/s10462-019-09729-0","volume":"53","author":"PD Liu","year":"2020","unstructured":"Liu PD, You XL (2020) Linguistic neutrosophic partitioned Maclaurin symmetric mean operators based on clustering algorithm and their application to multi-criteria group decision-making. Artif Intell Rev 53(3):2131\u20132170","journal-title":"Artif Intell Rev"},{"key":"7239_CR28","doi-asserted-by":"publisher","first-page":"1971","DOI":"10.1007\/s00500-019-04025-z","volume":"24","author":"PD Liu","year":"2020","unstructured":"Liu PD, Khan Q, Mahmood T (2020a) Group decision making based on power Heronian aggregation operators under neutrosophic cubic environment. Soft Comput 24:1971\u20131997","journal-title":"Soft Comput"},{"key":"7239_CR29","doi-asserted-by":"publisher","first-page":"830","DOI":"10.1016\/j.ins.2019.10.013","volume":"512","author":"PD Liu","year":"2020","unstructured":"Liu PD, Chen SM, Wang YM (2020b) Multiattribute group decision making based on intuitionistic fuzzy partitioned Maclaurin symmetric mean operators. Inf Sci 512:830\u2013854","journal-title":"Inf Sci"},{"issue":"3","key":"7239_CR30","doi-asserted-by":"publisher","first-page":"1971","DOI":"10.1007\/s00500-019-04025-z","volume":"24","author":"P Liu","year":"2020","unstructured":"Liu P, Khan Q, Mahmood T (2020c) Group decision making based on power Heronian aggregation operators under neutrosophic cubic environment. Soft Comput 24(3):1971\u20131997","journal-title":"Soft Comput"},{"key":"7239_CR31","doi-asserted-by":"crossref","unstructured":"Maclaurin C (1729) A second letter to Martin Folkes, Esq; concerning the roots of equations, with demonstration of other rules of algebra. Philos Trans R Soc London Ser A 36:59\u201396","DOI":"10.1098\/rstl.1729.0011"},{"issue":"1","key":"7239_CR32","doi-asserted-by":"publisher","first-page":"19","DOI":"10.20454\/ijas.2016.1055","volume":"5","author":"F Mehmood","year":"2016","unstructured":"Mehmood F, Mahmood T, Khan Q (2016) Cubic hesitant fuzzy sets and their applications to multi criteria decision making. Int J Algebra Stat 5(1):19\u201351","journal-title":"Int J Algebra Stat"},{"issue":"4","key":"7239_CR33","doi-asserted-by":"publisher","first-page":"19","DOI":"10.1016\/S0898-1221(99)00056-5","volume":"37","author":"D Molodtsov","year":"1999","unstructured":"Molodtsov D (1999) Soft set theory - First results. Comput Math Appl 37(4):19\u201331","journal-title":"Comput Math Appl"},{"issue":"2","key":"7239_CR34","first-page":"291","volume":"8","author":"G Muhiuddin","year":"2014","unstructured":"Muhiuddin G, Al-Roqi AM (2014) Cubic soft sets with applications in BCK\/BCI-algebras. Ann Fuzzy Math Inf 8(2):291\u2013304","journal-title":"Ann Fuzzy Math Inf"},{"key":"7239_CR35","doi-asserted-by":"publisher","first-page":"639","DOI":"10.3233\/JIFS-179437","volume":"38","author":"H Nguyen","year":"2020","unstructured":"Nguyen H (2020) Some new operations on Atanassov\u2019s intuitionistic fuzzy sets in decision-making problems. J Intell Fuzzy Syst 38:639\u2013651","journal-title":"J Intell Fuzzy Syst"},{"key":"7239_CR36","first-page":"20","volume":"17","author":"S Pramanik","year":"2017","unstructured":"Pramanik S, Dey PP, Giri BC, Smarandache F (2017) An extended TOPSIS for multi-attribute decision making problems with neutrosophic cubic information. Neutrosophic Sets Syst 17:20\u201328","journal-title":"Neutrosophic Sets Syst"},{"issue":"5","key":"7239_CR37","doi-asserted-by":"publisher","first-page":"2177","DOI":"10.3233\/IFS-141182","volume":"27","author":"JD Qin","year":"2014","unstructured":"Qin JD, Liu XW (2014) An approach to intuitionistic fuzzy multiple attribute decision making based on Maclaurin symmetric mean operators. J Intell Fuzzy Syst 27(5):2177\u20132190","journal-title":"J Intell Fuzzy Syst"},{"issue":"1","key":"7239_CR38","doi-asserted-by":"publisher","first-page":"171","DOI":"10.3233\/IFS-151584","volume":"29","author":"JD Qin","year":"2015","unstructured":"Qin JD, Liu XW (2015) Approaches to uncertain linguistic multiple attribute decision making based on dual Maclaurin symmetric mean. J Intell Fuzzy Syst 29(1):171\u2013186","journal-title":"J Intell Fuzzy Syst"},{"key":"7239_CR39","first-page":"1","volume-title":"An unifying field in logics. Neutrosophy: Neutrosophic probability, set and logic","author":"F Smarandache","year":"1999","unstructured":"Smarandache F (1999) An unifying field in logics. Neutrosophy: Neutrosophic probability, set and logic. American Research Press, Rehoboth, pp 1\u2013141"},{"issue":"2","key":"7239_CR40","doi-asserted-by":"publisher","first-page":"191","DOI":"10.1016\/0165-0114(86)90077-1","volume":"20","author":"IB Turksen","year":"1986","unstructured":"Turksen IB (1986) Interval valued fuzzy sets based on normal forms. Fuzzy Set Syst 20(2):191\u2013210","journal-title":"Fuzzy Set Syst"},{"issue":"1","key":"7239_CR41","doi-asserted-by":"publisher","first-page":"503","DOI":"10.2991\/ijcis.d.201215.002","volume":"14","author":"L Wang","year":"2021","unstructured":"Wang L, Garg H (2021) Algorithm for multiple attribute decision-making with interactive archimedean norm operations under Pythagorean fuzzy uncertainty. Int J Comput Intell Syst 14(1):503\u2013527","journal-title":"Int J Comput Intell Syst"},{"key":"7239_CR42","first-page":"10","volume":"1","author":"HB Wang","year":"2010","unstructured":"Wang HB, Smarandache F, Zhang YQ, Sunderraman R (2010) Single valued neutrosophic sets. Rev Air Force Acad 1:10\u201314","journal-title":"Rev Air Force Acad"},{"issue":"5","key":"7239_CR43","doi-asserted-by":"publisher","first-page":"1529","DOI":"10.1007\/s00521-016-2747-0","volume":"30","author":"JQ Wang","year":"2018","unstructured":"Wang JQ, Yang Y, Li L (2018) Multi-criteria decision-making method based on single-valued neutrosophic linguistic Maclaurin symmetric mean operators. Neural Comput Appl 30(5):1529\u20131547","journal-title":"Neural Comput Appl"},{"key":"7239_CR44","unstructured":"Wang H, Smarandache F, Sunderraman R, Zhang YQ (2005) Interval neutrosophic sets and logic: Theory and applications in computing, Hexis, Phoenix, AZ."},{"issue":"22","key":"7239_CR45","doi-asserted-by":"publisher","first-page":"7435","DOI":"10.1007\/s00500-018-3194-x","volume":"22","author":"J Ye","year":"2018","unstructured":"Ye J (2018) Operations and aggregation method of neutrosophic cubic numbers for multiple attribute decision-making. Soft Comput 22(22):7435\u20137444","journal-title":"Soft Comput"},{"issue":"3","key":"7239_CR46","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"},{"key":"7239_CR47","doi-asserted-by":"publisher","first-page":"76","DOI":"10.1016\/j.ins.2019.03.018","volume":"488","author":"SZ Zeng","year":"2019","unstructured":"Zeng SZ, Chen MS, Kuo LW (2019) Multiattribute decision making based on novel score function of intuitionistic fuzzy values and modified VIKOR method. Inf Sci 488:76\u201392","journal-title":"Inf Sci"}],"container-title":["Soft Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00500-022-07239-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00500-022-07239-w\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00500-022-07239-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,10,21]],"date-time":"2022-10-21T05:05:09Z","timestamp":1666328709000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00500-022-07239-w"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,7,18]]},"references-count":47,"journal-issue":{"issue":"17","published-print":{"date-parts":[[2022,9]]}},"alternative-id":["7239"],"URL":"https:\/\/doi.org\/10.1007\/s00500-022-07239-w","relation":{},"ISSN":["1432-7643","1433-7479"],"issn-type":[{"type":"print","value":"1432-7643"},{"type":"electronic","value":"1433-7479"}],"subject":[],"published":{"date-parts":[[2022,7,18]]},"assertion":[{"value":"22 May 2022","order":1,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"18 July 2022","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"All the authors declare that they do not have any 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"}}]}}