{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,14]],"date-time":"2025-11-14T17:07:45Z","timestamp":1763140065935,"version":"3.45.0"},"reference-count":66,"publisher":"Springer Science and Business Media LLC","issue":"12","license":[{"start":{"date-parts":[[2025,10,29]],"date-time":"2025-10-29T00:00:00Z","timestamp":1761696000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0"},{"start":{"date-parts":[[2025,10,29]],"date-time":"2025-10-29T00:00:00Z","timestamp":1761696000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0"}],"funder":[{"DOI":"10.13039\/501100012695","name":"Sz\u00e9 Istv\u00e1n Egyetem","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100012695","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Complex Intell. Syst."],"published-print":{"date-parts":[[2025,12]]},"DOI":"10.1007\/s40747-025-02113-2","type":"journal-article","created":{"date-parts":[[2025,10,29]],"date-time":"2025-10-29T06:55:56Z","timestamp":1761720956000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A complete ranking principle for trapezoidal Hesitant fuzzy sets and its application in solving trapezoidal Hesitant fuzzy linear programming problems"],"prefix":"10.1007","volume":"11","author":[{"given":"Rakhi","family":"Bihari","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4374-1939","authenticated-orcid":false,"given":"S.","family":"Jeevaraj","sequence":"additional","affiliation":[]},{"given":"Dragan","family":"Pamucar","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,10,29]]},"reference":[{"issue":"13","key":"2113_CR1","doi-asserted-by":"crossref","first-page":"2972","DOI":"10.3390\/math11132972","volume":"11","author":"S Abdullah","year":"2023","unstructured":"Abdullah S, Almagrabi AO, Ali N (2023) A new method for commercial-scale water purification selection using linguistic neural networks. Mathematics 11(13):2972","journal-title":"Mathematics"},{"issue":"1","key":"2113_CR2","doi-asserted-by":"crossref","first-page":"61","DOI":"10.31181\/sor2120257","volume":"2","author":"A Alamin","year":"2025","unstructured":"Alamin A, Rahaman M, Mondal SP (2025) Geometric approach for solving first order non-homogenous fuzzy difference equation. Spectr Oper Res 2(1):61\u201371","journal-title":"Spectr Oper Res"},{"key":"2113_CR3","doi-asserted-by":"crossref","first-page":"232","DOI":"10.1016\/j.asoc.2015.09.035","volume":"38","author":"JCR Alcantud","year":"2016","unstructured":"Alcantud JCR, de Andr\u00e9s Calle R, Torrecillas MJM (2016) Hesitant fuzzy worth: an innovative ranking methodology for hesitant fuzzy subsets. Appl Soft Comput 38:232\u2013243","journal-title":"Appl Soft Comput"},{"key":"2113_CR4","doi-asserted-by":"crossref","first-page":"48","DOI":"10.1016\/j.inffus.2017.08.005","volume":"41","author":"JCR Alcantud","year":"2018","unstructured":"Alcantud JCR, Torra V (2018) Decomposition theorems and extension principles for hesitant fuzzy sets. Information Fusion 41:48\u201356","journal-title":"Information Fusion"},{"key":"2113_CR5","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1007\/s41872-018-0052-x","volume":"7","author":"SK Bharati","year":"2018","unstructured":"Bharati SK (2018) Solving optimization problems under hesitant fuzzy environment. Life Cycle Reliability and Safety Engineering 7:127\u2013136","journal-title":"Life Cycle Reliability and Safety Engineering"},{"issue":"5","key":"2113_CR6","doi-asserted-by":"crossref","first-page":"391","DOI":"10.1016\/j.omega.2004.07.003","volume":"33","author":"A Biswas","year":"2005","unstructured":"Biswas A, Pal BB (2005) Application of fuzzy goal programming technique to land use planning in agricultural system. Omega 33(5):391\u2013398","journal-title":"Omega"},{"issue":"4","key":"2113_CR7","doi-asserted-by":"crossref","first-page":"2197","DOI":"10.1016\/j.apm.2012.04.031","volume":"37","author":"N Chen","year":"2013","unstructured":"Chen N, Xu Z, Xia M (2013) Correlation coefficients of hesitant fuzzy sets and their applications to clustering analysis. Appl Math Model 37(4):2197\u20132211","journal-title":"Appl Math Model"},{"issue":"3","key":"2113_CR8","doi-asserted-by":"crossref","first-page":"6833","DOI":"10.1016\/j.eswa.2008.08.015","volume":"36","author":"SM Chen","year":"2009","unstructured":"Chen SM, Chen JH (2009) Fuzzy risk analysis based on ranking generalized fuzzy numbers with different heights and different spreads. Expert Syst Appl 36(3):6833\u20136842","journal-title":"Expert Syst Appl"},{"issue":"1","key":"2113_CR9","doi-asserted-by":"crossref","first-page":"687","DOI":"10.1007\/s40747-021-00535-2","volume":"8","author":"SK Das","year":"2022","unstructured":"Das SK (2022) An approach to optimize the cost of transportation problem based on triangular fuzzy programming problem. Complex & intelligent systems 8(1):687\u2013699","journal-title":"Complex & intelligent systems"},{"issue":"6","key":"2113_CR10","doi-asserted-by":"crossref","first-page":"613","DOI":"10.1080\/00207727808941724","volume":"9","author":"D Dubois","year":"1978","unstructured":"Dubois D, Prade H (1978) Operations on fuzzy numbers. Int J Syst Sci 9(6):613\u2013626","journal-title":"Int J Syst Sci"},{"issue":"8","key":"2113_CR11","doi-asserted-by":"crossref","first-page":"752","DOI":"10.1002\/int.21600","volume":"28","author":"B Farhadinia","year":"2013","unstructured":"Farhadinia B (2013) A novel method of ranking hesitant fuzzy values for multiple attribute decision-making problems. Int J Intell Syst 28(8):752\u2013767","journal-title":"Int J Intell Syst"},{"key":"2113_CR12","doi-asserted-by":"crossref","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","journal-title":"Inf Sci"},{"key":"2113_CR13","doi-asserted-by":"crossref","unstructured":"Goldani N, Ishizaka A (2024) A hybrid fuzzy multi-criteria group decision-making method and its application to healthcare waste treatment technology selection. Annals of Operations Research, 1\u201326","DOI":"10.1007\/s10479-024-06036-y"},{"key":"2113_CR14","doi-asserted-by":"crossref","unstructured":"Gonz\u00e1lez-Arteaga T, Alcantud JCR, de\u00a0Andr\u00e9s\u00a0Calle R (2015) New correlation coefficients for hesitant fuzzy sets. In: 2015 Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and Technology (IFSA-EUSFLAT-15), 427\u2013434. Atlantis Press","DOI":"10.2991\/ifsa-eusflat-15.2015.62"},{"issue":"6","key":"2113_CR15","first-page":"282","volume":"6","author":"X Gu","year":"2011","unstructured":"Gu X, Wang Y, Yang B (2011) A method for hesitant fuzzy multiple attribute decision making and its application to risk investment. J Converg Inf Technol 6(6):282\u2013287","journal-title":"J Converg Inf Technol"},{"issue":"6","key":"2113_CR16","doi-asserted-by":"crossref","first-page":"1968","DOI":"10.1007\/s40815-018-0496-1","volume":"20","author":"X Guan","year":"2018","unstructured":"Guan X, Sun G, Yi X, Zhou Z (2018) Synthetic correlation coefficient between hesitant fuzzy sets with applications. Int J Fuzzy Syst 20(6):1968\u20131985","journal-title":"Int J Fuzzy Syst"},{"issue":"2","key":"2113_CR17","first-page":"983","volume":"28","author":"G Hesamian","year":"2015","unstructured":"Hesamian G, Shams M (2015) Measuring similarity and ordering based on hesitant fuzzy linguistic term sets. Journal of Intelligent & Fuzzy Systems 28(2):983\u2013990","journal-title":"Journal of Intelligent & Fuzzy Systems"},{"issue":"1","key":"2113_CR18","doi-asserted-by":"crossref","first-page":"316","DOI":"10.31181\/sdmap31202644","volume":"3","author":"A Hussain","year":"2026","unstructured":"Hussain A, Raza CA, Ulllah K (2026) Advanced decision-making with complex q-rung orthopair fuzzy muirhead mean models. Spectrum of Decision Making and Applications 3(1):316\u2013338","journal-title":"Spectrum of Decision Making and Applications"},{"issue":"1","key":"2113_CR19","doi-asserted-by":"crossref","first-page":"41","DOI":"10.31181\/sor2120259","volume":"2","author":"J Kannan","year":"2025","unstructured":"Kannan J, Jayakumar V, Pethaperumal M (2025) Advanced fuzzy-based decision-making: the linear diophantine fuzzy codas method for logistic specialist selection. Spectrum of operational research 2(1):41\u201360","journal-title":"Spectrum of operational research"},{"issue":"12","key":"2113_CR20","doi-asserted-by":"crossref","first-page":"7709","DOI":"10.1002\/int.22604","volume":"36","author":"A Keikha","year":"2021","unstructured":"Keikha A (2021) Generalized hesitant fuzzy numbers: introducing, arithmetic operations, aggregation operators, and an application. Int J Intell Syst 36(12):7709\u20137730","journal-title":"Int J Intell Syst"},{"issue":"4","key":"2113_CR21","first-page":"3517","volume":"42","author":"IU Khan","year":"2022","unstructured":"Khan IU, Aftab M (2022) Dynamic programming approach for fuzzy linear programming problems flps and its application to optimal resource allocation problems in education system. Journal of Intelligent & Fuzzy Systems 42(4):3517\u20133535","journal-title":"Journal of Intelligent & Fuzzy Systems"},{"issue":"4","key":"2113_CR22","doi-asserted-by":"crossref","first-page":"2053","DOI":"10.1007\/s40747-021-00313-0","volume":"7","author":"R Kumar","year":"2021","unstructured":"Kumar R, Dhiman G, Kumar N, Chandrawat RK, Joshi V, Kaur A (2021) A novel approach to optimize the production cost of railway coaches of india using situational-based composite triangular and trapezoidal fuzzy lpp models. Complex & Intelligent Systems 7(4):2053\u20132068","journal-title":"Complex & Intelligent Systems"},{"issue":"1","key":"2113_CR23","doi-asserted-by":"crossref","first-page":"100","DOI":"10.31181\/sdmap31202641","volume":"3","author":"D Li","year":"2026","unstructured":"Li D, Wan G, Rong Y (2026) An enhanced spherical cubic fuzzy waspas method and its application for the assessment of service quality of crowdsourcing logistics platform. Spectrum of Decision Making and Applications 3(1):100\u2013123","journal-title":"Spectrum of Decision Making and Applications"},{"key":"2113_CR24","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1016\/j.ins.2015.03.076","volume":"321","author":"D Li","year":"2015","unstructured":"Li D, Zeng W, Zhao Y (2015) Note on distance measure of hesitant fuzzy sets. Inf Sci 321:103\u2013115","journal-title":"Inf Sci"},{"key":"2113_CR25","doi-asserted-by":"crossref","first-page":"223","DOI":"10.1016\/j.omega.2018.06.003","volume":"83","author":"Z Li","year":"2019","unstructured":"Li Z, Zhang Q, Liao H (2019) Efficient-equitable-ecological evaluation of regional water resource coordination considering both visible and virtual water. Omega 83:223\u2013235","journal-title":"Omega"},{"key":"2113_CR26","doi-asserted-by":"crossref","DOI":"10.1016\/j.omega.2019.03.010","volume":"93","author":"H Liao","year":"2020","unstructured":"Liao H, Wu X, Mi X, Herrera F (2020) An integrated method for cognitive complex multiple experts multiple criteria decision making based on electre iii with weighted borda rule. Omega 93:102052","journal-title":"Omega"},{"issue":"1","key":"2113_CR27","first-page":"65","volume":"27","author":"H Liao","year":"2014","unstructured":"Liao H, Xu Z (2014) Subtraction and division operations over hesitant fuzzy sets. Journal of intelligent & fuzzy systems 27(1):65\u201372","journal-title":"Journal of intelligent & fuzzy systems"},{"key":"2113_CR28","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1016\/j.knosys.2015.02.020","volume":"82","author":"H Liao","year":"2015","unstructured":"Liao H, Xu Z, Zeng X-J (2015) Novel correlation coefficients between hesitant fuzzy sets and their application in decision making. Knowl-Based Syst 82:115\u2013127","journal-title":"Knowl-Based Syst"},{"issue":"3","key":"2113_CR29","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1016\/0165-0114(92)90223-Q","volume":"50","author":"TS Liou","year":"1992","unstructured":"Liou TS, Wang MJJ (1992) Ranking fuzzy numbers with integral value. Fuzzy Sets Syst 50(3):247\u2013255","journal-title":"Fuzzy Sets Syst"},{"issue":"12","key":"2113_CR30","doi-asserted-by":"crossref","first-page":"153","DOI":"10.3390\/sym8120153","volume":"8","author":"X Liu","year":"2016","unstructured":"Liu X, Wang Z, Zhang S (2016) A modification on the hesitant fuzzy set lexicographical ranking method. Symmetry 8(12):153","journal-title":"Symmetry"},{"key":"2113_CR31","volume":"183","author":"X Liu","year":"2021","unstructured":"Liu X, Wang Z, Zhang S, Garg H (2021) Novel correlation coefficient between hesitant fuzzy sets with application to medical diagnosis. Expert Syst Appl 183:115393","journal-title":"Expert Syst Appl"},{"key":"2113_CR32","doi-asserted-by":"crossref","first-page":"445","DOI":"10.1007\/s12559-014-9313-9","volume":"7","author":"F Meng","year":"2015","unstructured":"Meng F, Chen X (2015) Correlation coefficients of hesitant fuzzy sets and their application based on fuzzy measures. Cogn Comput 7:445\u2013463","journal-title":"Cogn Comput"},{"key":"2113_CR33","doi-asserted-by":"crossref","first-page":"287","DOI":"10.1016\/j.ins.2014.02.012","volume":"267","author":"F Meng","year":"2014","unstructured":"Meng F, Chen X, Zhang Q (2014) Multi-attribute decision analysis under a linguistic hesitant fuzzy environment. Inf Sci 267:287\u2013305","journal-title":"Inf Sci"},{"issue":"4","key":"2113_CR34","doi-asserted-by":"crossref","first-page":"531","DOI":"10.1080\/01605682.2018.1447252","volume":"70","author":"F Meng","year":"2019","unstructured":"Meng F, Tang J (2019) New ranking order for linguistic hesitant fuzzy sets. Journal of the Operational Research Society 70(4):531\u2013540","journal-title":"Journal of the Operational Research Society"},{"key":"2113_CR35","doi-asserted-by":"crossref","first-page":"13","DOI":"10.58496\/BJM\/2024\/002","volume":"2024","author":"AK Oleiwi","year":"2024","unstructured":"Oleiwi AK, Saleh HM, Mahmood AM, AVCI I et al (2024) A survey of mcdm-based software engineering method. Babylonian Journal of Mathematics 2024:13\u201318","journal-title":"Babylonian Journal of Mathematics"},{"issue":"8","key":"2113_CR36","doi-asserted-by":"crossref","first-page":"5837","DOI":"10.1016\/j.apm.2012.11.016","volume":"37","author":"D-H Peng","year":"2013","unstructured":"Peng D-H, Gao C-Y, Gao Z-F (2013) Generalized hesitant fuzzy synergetic weighted distance measures and their application to multiple criteria decision-making. Appl Math Model 37(8):5837\u20135850","journal-title":"Appl Math Model"},{"key":"2113_CR37","doi-asserted-by":"crossref","first-page":"357","DOI":"10.1016\/j.knosys.2012.08.019","volume":"37","author":"G Qian","year":"2013","unstructured":"Qian G, Wang H, Feng X (2013) Generalized hesitant fuzzy sets and their application in decision support system. Knowl-Based Syst 37:357\u2013365","journal-title":"Knowl-Based Syst"},{"issue":"2","key":"2113_CR38","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1109\/TFUZZ.2019.2902109","volume":"28","author":"M Ranjbar","year":"2019","unstructured":"Ranjbar M, Effati S (2019) Symmetric and right-hand-side hesitant fuzzy linear programming. IEEE Trans Fuzzy Syst 28(2):215\u2013227","journal-title":"IEEE Trans Fuzzy Syst"},{"key":"2113_CR39","doi-asserted-by":"crossref","DOI":"10.1016\/j.engappai.2022.105047","volume":"114","author":"M Ranjbar","year":"2022","unstructured":"Ranjbar M, Effati S, Miri SM (2022) Fully hesitant fuzzy linear programming with hesitant fuzzy numbers. Eng Appl Artif Intell 114:105047","journal-title":"Eng Appl Artif Intell"},{"key":"2113_CR40","doi-asserted-by":"crossref","DOI":"10.1016\/j.eswa.2020.113363","volume":"151","author":"M Ranjbar","year":"2020","unstructured":"Ranjbar M, Miri SM, Effati S (2020) Hesitant fuzzy numbers with ($$\\alpha $$, k)-cuts in compact intervals and applications. Expert Syst Appl 151:113363","journal-title":"Expert Syst Appl"},{"issue":"6","key":"2113_CR41","doi-asserted-by":"crossref","first-page":"495","DOI":"10.1002\/int.21654","volume":"29","author":"RM Rodr\u00edguez","year":"2014","unstructured":"Rodr\u00edguez RM, Mart\u00ednez L, Torra V, Xu Z, Herrera F (2014) Hesitant fuzzy sets: state of the art and future directions. Int J Intell Syst 29(6):495\u2013524","journal-title":"Int J Intell Syst"},{"issue":"1","key":"2113_CR42","first-page":"137","volume":"20","author":"S Saghi","year":"2023","unstructured":"Saghi S, Nazemi A, Effati S, Ranjbar M (2023) Simplex algorithm for hesitant fuzzy linear programming problem with hesitant cost coefficient. Iranian Journal of Fuzzy Systems 20(1):137\u2013152","journal-title":"Iranian Journal of Fuzzy Systems"},{"issue":"1","key":"2113_CR43","doi-asserted-by":"crossref","first-page":"219","DOI":"10.31181\/sdmap21202525","volume":"2","author":"SK Sahoo","year":"2025","unstructured":"Sahoo SK, Pamucar D, Goswami SS (2025) A review of multi-criteria decision-making (mcdm) applications to solve energy management problems from 2010\u20132025: current state and future research. Spectrum of Decision Making and Applications 2(1):219\u2013241","journal-title":"Spectrum of Decision Making and Applications"},{"key":"2113_CR44","doi-asserted-by":"crossref","first-page":"521","DOI":"10.1016\/j.eswa.2017.09.048","volume":"92","author":"G Sun","year":"2018","unstructured":"Sun G, Guan X, Yi X, Zhou Z (2018) Grey relational analysis between hesitant fuzzy sets with applications to pattern recognition. Expert Syst Appl 92:521\u2013532","journal-title":"Expert Syst Appl"},{"issue":"4","key":"2113_CR45","doi-asserted-by":"crossref","first-page":"529","DOI":"10.1007\/s12559-019-9623-z","volume":"11","author":"G Sun","year":"2019","unstructured":"Sun G, Guan X, Yi X, Zhou Z (2019) Improvements on correlation coefficients of hesitant fuzzy sets and their applications. Cogn Comput 11(4):529\u2013544","journal-title":"Cogn Comput"},{"key":"2113_CR46","doi-asserted-by":"crossref","first-page":"16","DOI":"10.58496\/ADSA\/2023\/002","volume":"2023","author":"HM Talib","year":"2023","unstructured":"Talib HM, Albahri A, Thierry O (2023) Fuzzy decision-making framework for sensitively prioritizing autism patients with moderate emergency level. Applied Data Science and Analysis 2023:16\u201341","journal-title":"Applied Data Science and Analysis"},{"issue":"06","key":"2113_CR47","doi-asserted-by":"crossref","first-page":"1611","DOI":"10.1142\/S0219622017500304","volume":"16","author":"J Tang","year":"2017","unstructured":"Tang J, An Q, Meng F, Chen X (2017) A natural method for ranking objects from hesitant fuzzy preference relations. International Journal of Information Technology & Decision Making 16(06):1611\u20131646","journal-title":"International Journal of Information Technology & Decision Making"},{"key":"2113_CR48","doi-asserted-by":"crossref","unstructured":"Tomsovic K (2002) A fuzzy linear programming approach to the reactive power\/voltage control problem. IEEE Trans Power Syst 7(1):287\u2013293","DOI":"10.1109\/59.141716"},{"issue":"6","key":"2113_CR49","first-page":"529","volume":"25","author":"V Torra","year":"2010","unstructured":"Torra V (2010) Hesitant fuzzy sets. Int J Intell Syst 25(6):529\u2013539","journal-title":"Int J Intell Syst"},{"key":"2113_CR50","doi-asserted-by":"crossref","unstructured":"Torra V, Narukawa Y (2009) On hesitant fuzzy sets and decision. In: 2009 IEEE international conference on fuzzy systems, pp. 1378\u20131382. IEEE","DOI":"10.1109\/FUZZY.2009.5276884"},{"key":"2113_CR51","doi-asserted-by":"crossref","unstructured":"Wu Z, Xu J (2016) Managing consistency and consensus in group decision making with hesitant fuzzy linguistic preference relations. Omega 65:28\u201340","DOI":"10.1016\/j.omega.2015.12.005"},{"key":"2113_CR52","doi-asserted-by":"crossref","unstructured":"Xia M, Xu Z (2011) Hesitant fuzzy information aggregation in decision making. Int J Approximate Reasoning 52(3):395\u2013407","DOI":"10.1016\/j.ijar.2010.09.002"},{"issue":"11","key":"2113_CR53","doi-asserted-by":"crossref","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(11):2128\u20132138","journal-title":"Inf Sci"},{"issue":"5","key":"2113_CR54","doi-asserted-by":"crossref","first-page":"410","DOI":"10.1002\/int.20474","volume":"26","author":"Z Xu","year":"2011","unstructured":"Xu Z, Xia M (2011) On distance and correlation measures of hesitant fuzzy information. Int J Intell Syst 26(5):410\u2013425","journal-title":"Int J Intell Syst"},{"issue":"2","key":"2113_CR55","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1016\/0020-0255(81)90017-7","volume":"24","author":"RR Yager","year":"1981","unstructured":"Yager RR (1981) A procedure for ordering fuzzy subsets of the unit interval. Inf Sci 24(2):143\u2013161","journal-title":"Inf Sci"},{"key":"2113_CR56","volume":"183","author":"H Yang","year":"2023","unstructured":"Yang H, Xu G, Wang F, Zhang Y (2023) A clustering-based method for large-scale group decision making in the hesitant fuzzy set environment. Computers & Industrial Engineering 183:109526","journal-title":"Computers & Industrial Engineering"},{"issue":"11","key":"2113_CR57","doi-asserted-by":"publisher","first-page":"135","DOI":"10.4156\/jcit.vol8.issue11.16","volume":"8","author":"J Ye","year":"2013","unstructured":"Ye J (2013) Multicriteria decision-making method using expected values in trapezoidal hesitant fuzzy setting. J Converg Inf Technol 8(11):135. https:\/\/doi.org\/10.4156\/jcit.vol8.issue11.16","journal-title":"J Converg Inf Technol"},{"issue":"05","key":"2113_CR58","doi-asserted-by":"crossref","first-page":"1550035","DOI":"10.1142\/S0217595915500359","volume":"32","author":"S-M Yu","year":"2015","unstructured":"Yu S-M, Zhou H, Chen X-H, Wang J-Q (2015) A multi-criteria decision-making method based on heronian mean operators under a linguistic hesitant fuzzy environment. Asia-Pacific J Oper Res 32(05):1550035","journal-title":"Asia-Pacific J Oper Res"},{"issue":"3","key":"2113_CR59","first-page":"338","volume":"8","author":"LA Zadeh","year":"1965","unstructured":"Zadeh LA (1965) Information and control. Fuzzy sets 8(3):338\u2013353","journal-title":"Fuzzy sets"},{"issue":"3","key":"2113_CR60","doi-asserted-by":"crossref","first-page":"565","DOI":"10.15388\/Informatica.2017.145","volume":"28","author":"X Zhang","year":"2017","unstructured":"Zhang X (2017) A closeness index-based todim method for hesitant qualitative group decision making. Informatica 28(3):565\u2013581","journal-title":"Informatica"},{"issue":"9","key":"2113_CR61","doi-asserted-by":"crossref","first-page":"952","DOI":"10.3390\/su8090952","volume":"8","author":"X Zhang","year":"2016","unstructured":"Zhang X, Xu Z, Liu M (2016) Hesitant trapezoidal fuzzy qualiflex method and its application in the evaluation of green supply chain initiatives. Sustainability 8(9):952","journal-title":"Sustainability"},{"key":"2113_CR62","volume":"296","author":"Y Zhang","year":"2026","unstructured":"Zhang Y, Kong M, Wang WZ, Deveci M, Bilican MS, Delen D (2026) A multi-criteria decision-making framework for metaverse adoption: evidence from higher education systems. Expert Syst Appl 296:129132","journal-title":"Expert Syst Appl"},{"issue":"5","key":"2113_CR63","doi-asserted-by":"crossref","first-page":"661","DOI":"10.1080\/01605682.2017.1400780","volume":"69","author":"H Zhou","year":"2018","unstructured":"Zhou H, Wang J-Q, Zhang H-Y (2018) Multi-criteria decision-making approaches based on distance measures for linguistic hesitant fuzzy sets. Journal of the operational research Society 69(5):661\u2013675","journal-title":"Journal of the operational research Society"},{"issue":"2","key":"2113_CR64","doi-asserted-by":"crossref","first-page":"314","DOI":"10.1080\/00207721.2015.1042089","volume":"47","author":"H Zhou","year":"2016","unstructured":"Zhou H, Wang J-Q, Zhang H-Y, Chen X-H (2016) Linguistic hesitant fuzzy multi-criteria decision-making method based on evidential reasoning. Int J Syst Sci 47(2):314\u2013327","journal-title":"Int J Syst Sci"},{"key":"2113_CR65","unstructured":"Zhou X, Li Q (2012) Some new similarity measures for hesitant fuzzy sets and their applications in multiple attribute decision making. arXiv preprint arXiv:1211.4125"},{"issue":"8","key":"2113_CR66","doi-asserted-by":"crossref","first-page":"1328","DOI":"10.1109\/TCYB.2013.2283021","volume":"44","author":"B Zhu","year":"2013","unstructured":"Zhu B, Xu Z, Xu J (2013) Deriving a ranking from hesitant fuzzy preference relations under group decision making. IEEE Transactions on Cybernetics 44(8):1328\u20131337","journal-title":"IEEE Transactions on Cybernetics"}],"container-title":["Complex & Intelligent Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40747-025-02113-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s40747-025-02113-2\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40747-025-02113-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,11,14]],"date-time":"2025-11-14T17:01:58Z","timestamp":1763139718000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s40747-025-02113-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,10,29]]},"references-count":66,"journal-issue":{"issue":"12","published-print":{"date-parts":[[2025,12]]}},"alternative-id":["2113"],"URL":"https:\/\/doi.org\/10.1007\/s40747-025-02113-2","relation":{},"ISSN":["2199-4536","2198-6053"],"issn-type":[{"type":"print","value":"2199-4536"},{"type":"electronic","value":"2198-6053"}],"subject":[],"published":{"date-parts":[[2025,10,29]]},"assertion":[{"value":"17 April 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"13 September 2025","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"29 October 2025","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"}},{"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"}}],"article-number":"486"}}