{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,18]],"date-time":"2026-01-18T06:30:47Z","timestamp":1768717847809,"version":"3.49.0"},"reference-count":45,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2024,11,5]],"date-time":"2024-11-05T00:00:00Z","timestamp":1730764800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2024,11,5]],"date-time":"2024-11-05T00:00:00Z","timestamp":1730764800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["71871072"],"award-info":[{"award-number":["71871072"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Int. J. Mach. Learn. & Cyber."],"published-print":{"date-parts":[[2025,4]]},"DOI":"10.1007\/s13042-024-02395-x","type":"journal-article","created":{"date-parts":[[2024,11,5]],"date-time":"2024-11-05T07:05:53Z","timestamp":1730790353000},"page":"2335-2359","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Decision making based on AND-logical quantification of uncertainty in pairwise comparisons"],"prefix":"10.1007","volume":"16","author":[{"given":"Ya-Ru","family":"Chen","sequence":"first","affiliation":[]},{"given":"Fang","family":"Liu","sequence":"additional","affiliation":[]},{"given":"Ji-Ting","family":"Mo","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2024,11,5]]},"reference":[{"key":"2395_CR1","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-48318-9","volume-title":"Multiple attribute decision making: methods and applications a state of the art survey","author":"CL Hwang","year":"1981","unstructured":"Hwang CL, Yoon K (1981) Multiple attribute decision making: methods and applications a state of the art survey. Springer-Verlag, Berlin"},{"key":"2395_CR2","doi-asserted-by":"crossref","DOI":"10.1142\/p505","volume-title":"Multi-objective group decision making: methods, software and applications with fuzzy set techniques","author":"J Lu","year":"2007","unstructured":"Lu J, Zhang GQ, Ruan D, Wu F (2007) Multi-objective group decision making: methods, software and applications with fuzzy set techniques. Sinapore World Scientific Publishing Co., Pte. Ltd, Sinapore"},{"key":"2395_CR3","volume-title":"Multi-criteria decision making in maritime studies and logistics: applications and cases","author":"PTW Lee","year":"2018","unstructured":"Lee PTW, Yang Z (2018) Multi-criteria decision making in maritime studies and logistics: applications and cases. Springer, Cham"},{"key":"2395_CR4","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4757-3157-6","volume-title":"Multi-criteria decision-making methods: a comparative study","author":"E Triantaphyllou","year":"2000","unstructured":"Triantaphyllou E (2000) Multi-criteria decision-making methods: a comparative study. Kluwer Academic Publishers, Boston"},{"key":"2395_CR5","doi-asserted-by":"crossref","first-page":"294","DOI":"10.1016\/j.ejor.2020.05.048","volume":"288","author":"P Amenta","year":"2021","unstructured":"Amenta P, Lucadamo A, Marcarelli G (2021) On the choice of weights for aggregating judgments in non-negotiable AHP group decision making. Eur J Oper Res 288:294\u2013301","journal-title":"Eur J Oper Res"},{"key":"2395_CR6","volume-title":"The analytic hierarchy process","author":"TL Saaty","year":"1980","unstructured":"Saaty TL (1980) The analytic hierarchy process. McGraw-Hill, New York"},{"key":"2395_CR7","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4615-1665-1","volume-title":"Models, methods, concepts & applications of the analytic hierarchy process","author":"TL Saaty","year":"2001","unstructured":"Saaty TL, Vargas LG (2001) Models, methods, concepts & applications of the analytic hierarchy process. Springer US"},{"issue":"2","key":"2395_CR8","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1016\/0165-0114(84)90032-0","volume":"12","author":"T Tanino","year":"1984","unstructured":"Tanino T (1984) Fuzzy preference orderings in group decision making. Fuzzy Sets Syst 12(2):117\u2013131","journal-title":"Fuzzy Sets Syst"},{"issue":"3","key":"2395_CR9","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":"1","key":"2395_CR10","doi-asserted-by":"crossref","first-page":"144","DOI":"10.1016\/S0377-2217(98)00383-X","volume":"120","author":"F Herrera","year":"2000","unstructured":"Herrera F, Herrera-Viedma E (2000) Choice functions and mechanisms for linguistic preference relations. Eur J Oper Res 120(1):144\u2013161","journal-title":"Eur J Oper Res"},{"issue":"1","key":"2395_CR11","doi-asserted-by":"crossref","first-page":"191","DOI":"10.1109\/TSMC.2020.3043016","volume":"51","author":"E Herrera-Viedma","year":"2021","unstructured":"Herrera-Viedma E, Palomares I, Li CC, Cabrerizo FJ, Dong Y, Chiclana F, Herrera F (2021) Revisiting fuzzy and linguistic decision making: Scenarios and challenges for making wiser decisions in a better way. IEEE Trans Syst Man Cybern 51(1):191\u2013208","journal-title":"IEEE Trans Syst Man Cybern"},{"issue":"4","key":"2395_CR12","doi-asserted-by":"crossref","first-page":"301","DOI":"10.1016\/0020-0255(75)90046-8","volume":"8","author":"LA Zadeh","year":"1975","unstructured":"Zadeh LA (1975) The concept of a linguistic variable and its application to approximate reasoning-II. Inf Sci 8(4):301\u2013357","journal-title":"Inf Sci"},{"issue":"1\u20133","key":"2395_CR13","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1016\/S0165-0114(83)80082-7","volume":"11","author":"PJM van Laarhoven","year":"1983","unstructured":"van Laarhoven PJM, Pedrycz W (1983) A fuzzy extension of Saaty\u2019s priority theory. Fuzzy Sets Syst 11(1\u20133):229\u2013241","journal-title":"Fuzzy Sets Syst"},{"key":"2395_CR14","doi-asserted-by":"crossref","first-page":"85","DOI":"10.1016\/j.fss.2020.07.006","volume":"409","author":"SP Wan","year":"2021","unstructured":"Wan SP, Cheng XJ, Chen CX, Dong JY (2021) L-R geometric consistency definition of triangular multiplicative preference relation in group decision making. Fuzzy Sets Syst 409:85\u2013113","journal-title":"Fuzzy Sets Syst"},{"key":"2395_CR15","doi-asserted-by":"crossref","first-page":"1055","DOI":"10.1007\/s13042-023-01955-x","volume":"15","author":"YY Zhou","year":"2024","unstructured":"Zhou YY, Zheng CL, Wu P, Zhou LG (2024) A new compatibility model for fuzzy group decision making by using trapezoidal fuzzy preference relations with COWA operator. Int J Mach Learn Cybern 15:1055\u20131073","journal-title":"Int J Mach Learn Cybern"},{"issue":"1","key":"2395_CR16","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1016\/0377-2217(87)90275-X","volume":"32","author":"TL Saaty","year":"1987","unstructured":"Saaty TL, Vargas LG (1987) Uncertainty and rank order in the analytic hierarchy process. Eur J Oper Res 32(1):107\u2013117","journal-title":"Eur J Oper Res"},{"key":"2395_CR17","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1016\/j.fss.2020.06.010","volume":"409","author":"XJ Cheng","year":"2021","unstructured":"Cheng XJ, Wan SP, Dong JY (2021) A new consistency definition of interval multiplicative preference relation. Fuzzy Sets Syst 409:55\u201384","journal-title":"Fuzzy Sets Syst"},{"key":"2395_CR18","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1016\/j.omega.2016.05.006","volume":"68","author":"FY Meng","year":"2017","unstructured":"Meng FY, Tan CQ, Chen XH (2017) Multiplicative consistency analysis for interval fuzzy preference relations: a comparative study. Omega 68:17\u201338","journal-title":"Omega"},{"issue":"1","key":"2395_CR19","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1007\/s10726-014-9383-9","volume":"24","author":"MM Xia","year":"2015","unstructured":"Xia MM, Chen J (2015) Studies on interval multiplicative preference relations and their application to group decision making. Group Decis Negot 24(1):115\u2013144","journal-title":"Group Decis Negot"},{"key":"2395_CR20","doi-asserted-by":"crossref","first-page":"108","DOI":"10.1016\/j.knosys.2016.10.005","volume":"114","author":"YC Dong","year":"2016","unstructured":"Dong YC, Li CC, Chiclana F, Herrera-Viedma E (2016) Average-case consistency measurement and analysis of interval-valued reciprocal preference relations. Knowl Based Syst 114:108\u2013117","journal-title":"Knowl Based Syst"},{"issue":"3","key":"2395_CR21","first-page":"783","volume":"19","author":"J Krejc\u0306\u00ed","year":"2019","unstructured":"Krejc\u0306\u00ed J (2019) On extension of multiplicative consistency to interval fuzzy preference relations. Oper Res 19(3):783\u2013815","journal-title":"Oper Res"},{"issue":"3","key":"2395_CR22","doi-asserted-by":"crossref","first-page":"217","DOI":"10.1023\/B:FODM.0000036864.33950.1b","volume":"3","author":"ZS Xu","year":"2004","unstructured":"Xu ZS (2004) On compatibility of interval fuzzy preference relations. Fuzzy Optim Decis Making 3(3):217\u2013225","journal-title":"Fuzzy Optim Decis Making"},{"key":"2395_CR23","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-29127-2","volume-title":"On intuitionistic fuzzy sets theory","author":"KT Atanassov","year":"2012","unstructured":"Atanassov KT (2012) On intuitionistic fuzzy sets theory. Springer, Berlin"},{"key":"2395_CR24","volume-title":"Decision and game theory in management with intuitionistic fuzzy sets","author":"DF Li","year":"2014","unstructured":"Li DF (2014) Decision and game theory in management with intuitionistic fuzzy sets. Springer, Berlin"},{"key":"2395_CR25","volume-title":"Intuitionistic preference modeling and interactive decision making","author":"ZS Xu","year":"2014","unstructured":"Xu ZS (2014) Intuitionistic preference modeling and interactive decision making. Springer, Berlin Heidelberg"},{"issue":"6","key":"2395_CR26","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":"2395_CR27","doi-asserted-by":"crossref","DOI":"10.1007\/978-94-011-3534-4","volume-title":"Rough sets: theoretical aspects of reasoning about data","author":"Z Pawlak","year":"1991","unstructured":"Pawlak Z (1991) Rough sets: theoretical aspects of reasoning about data. Springer Science & Business Media"},{"key":"2395_CR28","volume-title":"Possibility theory","author":"D Dubois","year":"1988","unstructured":"Dubois D, Prade H (1988) Possibility theory. Plenum Press, New York"},{"key":"2395_CR29","volume-title":"Uncertainty theory","author":"BD Liu","year":"2017","unstructured":"Liu BD (2017) Uncertainty theory, 5th edn. Uncertainty Theory Laboratory","edition":"5"},{"issue":"5","key":"2395_CR30","doi-asserted-by":"crossref","first-page":"288","DOI":"10.1016\/S0167-6911(82)80025-X","volume":"1","author":"JL Deng","year":"1982","unstructured":"Deng JL (1982) Control problems of grey systems. Syst Control Lett 1(5):288\u2013294","journal-title":"Syst Control Lett"},{"key":"2395_CR31","doi-asserted-by":"crossref","DOI":"10.1016\/j.omega.2019.06.008","volume":"97","author":"A Hocine","year":"2020","unstructured":"Hocine A, Kouaissah N (2020) XOR analytic hierarchy process and its application in the renewable energy sector. Omega 97:102082","journal-title":"Omega"},{"key":"2395_CR32","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1016\/j.matcom.2022.12.030","volume":"207","author":"F Liu","year":"2023","unstructured":"Liu F, Chen YR, Zhou DH (2023) A two-dimensional approach to flexibility degree of XOR numbers with application to group decision making. Math Comput Simul 207:267\u2013287","journal-title":"Math Comput Simul"},{"key":"2395_CR33","volume-title":"Interval analysis","author":"RE Moore","year":"1966","unstructured":"Moore RE (1966) Interval analysis. Prentice-Hall, Englewood Cliffs"},{"issue":"1\u20132","key":"2395_CR34","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1007\/s10479-016-2166-8","volume":"248","author":"M Brunelli","year":"2017","unstructured":"Brunelli M (2017) Studying a set of properties of inconsistency indices for pairwise comparisons. Ann Oper Res 248(1\u20132):143\u2013161","journal-title":"Ann Oper Res"},{"issue":"1","key":"2395_CR35","doi-asserted-by":"crossref","first-page":"225","DOI":"10.1016\/j.ejor.2013.10.019","volume":"235","author":"G Kou","year":"2014","unstructured":"Kou G, Lin C (2014) A cosine maximization method for the priority vector derivation in AHP. Eur J Oper Res 235(1):225\u2013232","journal-title":"Eur J Oper Res"},{"key":"2395_CR36","volume":"94","author":"F Liu","year":"2020","unstructured":"Liu F, Zhang JW, Zou SC (2020) A decision making model based on the leading principal submatrices of a reciprocal preference relation. Appl Soft Comput 94:106448","journal-title":"Appl Soft Comput"},{"key":"2395_CR37","doi-asserted-by":"crossref","first-page":"1226","DOI":"10.1057\/palgrave.jors.2600474","volume":"48","author":"J Barzilai","year":"1997","unstructured":"Barzilai J (1997) Deriving weights from pairwise comparison matrices. J Oper Res Soc 48:1226\u20131232","journal-title":"J Oper Res Soc"},{"issue":"3\u20135","key":"2395_CR38","doi-asserted-by":"crossref","first-page":"327","DOI":"10.1016\/0270-0255(87)90489-1","volume":"9","author":"GB Crawford","year":"1987","unstructured":"Crawford GB (1987) The geometric mean procedure for estimating the scale of a judgment matrix. Math Model 9(3\u20135):327\u2013334","journal-title":"Math Model"},{"issue":"4","key":"2395_CR39","doi-asserted-by":"crossref","first-page":"387","DOI":"10.1080\/07900629948682","volume":"15","author":"AT Wolf","year":"1999","unstructured":"Wolf AT, Natharius JA, Danielson JJ, Ward BS, Pender JK (1999) International river basins of the world. Int J Water Resour D 15(4):387\u2013427","journal-title":"Int J Water Resour D"},{"issue":"6","key":"2395_CR40","doi-asserted-by":"crossref","first-page":"343","DOI":"10.2166\/aqua.2011.016","volume":"60","author":"E Cabrera","year":"2011","unstructured":"Cabrera E, Cobacho R, Estruch V, Aznar J (2011) Analytical hierarchical process (AHP) as a decision support tool in water resources management. J Water Supply Res T 60(6):343\u2013351","journal-title":"J Water Supply Res T"},{"issue":"5","key":"2395_CR41","doi-asserted-by":"crossref","first-page":"909","DOI":"10.1007\/s11269-006-9108-1","volume":"21","author":"E Kampragou","year":"2007","unstructured":"Kampragou E, Eleftheriadou E, Mylopoulos Y (2007) Implementing equitable water allocation in transboundary catchments: The case of river nestos\/Mesta. Water Resour Manag 21(5):909\u2013918","journal-title":"Water Resour Manag"},{"issue":"12","key":"2395_CR42","doi-asserted-by":"crossref","first-page":"4001","DOI":"10.1007\/s11269-014-0723-y","volume":"28","author":"Z Srdjevic","year":"2014","unstructured":"Srdjevic Z, Srdjevic B (2014) Modelling multicriteria decision making process for sharing benefits from the reservoir at Serbia-Romania border. Water Resour Manag 28(12):4001\u20134018","journal-title":"Water Resour Manag"},{"key":"2395_CR43","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1016\/j.asoc.2014.08.062","volume":"25","author":"ZM Zhang","year":"2014","unstructured":"Zhang ZM, Wu C (2014) Deriving the priority weights from hesitant multiplicative preference relations in group decision making. Appl Soft Comput 25:107\u2013117","journal-title":"Appl Soft Comput"},{"key":"2395_CR44","volume-title":"The analytic network process","author":"TL Saaty","year":"2001","unstructured":"Saaty TL (2001) The analytic network process. RWS Publications, Pittsburgh"},{"key":"2395_CR45","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1016\/j.omega.2014.11.009","volume":"53","author":"J Rezaei","year":"2015","unstructured":"Rezaei J (2015) Best-worst multi-criteria decision-making method. Omega 53:49\u201357","journal-title":"Omega"}],"container-title":["International Journal of Machine Learning and Cybernetics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s13042-024-02395-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s13042-024-02395-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s13042-024-02395-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,4,7]],"date-time":"2025-04-07T07:32:44Z","timestamp":1744011164000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s13042-024-02395-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,11,5]]},"references-count":45,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2025,4]]}},"alternative-id":["2395"],"URL":"https:\/\/doi.org\/10.1007\/s13042-024-02395-x","relation":{},"ISSN":["1868-8071","1868-808X"],"issn-type":[{"value":"1868-8071","type":"print"},{"value":"1868-808X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,11,5]]},"assertion":[{"value":"2 May 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"20 September 2024","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"5 November 2024","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"No conflict of interest exists.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}},{"value":"This article does not contain any studies with human participants performed by any of the authors.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Research involving human participants and\/or animals"}},{"value":"Not applicable.","order":4,"name":"Ethics","group":{"name":"EthicsHeading","label":"Informed consent"}}]}}