{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,6]],"date-time":"2025-12-06T21:50:28Z","timestamp":1765057828786},"reference-count":42,"publisher":"Springer Science and Business Media LLC","issue":"18","license":[{"start":{"date-parts":[[2023,5,29]],"date-time":"2023-05-29T00:00:00Z","timestamp":1685318400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,5,29]],"date-time":"2023-05-29T00:00:00Z","timestamp":1685318400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Appl Intell"],"published-print":{"date-parts":[[2023,9]]},"DOI":"10.1007\/s10489-023-04653-x","type":"journal-article","created":{"date-parts":[[2023,5,29]],"date-time":"2023-05-29T15:01:40Z","timestamp":1685372500000},"page":"21283-21298","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["A reference ideal model with evidential reasoning for probabilistic-based expressions"],"prefix":"10.1007","volume":"53","author":[{"given":"Yue","family":"He","sequence":"first","affiliation":[]},{"given":"Dongling","family":"Xu","sequence":"additional","affiliation":[]},{"given":"Jianbo","family":"Yang","sequence":"additional","affiliation":[]},{"given":"Zeshui","family":"Xu","sequence":"additional","affiliation":[]},{"given":"Nana","family":"Liu","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2023,5,29]]},"reference":[{"key":"4653_CR1","unstructured":"Zhu B (2014) Decision making methods and applications. Southeast University"},{"key":"4653_CR2","doi-asserted-by":"publisher","first-page":"481","DOI":"10.1007\/s10700-016-9257-5","volume":"16","author":"ZS Xu","year":"2017","unstructured":"Xu ZS, Zhou W (2017) Consensus building with a group of decision makers under the hesitant probabilistic fuzzy environment. Fuzzy Optim Decis Mak 16:481\u2013503. https:\/\/doi.org\/10.1007\/s10700-016-9257-5","journal-title":"Fuzzy Optim Decis Mak"},{"key":"4653_CR3","doi-asserted-by":"publisher","first-page":"2523","DOI":"10.3233\/JIFS-16503","volume":"32","author":"J Ding","year":"2017","unstructured":"Ding J, Xu ZS, Zhao N (2017) An interactive approach to probabilistic hesitant fuzzy multi-attribute group decision making with incomplete weight information. J Intell Fuzzy Syst 32:2523\u20132536. https:\/\/doi.org\/10.3233\/JIFS-16503","journal-title":"J Intell Fuzzy Syst"},{"key":"4653_CR4","doi-asserted-by":"publisher","unstructured":"Guo J, Yin JL, Zhang L, et al (2020) Extended TODIM method for CCUS storage site selection under probabilistic hesitant fuzzy environment. Appl Soft Comput 93:106381. https:\/\/doi.org\/10.1016\/j.asoc.2020.106381","DOI":"10.1016\/j.asoc.2020.106381"},{"key":"4653_CR5","doi-asserted-by":"publisher","first-page":"2319","DOI":"10.1007\/s40815-020-00944-4","volume":"22","author":"FF Jin","year":"2020","unstructured":"Jin FF, Garg H, Pei LD et al (2020) Multiplicative consistency adjustment model and data envelopment analysis-driven decision-making process with probabilistic hesitant fuzzy preference relations. Int J Fuzzy Syst 22:2319\u20132332. https:\/\/doi.org\/10.1007\/s40815-020-00944-4","journal-title":"Int J Fuzzy Syst"},{"key":"4653_CR6","doi-asserted-by":"publisher","unstructured":"Liu JP, Huang C, Song JS, et al (2021) Group decision making based on the modified probability calculation method and DEA cross-efficiency with probabilistic hesitant fuzzy preference relations. Comput Ind Eng 156:107262. https:\/\/doi.org\/10.1016\/j.cie.2021.107262","DOI":"10.1016\/j.cie.2021.107262"},{"key":"4653_CR7","doi-asserted-by":"publisher","first-page":"7665","DOI":"10.1002\/int.22527","volume":"36","author":"LX Di","year":"2021","unstructured":"Di LX, Wang ZW, Zhang ST, Garg H (2021) An approach to probabilistic hesitant fuzzy risky multiattribute decision making with unknown probability information. Int J Intell Syst 36:7665\u20137684. https:\/\/doi.org\/10.1002\/int.22527","journal-title":"Int J Intell Syst"},{"key":"4653_CR8","doi-asserted-by":"publisher","unstructured":"Garg H, Krishankumar R, Ravichandran KS (2022) Decision framework with integrated methods for group decision-making under probabilistic hesitant fuzzy context and unknown weights. Expert Syst Appl 200:117082. https:\/\/doi.org\/10.1016\/j.eswa.2022.117082","DOI":"10.1016\/j.eswa.2022.117082"},{"key":"4653_CR9","doi-asserted-by":"publisher","unstructured":"Pang Q, Wang H, Xu ZS (2016) Probabilistic linguistic term sets in multi-attribute group decision making. Inf Sci (Ny) 369:128\u2013143. https:\/\/doi.org\/10.1016\/j.ins.2016.06.021","DOI":"10.1016\/j.ins.2016.06.021"},{"key":"4653_CR10","doi-asserted-by":"publisher","unstructured":"Zhang YX, Xu ZS, Wang H, Liao HC (2016) Consistency-based risk assessment with probabilistic linguistic preference relation. Appl Soft Comput 49:817\u2013833. https:\/\/doi.org\/10.1016\/j.asoc.2016.08.045","DOI":"10.1016\/j.asoc.2016.08.045"},{"key":"4653_CR11","doi-asserted-by":"publisher","first-page":"2002","DOI":"10.1111\/itor.13049","volume":"29","author":"S Yu","year":"2022","unstructured":"Yu S, Du Z, Zhang X (2022) Clustering analysis and punishment-driven consensus-reaching process for probabilistic linguistic large-group decision-making with application to car-sharing platform selection. Int Trans Oper Res 29:2002\u20132029. https:\/\/doi.org\/10.1111\/itor.13049","journal-title":"Int Trans Oper Res"},{"key":"4653_CR12","doi-asserted-by":"publisher","unstructured":"You XL, Hou FJ (2022) A self-confidence and leadership based feedback mechanism for consensus of group decision making with probabilistic linguistic preference relation. Inf Sci (Ny) 582:547\u2013572. https:\/\/doi.org\/10.1016\/j.ins.2021.09.044","DOI":"10.1016\/j.ins.2021.09.044"},{"key":"4653_CR13","doi-asserted-by":"publisher","unstructured":"Du YF, Liu D (2021) An integrated method for multi-granular probabilistic linguistic multiple attribute decision-making with prospect theory. Comput Ind Eng 159:107500. https:\/\/doi.org\/10.1016\/j.cie.2021.107500","DOI":"10.1016\/j.cie.2021.107500"},{"key":"4653_CR14","doi-asserted-by":"publisher","unstructured":"Zhang YX, Hao ZN, Xu ZS, et al (2021) A process-oriented probabilistic linguistic decision-making model with unknown attribute weights. Knowledge-Based Syst 235:107594. https:\/\/doi.org\/10.1016\/j.knosys.2021.107594","DOI":"10.1016\/j.knosys.2021.107594"},{"key":"4653_CR15","doi-asserted-by":"publisher","DOI":"10.1515\/9780691214696","volume-title":"Mathematical theory of evidence","author":"GA Shafer","year":"1976","unstructured":"Shafer GA (1976) Mathematical theory of evidence. Princeton University Press, Princeton"},{"key":"4653_CR16","doi-asserted-by":"publisher","first-page":"289","DOI":"10.1109\/TSMCA.2002.802746","volume":"32","author":"J-B Yang","year":"2002","unstructured":"Yang J-B, Xu D-L (2002) On the evidential reasoning algorithm for multiple attribute decision analysis under uncertainty. IEEE Trans Syst Man, Cybern - Part A Syst Humans 32:289\u2013304. https:\/\/doi.org\/10.1109\/TSMCA.2002.802746","journal-title":"IEEE Trans Syst Man, Cybern - Part A Syst Humans"},{"key":"4653_CR17","doi-asserted-by":"publisher","first-page":"376","DOI":"10.1109\/TSMCA.2002.802809","volume":"32","author":"J-B Yang","year":"2002","unstructured":"Yang J-B, Xu D-L (2002) Nonlinear information aggregation via evidential reasoning in multiattribute decision analysis under uncertainty. IEEE Trans Syst Man, Cybern - Part A Syst Humans 32:376\u2013393. https:\/\/doi.org\/10.1109\/TSMCA.2002.802809","journal-title":"IEEE Trans Syst Man, Cybern - Part A Syst Humans"},{"key":"4653_CR18","doi-asserted-by":"publisher","first-page":"266","DOI":"10.1109\/TSMCA.2005.851270","volume":"36","author":"J-B Yang","year":"2006","unstructured":"Yang J-B, Liu J, Wang J et al (2006) Belief rule-base inference methodology using the evidential reasoning approach-RIMER. IEEE Trans Syst Man, Cybern - Part A Syst Humans 36:266\u2013285. https:\/\/doi.org\/10.1109\/TSMCA.2005.851270","journal-title":"IEEE Trans Syst Man, Cybern - Part A Syst Humans"},{"key":"4653_CR19","doi-asserted-by":"publisher","unstructured":"Wang Y-M, Yang J-B, Xu D-L, Chin K-S (2006) The evidential reasoning approach for multiple attribute decision analysis using interval belief degrees. Eur J Oper Res 175:35\u201366. https:\/\/doi.org\/10.1016\/j.ejor.2005.03.034","DOI":"10.1016\/j.ejor.2005.03.034"},{"key":"4653_CR20","doi-asserted-by":"publisher","unstructured":"Wang Y-M, Yang J-B, Xu D-L, Chin K-S (2007) On the combination and normalization of interval-valued belief structures. Inf Sci (Ny) 177:1230\u20131247. https:\/\/doi.org\/10.1016\/j.ins.2006.07.025","DOI":"10.1016\/j.ins.2006.07.025"},{"key":"4653_CR21","doi-asserted-by":"publisher","first-page":"683","DOI":"10.1109\/TFUZZ.2008.928599","volume":"17","author":"M Guo","year":"2009","unstructured":"Guo M, Yang J-B, Chin K-S et al (2009) Evidential reasoning approach for multiattribute decision analysis under both fuzzy and interval uncertainty. IEEE Trans Fuzzy Syst 17:683\u2013697. https:\/\/doi.org\/10.1109\/TFUZZ.2008.928599","journal-title":"IEEE Trans Fuzzy Syst"},{"key":"4653_CR22","doi-asserted-by":"publisher","first-page":"142","DOI":"10.1016\/j.knosys.2017.12.013","volume":"143","author":"M Zhou","year":"2018","unstructured":"Zhou M, Liu B-X, Chen Y-W, Yang J-B (2018) Evidential reasoning rule for MADM with both weights and reliabilities in group decision making. Knowledge-Based Syst 143:142\u2013161. https:\/\/doi.org\/10.1016\/j.knosys.2017.12.013","journal-title":"Knowledge-Based Syst"},{"key":"4653_CR23","doi-asserted-by":"crossref","unstructured":"Wang H, Zhang H-T (2018) Multi-attribute group decision-making based on the evidential reasoning with different probabilistic linguistic term sets. In: 2018 International Conference on Applied Mechanics, Mathematics, Modeling and Simulation. pp 209\u2013216","DOI":"10.12783\/dtcse\/ammms2018\/27258"},{"key":"4653_CR24","doi-asserted-by":"publisher","first-page":"584","DOI":"10.1007\/s40815-020-00967-x","volume":"23","author":"R Fang","year":"2020","unstructured":"Fang R, Liao HC (2020) A prospect theory-based evidential reasoning approach for multi-expert multi-criteria decision-making with uncertainty considering the psychological cognition of experts. Int J Fuzzy Syst 23:584\u2013598. https:\/\/doi.org\/10.1007\/s40815-020-00967-x","journal-title":"Int J Fuzzy Syst"},{"key":"4653_CR25","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1109\/TSMC.2018.2815716","volume":"99","author":"ZZ Ma","year":"2018","unstructured":"Ma ZZ, Zhu JJ, Chen Y (2018) A probabilistic linguistic group decision-making method from a reliability perspective based on evidential reasoning. IEEE Trans Syst Man, Cybern Syst 99:1\u201315. https:\/\/doi.org\/10.1109\/TSMC.2018.2815716","journal-title":"IEEE Trans Syst Man, Cybern Syst"},{"key":"4653_CR26","doi-asserted-by":"publisher","unstructured":"Qin JD, Xi Y, Pedrycz W (2020) Failure mode and effects analysis (FMEA) for risk assessment based on interval type-2 fuzzy evidential reasoning method. Appl Soft Comput 89:106134. https:\/\/doi.org\/10.1016\/j.asoc.2020.106134","DOI":"10.1016\/j.asoc.2020.106134"},{"key":"4653_CR27","doi-asserted-by":"publisher","first-page":"3607","DOI":"10.1109\/TFUZZ.2021.3079495","volume":"29","author":"YL Dong","year":"2021","unstructured":"Dong YL, De LX, Dezert J et al (2021) Evidential reasoning with hesitant fuzzy belief structures for human activity recognition. IEEE Trans Fuzzy Syst 29:3607\u20133619. https:\/\/doi.org\/10.1109\/TFUZZ.2021.3079495","journal-title":"IEEE Trans Fuzzy Syst"},{"key":"4653_CR28","doi-asserted-by":"publisher","unstructured":"Dymova L, Kaczmarek K, Sevastjanov P (2022) An extension of rule base evidential reasoning in the interval-valued intuitionistic fuzzy setting applied to the type 2 diabetes diagnostic. Expert Syst Appl 201:117100. https:\/\/doi.org\/10.1016\/j.eswa.2022.117100","DOI":"10.1016\/j.eswa.2022.117100"},{"key":"4653_CR29","doi-asserted-by":"publisher","unstructured":"Zhang S, Xu ZS, He Y (2017) Operations and integrations of probabilistic hesitant fuzzy information in decision making. Inf Fusion 38:1\u201311. https:\/\/doi.org\/10.1016\/j.inffus.2017.02.001","DOI":"10.1016\/j.inffus.2017.02.001"},{"key":"4653_CR30","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1109\/21.259681","volume":"24","author":"JB Yang","year":"1994","unstructured":"Yang JB, Singh MG (1994) An evidential reasoning approach for multiple-attribute decision making with uncertainty. IEEE Trans Syst Man Cybern 24:1\u201318. https:\/\/doi.org\/10.1109\/21.259681","journal-title":"IEEE Trans Syst Man Cybern"},{"key":"4653_CR31","doi-asserted-by":"publisher","first-page":"1458","DOI":"10.1109\/21.310529","volume":"24","author":"J-B Yang","year":"1994","unstructured":"Yang J-B, Sen P (1994) A general multi-level evaluation process for hybrid MADM with uncertainty. IEEE Trans Syst Man Cybern 24:1458\u20131473. https:\/\/doi.org\/10.1109\/21.310529","journal-title":"IEEE Trans Syst Man Cybern"},{"key":"4653_CR32","first-page":"180","volume-title":"International Conference on Belief Functions","author":"J-B Yang","year":"2014","unstructured":"Yang J-B, Xu D-L (2014) A study on generalising bayesian inference to evidential reasoning. In: Cuzzolin F (ed) International Conference on Belief Functions. Springer International Publishing, Cham, pp 180\u2013189"},{"key":"4653_CR33","doi-asserted-by":"publisher","unstructured":"Cables E, Lamata MT, Verdegay JL (2016) RIM-reference ideal method in multicriteria decision making. Inf Sci (Ny) 337\u2013338:1\u201310. https:\/\/doi.org\/10.1016\/j.ins.2015.12.011","DOI":"10.1016\/j.ins.2015.12.011"},{"key":"4653_CR34","first-page":"21","volume":"8","author":"Y-M Wang","year":"1997","unstructured":"Wang Y-M (1997) Using the method of maximizing deviation to make decision for multiindices. J Syst Eng Electron 8:21\u201326","journal-title":"J Syst Eng Electron"},{"key":"4653_CR35","unstructured":"(2006) WHO air quality guidelines for particulate matter, ozone, nitrogen dioxide and sulfur dioxide: Summary of risk assessment. Geneva"},{"key":"4653_CR36","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, Mart\u00ednez L (2021) Consensus-Based Linguistic Distribution Large-Scale Group Decision Making Using Statistical Inference and Regret Theory. Gr Decis Negot 30:813\u2013845. https:\/\/doi.org\/10.1007\/s10726-021-09736-z","journal-title":"Gr Decis Negot"},{"key":"4653_CR37","doi-asserted-by":"publisher","unstructured":"Zheng YH, He Y, Xu ZS, Pedrycz W (2018) Assessment for hierarchical medical policy proposals using hesitant fuzzy linguistic analytic network process. Knowledge-Based Syst 161:254\u2013267. https:\/\/doi.org\/10.1016\/j.knosys.2018.07.005","DOI":"10.1016\/j.knosys.2018.07.005"},{"key":"4653_CR38","doi-asserted-by":"publisher","first-page":"833","DOI":"10.1007\/s10479-018-3093-7","volume":"293","author":"C Fu","year":"2020","unstructured":"Fu C, Liu WY, Chang WJ (2020) Data-driven multiple criteria decision making for diagnosis of thyroid cancer. Ann Oper Res 293:833\u2013862. https:\/\/doi.org\/10.1007\/s10479-018-3093-7","journal-title":"Ann Oper Res"},{"key":"4653_CR39","doi-asserted-by":"publisher","unstructured":"Joshi R, Banwet DK, Shankar R (2011) A Delphi-AHP-TOPSIS based benchmarking framework for performance improvement of a cold chain. Expert Syst Appl 38:10170\u201310182. https:\/\/doi.org\/10.1016\/j.eswa.2011.02.072","DOI":"10.1016\/j.eswa.2011.02.072"},{"key":"4653_CR40","doi-asserted-by":"publisher","unstructured":"Li H, Adeli H, Sun J, Han J-G (2011) Hybridizing principles of TOPSIS with case-based reasoning for business failure prediction. Comput Oper Res 38:409\u2013419. https:\/\/doi.org\/10.1016\/j.cor.2010.06.008","DOI":"10.1016\/j.cor.2010.06.008"},{"key":"4653_CR41","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-48318-9","volume-title":"Multiple attribute decision making methods and applications","author":"CL Hwang","year":"1981","unstructured":"Hwang CL, Yoon K (1981) Multiple attribute decision making methods and applications. Springer, Berlin"},{"key":"4653_CR42","doi-asserted-by":"publisher","unstructured":"Wu XL, Liao HC (2019) A consensus-based probabilistic linguistic gained and lost dominance score method. Eur J Oper Res 272:1017\u20131027. https:\/\/doi.org\/10.1016\/j.ejor.2018.07.044","DOI":"10.1016\/j.ejor.2018.07.044"}],"container-title":["Applied Intelligence"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10489-023-04653-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10489-023-04653-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10489-023-04653-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,9,19]],"date-time":"2023-09-19T11:15:13Z","timestamp":1695122113000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10489-023-04653-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,5,29]]},"references-count":42,"journal-issue":{"issue":"18","published-print":{"date-parts":[[2023,9]]}},"alternative-id":["4653"],"URL":"https:\/\/doi.org\/10.1007\/s10489-023-04653-x","relation":{},"ISSN":["0924-669X","1573-7497"],"issn-type":[{"value":"0924-669X","type":"print"},{"value":"1573-7497","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,5,29]]},"assertion":[{"value":"18 April 2023","order":1,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"29 May 2023","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors have no relevant financial or non-financial interests to disclose.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing interests"}}]}}