{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T15:41:19Z","timestamp":1776786079799,"version":"3.51.2"},"reference-count":25,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2020,11,5]],"date-time":"2020-11-05T00:00:00Z","timestamp":1604534400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2020,11,5]],"date-time":"2020-11-05T00:00:00Z","timestamp":1604534400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Fuzzy Optim Decis Making"],"published-print":{"date-parts":[[2021,9]]},"DOI":"10.1007\/s10700-020-09348-3","type":"journal-article","created":{"date-parts":[[2020,11,5]],"date-time":"2020-11-05T09:02:46Z","timestamp":1604566966000},"page":"397-428","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["An inverse prospect theory-based algorithm in extended incomplete additive probabilistic linguistic preference relation environment and its application in financial products selection"],"prefix":"10.1007","volume":"20","author":[{"given":"Nana","family":"Liu","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zeshui","family":"Xu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yue","family":"He","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiao-Jun","family":"Zeng","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2020,11,5]]},"reference":[{"issue":"2","key":"9348_CR1","doi-asserted-by":"publisher","first-page":"155","DOI":"10.1002\/int.20262","volume":"23","author":"S Alonso","year":"2010","unstructured":"Alonso, S., Chiclana, F., Herrera, F., Herrera-Viedma, E., Alcal\u00e1-Fdez, J., & Porcel, C. (2010). A consistency-based procedure to estimate missing pairwise preference values. International Journal of Intelligent Systems, 23(2), 155\u2013175.","journal-title":"International Journal of Intelligent Systems"},{"issue":"2","key":"9348_CR2","doi-asserted-by":"publisher","first-page":"169","DOI":"10.1016\/j.knosys.2009.11.019","volume":"23","author":"FJ Cabrerizo","year":"2010","unstructured":"Cabrerizo, F. J., P\u00e9rez, I. J., & Herrera-Viedma, E. (2010). Managing the consensus in group decision making in an unbalanced fuzzy linguistic context with incomplete information. Knowledge-Based Systems, 23(2), 169\u2013181.","journal-title":"Knowledge-Based Systems"},{"key":"9348_CR3","doi-asserted-by":"publisher","first-page":"898","DOI":"10.1016\/j.asoc.2015.03.013","volume":"35","author":"YC Dong","year":"2015","unstructured":"Dong, Y. C., Nan, L., & Liang, H. M. (2015). Consensus building in multiperson decision making with heterogeneous preference representation structures: A perspective based on prospect theory. Applied Soft Computing, 35, 898\u2013910.","journal-title":"Applied Soft Computing"},{"issue":"21","key":"9348_CR4","doi-asserted-by":"publisher","first-page":"6515","DOI":"10.1007\/s00500-016-2211-1","volume":"21","author":"XJ Gou","year":"2017","unstructured":"Gou, X. J., Xu, Z. S., & Liao, H. C. (2017). Multiple criteria decision making based on Bonferroni means with hesitant fuzzy linguistic information. Soft Computing, 21(21), 6515\u20136529.","journal-title":"Soft Computing"},{"issue":"8","key":"9348_CR5","doi-asserted-by":"publisher","first-page":"836","DOI":"10.1002\/asi.23844","volume":"68","author":"J Gunaratne","year":"2017","unstructured":"Gunaratne, J., & Nov, O. (2017). Using interactive \u201cNutrition labels\u201d for financial products to assist decision making under uncertainty. Journal of the Association for Information Science and Technology, 68(8), 836\u20131849.","journal-title":"Journal of the Association for Information Science and Technology"},{"issue":"4","key":"9348_CR6","doi-asserted-by":"publisher","first-page":"223","DOI":"10.1016\/0020-0255(95)00025-K","volume":"85","author":"F Herrera","year":"1995","unstructured":"Herrera, F., Herrera-Viedma, E., & Verdegay, J. L. (1995). A sequential selection process in group decision making with a linguistic assessment approach. Information Sciences, 85(4), 223\u2013239.","journal-title":"Information Sciences"},{"issue":"5","key":"9348_CR7","doi-asserted-by":"publisher","first-page":"1283","DOI":"10.1080\/00207543.2018.1470343","volume":"57","author":"J Huang","year":"2019","unstructured":"Huang, J., You, X. Y., Liu, H. C., & Si, S. L. (2019). New approach for quality function deployment based on proportional hesitant fuzzy linguistic term sets and prospect theory. International Journal of Production Research, 57(5), 1283\u20131299.","journal-title":"International Journal of Production Research"},{"issue":"2","key":"9348_CR8","first-page":"263","volume":"47","author":"D Kahneman","year":"1979","unstructured":"Kahneman, D., & Tversky, A. (1979). Prospect theory: An analysis of decision under risk. Handbook of the Fundamentals of Financial Decision Making, 47(2), 263\u2013292.","journal-title":"Handbook of the Fundamentals of Financial Decision Making"},{"key":"9348_CR9","first-page":"370","volume":"33","author":"SL Liu","year":"2017","unstructured":"Liu, S. L., & Liu, X. W. (2017). A prospect theory-based methodfor linguistic decision making under risk. Journal of Southeast University (English Edition), 33, 370\u2013376.","journal-title":"Journal of Southeast University (English Edition)"},{"key":"9348_CR10","doi-asserted-by":"crossref","unstructured":"Liu, X. L., & Wei, Y. (2013). A new multi-period linguistic aggregation operator and its application to financial product selection. In International conference on graphic and image processing.","DOI":"10.1117\/12.2010524"},{"key":"9348_CR11","unstructured":"Luciano, E. V., & Lafuente, A. G. (2008). Clan theory and its application in the selection of financial products. In The 12th conference on information processing and management of uncertainty in knowledge-based systems, Malaga, Spain, pp. 737\u2013744."},{"issue":"11","key":"9348_CR12","doi-asserted-by":"publisher","first-page":"2085","DOI":"10.1016\/j.ins.2010.01.028","volume":"180","author":"JM Merigo","year":"2010","unstructured":"Merigo, J. M., & Lafuente, A. G. (2010). New decision-making techniques and their application in the selection of financial products. Information Sciences, 180(11), 2085\u20132094.","journal-title":"Information Sciences"},{"key":"9348_CR13","doi-asserted-by":"publisher","first-page":"128","DOI":"10.1016\/j.ins.2016.06.021","volume":"369","author":"Q Pang","year":"2016","unstructured":"Pang, Q., Wang, H., & Xu, Z. S. (2016). Probabilistic linguistic term sets in multi-attribute group decision making. Information Sciences, 369, 128\u2013143.","journal-title":"Information Sciences"},{"issue":"1","key":"9348_CR14","doi-asserted-by":"publisher","first-page":"32","DOI":"10.1016\/j.knosys.2009.07.007","volume":"23","author":"C Porcel","year":"2010","unstructured":"Porcel, C., & Herrera-Viedma, E. (2010). Dealing with incomplete information in a fuzzy linguistic recommender system to disseminate information in university digital libraries. Knowledge-Based Systems, 23(1), 32\u201339.","journal-title":"Knowledge-Based Systems"},{"key":"9348_CR15","doi-asserted-by":"publisher","DOI":"10.1109\/TEM.2019.2962180","author":"PJ Ren","year":"2020","unstructured":"Ren, P. J., Hao, Z. N., Zeng, X., & Xu, Z. S. (2020). Decision models based on incomplete hesitant fuzzy linguistic preference relation with application to site section of hydropower stations. IEEE Transcations on Engineering Management. https:\/\/doi.org\/10.1109\/TEM.2019.2962180.","journal-title":"IEEE Transcations on Engineering Management"},{"issue":"3","key":"9348_CR16","doi-asserted-by":"publisher","first-page":"296","DOI":"10.1108\/10662241011050722","volume":"20","author":"RM Rodriguez","year":"2010","unstructured":"Rodriguez, R. M., Espinilla, M., Sanchez, P. J., & Mart\u00ednez, L. (2010). Using linguistic incomplete preference relations to cold start recommendations. Internet Research Electronic Networking Applications and Policy, 20(3), 296\u2013315.","journal-title":"Internet Research Electronic Networking Applications and Policy"},{"key":"9348_CR17","doi-asserted-by":"publisher","first-page":"251","DOI":"10.1086\/296365","volume":"59","author":"A Tversky","year":"1986","unstructured":"Tversky, A., & Kahneman, D. (1986). Rational choice and the framing of decisions. The Journal of Business, 59, 251\u2013278.","journal-title":"The Journal of Business"},{"issue":"4","key":"9348_CR18","doi-asserted-by":"publisher","first-page":"297","DOI":"10.1007\/BF00122574","volume":"5","author":"A Tversky","year":"1992","unstructured":"Tversky, A., & Kahneman, D. (1992). Advances in prospect theory: Cumulative representation of uncertainty. Journal of Risk and Uncertainty, 5(4), 297\u2013323.","journal-title":"Journal of Risk and Uncertainty"},{"key":"9348_CR19","doi-asserted-by":"publisher","first-page":"66","DOI":"10.1016\/j.asoc.2015.09.058","volume":"42","author":"H Wang","year":"2016","unstructured":"Wang, H., & Xu, Z. S. (2016). Interactive algorithms for improving incomplete linguistic preference relations based on consistency measures. Applied Soft Computing, 42, 66\u201379.","journal-title":"Applied Soft Computing"},{"key":"9348_CR20","doi-asserted-by":"publisher","first-page":"1227","DOI":"10.1016\/j.energy.2018.01.115","volume":"147","author":"YN Wu","year":"2018","unstructured":"Wu, Y. N., Xu, C. B., & Zhang, T. (2018). Evaluation of renewable power sources using a fuzzy MCDM based on cumulative prospect theory: A case in China. Energy, 147, 1227\u20131239.","journal-title":"Energy"},{"issue":"5","key":"9348_CR21","doi-asserted-by":"publisher","first-page":"1349","DOI":"10.1007\/s40815-019-00635-9","volume":"21","author":"WY Xie","year":"2019","unstructured":"Xie, W. Y., Xu, Z. S., & Ren, Z. L. (2019). An analysis on the influence of Chinese \u201cnew four inventions\u201d under the incomplete hybrid probabilistic linguistic environment. International Journal of Fuzzy Systems, 21(5), 1349\u20131366.","journal-title":"International Journal of Fuzzy Systems"},{"issue":"3","key":"9348_CR22","doi-asserted-by":"publisher","first-page":"261","DOI":"10.1016\/j.ijar.2003.10.011","volume":"36","author":"ZS Xu","year":"2004","unstructured":"Xu, Z. S. (2004). Goal programming models for obtaining the priority vector of incomplete fuzzy preference relation. International Journal of Approximate Reasoning, 36(3), 261\u2013270.","journal-title":"International Journal of Approximate Reasoning"},{"issue":"3","key":"9348_CR23","doi-asserted-by":"publisher","first-page":"175","DOI":"10.1007\/s10700-005-1887-y","volume":"4","author":"ZS Xu","year":"2005","unstructured":"Xu, Z. S. (2005). A procedure for decision making based on incomplete fuzzy preference relation. Fuzzy Optimization and Decision Making, 4(3), 175\u2013189.","journal-title":"Fuzzy Optimization and Decision Making"},{"key":"9348_CR24","doi-asserted-by":"publisher","first-page":"27","DOI":"10.1016\/j.cie.2014.02.004","volume":"71","author":"Z Zhang","year":"2014","unstructured":"Zhang, Z., & Guo, C. (2014). An approach to group decision making with heterogeneous incomplete uncertain preference relations. Computers & Industrial Engineering, 71, 27\u201336.","journal-title":"Computers & Industrial Engineering"},{"key":"9348_CR25","doi-asserted-by":"publisher","first-page":"817","DOI":"10.1016\/j.asoc.2016.08.045","volume":"49","author":"YX Zhang","year":"2016","unstructured":"Zhang, Y. X., Xu, Z. S., Wang, H., & Liao, H. C. (2016). Consistency-based risk assessment with probabilistic linguistic preference relation. Applied Soft Computing, 49, 817\u2013833.","journal-title":"Applied Soft Computing"}],"container-title":["Fuzzy Optimization and Decision Making"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10700-020-09348-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10700-020-09348-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10700-020-09348-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,7,27]],"date-time":"2021-07-27T15:05:05Z","timestamp":1627398305000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10700-020-09348-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,11,5]]},"references-count":25,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2021,9]]}},"alternative-id":["9348"],"URL":"https:\/\/doi.org\/10.1007\/s10700-020-09348-3","relation":{},"ISSN":["1568-4539","1573-2908"],"issn-type":[{"value":"1568-4539","type":"print"},{"value":"1573-2908","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,11,5]]},"assertion":[{"value":"24 September 2020","order":1,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"5 November 2020","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}