{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,14]],"date-time":"2026-05-14T14:54:45Z","timestamp":1778770485877,"version":"3.51.4"},"reference-count":25,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2022,6,3]],"date-time":"2022-06-03T00:00:00Z","timestamp":1654214400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2022,6,3]],"date-time":"2022-06-03T00:00:00Z","timestamp":1654214400000},"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":["61873329"],"award-info":[{"award-number":["61873329"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12026225"],"award-info":[{"award-number":["12026225"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Fuzzy Optim Decis Making"],"published-print":{"date-parts":[[2023,6]]},"DOI":"10.1007\/s10700-022-09389-w","type":"journal-article","created":{"date-parts":[[2022,6,3]],"date-time":"2022-06-03T08:03:59Z","timestamp":1654243439000},"page":"195-211","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":131,"title":["Uncertain hypothesis test for uncertain differential equations"],"prefix":"10.1007","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8218-0305","authenticated-orcid":false,"given":"Tingqing","family":"Ye","sequence":"first","affiliation":[]},{"given":"Baoding","family":"Liu","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2022,6,3]]},"reference":[{"issue":"2","key":"9389_CR1","doi-asserted-by":"publisher","first-page":"2573","DOI":"10.3233\/JIFS-18353","volume":"35","author":"W Lio","year":"2018","unstructured":"Lio, W., & Liu, B. (2018). Residual and confidence interval for uncertain regression model with imprecise observations. Journal of Intelligent & Fuzzy Systems, 35(2), 2573\u20132583.","journal-title":"Journal of Intelligent & Fuzzy Systems"},{"issue":"2","key":"9389_CR2","doi-asserted-by":"publisher","first-page":"177","DOI":"10.1007\/s10700-020-09337-6","volume":"20","author":"W Lio","year":"2021","unstructured":"Lio, W., & Liu, B. (2021). Initial value estimation of uncertain differential equations and zero-day of COVID-19 spread in China. Fuzzy Optimization and Decision Making, 20(2), 177\u2013188.","journal-title":"Fuzzy Optimization and Decision Making"},{"key":"9389_CR3","unstructured":"Liu, B. (2007). Uncertainty Theory (2nd ed.). Springer."},{"issue":"1","key":"9389_CR4","first-page":"3","volume":"2","author":"B Liu","year":"2008","unstructured":"Liu, B. (2008). Fuzzy process, hybrid process and uncertain process. Journal of Uncertain Systems, 2(1), 3\u201316.","journal-title":"Journal of Uncertain Systems"},{"issue":"1","key":"9389_CR5","first-page":"3","volume":"3","author":"B Liu","year":"2009","unstructured":"Liu, B. (2009). Some research problems in uncertainty theory. Journal of Uncertain Systems, 3(1), 3\u201310.","journal-title":"Journal of Uncertain Systems"},{"key":"9389_CR6","unstructured":"Liu, B. (2010). Uncertainty theory: A branch of mathematics for modeling human uncertainty. Springer."},{"key":"9389_CR7","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1186\/2195-5468-1-1","volume":"1","author":"B Liu","year":"2013","unstructured":"Liu, B. (2013). Toward uncertain finance theory. Journal of Uncertainty Analysis and Applications, 1, 1.","journal-title":"Journal of Uncertainty Analysis and Applications"},{"key":"9389_CR8","doi-asserted-by":"crossref","unstructured":"Liu, Y. (2021a). Uncertain circuit equation. Journal of Uncertain Systems, 14(3), 2150018.","DOI":"10.1142\/S1752890921500185"},{"issue":"6","key":"9389_CR9","doi-asserted-by":"publisher","first-page":"2773","DOI":"10.1007\/s00500-022-06766-w","volume":"26","author":"Y Liu","year":"2022","unstructured":"Liu, Y., & Liu, B. (2022). Estimating unknown parameters in uncertain differential equation by maximum likelihood estimation. Soft Computing, 26(6), 2773\u20132780.","journal-title":"Soft Computing"},{"key":"9389_CR10","doi-asserted-by":"crossref","unstructured":"Liu, Y., & Liu, B. (2022). Residual analysis and parameter estimation of uncertain differential equation. Fuzzy Optimization and Decision Making. https:\/\/doi.org\/10.1007\/s10700-021-09379-4.","DOI":"10.1007\/s10700-021-09379-4"},{"key":"9389_CR11","doi-asserted-by":"crossref","unstructured":"Liu, Z. (2021b). Uncertain growth model for the cumulative number of COVID-19 infections in China. Fuzzy Optimization and Decision Making, 20(2), 229\u2013242.","DOI":"10.1007\/s10700-020-09340-x"},{"key":"9389_CR12","doi-asserted-by":"crossref","unstructured":"Liu, Z., & Yang, Y. (2021). Uncertain pharmacokinetic model based on uncertain differential equation. Applied Mathematics and Computation, 404, 126118.","DOI":"10.1016\/j.amc.2021.126118"},{"key":"9389_CR13","doi-asserted-by":"crossref","unstructured":"Liu, Z., & Kang, R. (2022). Software belief reliability growth model based on uncertain differential equation. IEEE Transactions on Reliability. https:\/\/doi.org\/10.1109\/TR.2022.3154770.","DOI":"10.1109\/TR.2022.3158336"},{"issue":"10","key":"9389_CR14","doi-asserted-by":"publisher","first-page":"2651","DOI":"10.1109\/TFUZZ.2019.2939984","volume":"28","author":"Y Sheng","year":"2020","unstructured":"Sheng, Y., Yao, K., & Chen, X. (2020). Least squares estimation in uncertain differential equations. IEEE Transactions on Fuzzy Systems, 28(10), 2651\u20132655.","journal-title":"IEEE Transactions on Fuzzy Systems"},{"key":"9389_CR15","doi-asserted-by":"crossref","unstructured":"Tang, H., & Yang, X. (2021). Uncertain chemical reaction equation. Applied Mathematics and Computation, 411, 126479.","DOI":"10.1016\/j.amc.2021.126479"},{"issue":"3","key":"9389_CR16","doi-asserted-by":"publisher","first-page":"263","DOI":"10.1007\/s10700-018-9298-z","volume":"18","author":"X Yang","year":"2019","unstructured":"Yang, X., & Liu, B. (2019). Uncertain time series analysis with imprecise observations. Fuzzy Optimization and Decision Making, 18(3), 263\u2013278.","journal-title":"Fuzzy Optimization and Decision Making"},{"key":"9389_CR17","doi-asserted-by":"crossref","unstructured":"Yang, X., Liu, Y., & Park, G. (2020). Parameter estimation of uncertain differential equation with application to financial market. Chaos, Solitons and Fractals, 139, 110026.","DOI":"10.1016\/j.chaos.2020.110026"},{"issue":"17","key":"9389_CR18","doi-asserted-by":"publisher","first-page":"5579","DOI":"10.1007\/s00500-017-2521-y","volume":"22","author":"K Yao","year":"2018","unstructured":"Yao, K., & Liu, B. (2018). Uncertain regression analysis: An approach for imprecise observations. Soft Computing, 22(17), 5579\u20135582.","journal-title":"Soft Computing"},{"issue":"1","key":"9389_CR19","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s10700-019-09310-y","volume":"19","author":"K Yao","year":"2020","unstructured":"Yao, K., & Liu, B. (2020). Parameter estimation in uncertain differential equations. Fuzzy Optimization and Decision Making, 19(1), 1\u201312.","journal-title":"Fuzzy Optimization and Decision Making"},{"key":"9389_CR20","doi-asserted-by":"publisher","first-page":"157","DOI":"10.1007\/s10700-021-09365-w","volume":"21","author":"T Ye","year":"2022","unstructured":"Ye, T., & Liu, B. (2022). Uncertain hypothesis test with application to uncertain regression analysis. Fuzzy Optimization and Decision Making, 21, 157\u2013174.","journal-title":"Fuzzy Optimization and Decision Making"},{"issue":"2","key":"9389_CR21","doi-asserted-by":"publisher","first-page":"209","DOI":"10.1007\/s10700-020-09339-4","volume":"20","author":"T Ye","year":"2021","unstructured":"Ye, T., & Yang, X. (2021). Analysis and prediction of confirmed COVID-19 cases in China with uncertain time series. Fuzzy Optimization and Decision Making, 20(2), 209\u2013228.","journal-title":"Fuzzy Optimization and Decision Making"},{"key":"9389_CR22","unstructured":"Ye, T., & Zheng, H. (2022). Analysis of birth rates in China with uncertain time series model. Technical report."},{"key":"9389_CR23","unstructured":"Ye, T. (2022). Analysis of labour income share in China with uncertain regression model. Technical report."},{"key":"9389_CR24","unstructured":"Ye, T. (2022). Difference order selection in uncertain time series analysis. Technical Report."},{"key":"9389_CR25","doi-asserted-by":"crossref","unstructured":"Ye, T. (2022). Modeling grain yield in China with uncertain time series analysis. Technical report.","DOI":"10.1142\/S1752890922430036"}],"container-title":["Fuzzy Optimization and Decision Making"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10700-022-09389-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10700-022-09389-w\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10700-022-09389-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,4,8]],"date-time":"2025-04-08T23:46:09Z","timestamp":1744155969000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10700-022-09389-w"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,6,3]]},"references-count":25,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2023,6]]}},"alternative-id":["9389"],"URL":"https:\/\/doi.org\/10.1007\/s10700-022-09389-w","relation":{},"ISSN":["1568-4539","1573-2908"],"issn-type":[{"value":"1568-4539","type":"print"},{"value":"1573-2908","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,6,3]]},"assertion":[{"value":"31 March 2022","order":1,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"3 June 2022","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}