{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,13]],"date-time":"2025-10-13T00:47:21Z","timestamp":1760316441849,"version":"build-2065373602"},"reference-count":32,"publisher":"Springer Science and Business Media LLC","issue":"15","license":[{"start":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T00:00:00Z","timestamp":1760227200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T00:00:00Z","timestamp":1760227200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"name":"Open Foundation of Key Laboratory of the Ministry of Education on Application of Artificial Intelligence in Equipment under Grant","award":["No.AAIE-2023-0102"],"award-info":[{"award-number":["No.AAIE-2023-0102"]}]},{"name":"The Natural Science Foundation of Heilongjiang Province under Grant","award":["No. PL2024G009"],"award-info":[{"award-number":["No. PL2024G009"]}]},{"name":"The Basic Research Support Program for Outstanding Young Teachers in Provincial Undergraduate Universities of Heilongjiang Province under Grant","award":["No. YQJH2024116"],"award-info":[{"award-number":["No. YQJH2024116"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Supercomput"],"DOI":"10.1007\/s11227-025-07929-w","type":"journal-article","created":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T16:23:10Z","timestamp":1760286190000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A new progressive belief rule-based model for imbalanced multi-classification"],"prefix":"10.1007","volume":"81","author":[{"given":"Ning","family":"Li","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yingmei","family":"Li","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wei","family":"He","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yimeng","family":"Niu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Naijia","family":"Guo","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2025,10,12]]},"reference":[{"issue":"4","key":"7929_CR1","doi-asserted-by":"publisher","first-page":"354","DOI":"10.3934\/DSFE.2023021","volume":"3","author":"L Dube","year":"2023","unstructured":"Dube L, Verster T (2023) Enhancing classification performance in imbalanced datasets: a comparative analysis of machine learning models. Data Sci Finance and Econ 3(4):354\u2013379. https:\/\/doi.org\/10.3934\/DSFE.2023021","journal-title":"Data Sci Finance and Econ"},{"issue":"5","key":"7929_CR2","doi-asserted-by":"publisher","first-page":"4765","DOI":"10.1007\/s10462-022-10275-5","volume":"56","author":"VG Costa","year":"2023","unstructured":"Costa VG, Pedreira CE (2023) Recent advances in decision trees: an updated survey. Artific Intell Rev 56(5):4765\u20134800. https:\/\/doi.org\/10.1007\/s10462-022-10275-5","journal-title":"Artific Intell Rev"},{"issue":"1","key":"7929_CR3","doi-asserted-by":"publisher","first-page":"113","DOI":"10.1186\/s40537-024-00973-y","volume":"11","author":"RK Halder","year":"2024","unstructured":"Halder RK, Uddin MN, Ashraf UM, Aryal S, Khraisat A (2024) Enhancing k-nearest neighbor algorithm: a comprehensive review and performance analysis of modifications. J Big Data 11(1):113. https:\/\/doi.org\/10.1186\/s40537-024-00973-y","journal-title":"J Big Data"},{"key":"7929_CR4","doi-asserted-by":"publisher","first-page":"109126","DOI":"10.1016\/j.ress.2023.109126","volume":"233","author":"A Roy","year":"2023","unstructured":"Roy A, Chakraborty S (2023) Support vector machine in structural reliability analysis: A review. Reliability Eng Syst Safety 233:109126. https:\/\/doi.org\/10.1016\/j.ress.2023.109126","journal-title":"Reliability Eng Syst Safety"},{"key":"7929_CR5","doi-asserted-by":"publisher","first-page":"140","DOI":"10.1016\/j.jclinepi.2023.07.017","volume":"161","author":"J Ma","year":"2023","unstructured":"Ma J, Dhiman P, Qi C, Bullock G, Smeden M, Riley RD, Collins GS (2023) Poor handling of continuous predictors in clinical prediction models using logistic regression: a systematic review. J Clin Epidemiol 161:140\u2013151. https:\/\/doi.org\/10.1016\/j.jclinepi.2023.07.017","journal-title":"J Clin Epidemiol"},{"issue":"4","key":"7929_CR6","doi-asserted-by":"publisher","first-page":"99","DOI":"10.1007\/s10462-024-10721-6","volume":"57","author":"X Zhao","year":"2024","unstructured":"Zhao X, Wang L, Zhang Y, X Han, Deveci M, Parmar M (2024) A review of convolutional neural networks in computer vision. Artif Intell Rev 57(4):99. https:\/\/doi.org\/10.1007\/s10462-024-10721-6","journal-title":"Artif Intell Rev"},{"key":"7929_CR7","doi-asserted-by":"publisher","first-page":"119451","DOI":"10.1016\/j.eswa.2022.119451","volume":"216","author":"G Hu","year":"2023","unstructured":"Hu G, He W, Sun C, Zhu H, Li K, Jiang L (2023) Hierarchical belief rule-based model for imbalanced multi-classification. Expert Syst Appl 216:119451. https:\/\/doi.org\/10.1016\/j.eswa.2022.119451","journal-title":"Expert Syst Appl"},{"issue":"2","key":"7929_CR8","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, Sii H-S, Wang H-W (2006) Belief rule-base inference methodology using the evidential reasoning approach-rimer. IEEE Trans Syst Man and Cybernet-Part A Syst Humans 36(2):266\u2013285. https:\/\/doi.org\/10.1109\/TSMCA.2005.851270","journal-title":"IEEE Trans Syst Man and Cybernet-Part A Syst Humans"},{"key":"7929_CR9","doi-asserted-by":"publisher","first-page":"111118","DOI":"10.1016\/j.asoc.2023.111118","volume":"151","author":"Q Zhang","year":"2024","unstructured":"Zhang Q, Zhao B, He W, Zhu H, Zhou G (2024) A behavior prediction method for complex system based on belief rule base with structural adaptive. Appl Soft Comput 151:111118. https:\/\/doi.org\/10.1016\/j.asoc.2023.111118","journal-title":"Appl Soft Comput"},{"issue":"1","key":"7929_CR10","doi-asserted-by":"publisher","first-page":"23","DOI":"10.1109\/TR.2013.2241251","volume":"62","author":"H-C Liu","year":"2013","unstructured":"Liu H-C, L Liu, G-L Lin (2013) Fuzzy failure mode and effects analysis using fuzzy evidential reasoning and belief rule-based methodology. IEEE Trans Reliab 62(1):23\u201336. https:\/\/doi.org\/10.1109\/TR.2013.2241251","journal-title":"IEEE Trans Reliab"},{"key":"7929_CR11","doi-asserted-by":"publisher","first-page":"110552","DOI":"10.1016\/j.knosys.2023.110552","volume":"271","author":"SF Nimmy","year":"2023","unstructured":"Nimmy SF, Hussain OK, Chakrabortty RK, Hussain FK, Saberi M (2023) An optimized belief-rule-based (brb) approach to ensure the trustworthiness of interpreted time-series decisions. Knowledge-Based Syst 271:110552. https:\/\/doi.org\/10.1016\/j.knosys.2023.110552","journal-title":"Knowledge-Based Syst"},{"key":"7929_CR12","doi-asserted-by":"publisher","DOI":"10.1109\/ACCESS.2025.3541391","author":"Y Zhao","year":"2025","unstructured":"Zhao Y, Zhang K, Duan X, S Che, N Ma (2025) A chronic kidney disease diagnostic model based on an interpretable deep belief rule base. IEEE Access. https:\/\/doi.org\/10.1109\/ACCESS.2025.3541391","journal-title":"IEEE Access"},{"key":"7929_CR13","doi-asserted-by":"publisher","first-page":"200198","DOI":"10.1016\/j.iswa.2023.200198","volume":"18","author":"Y Gao","year":"2023","unstructured":"Gao Y, Wu J, Feng Z, Hu G, Chen Y, He W (2023) A new brb model for technical analysis of the stock market. Intell Syst Appl 18:200198. https:\/\/doi.org\/10.1016\/j.iswa.2023.200198","journal-title":"Intell Syst Appl"},{"key":"7929_CR14","doi-asserted-by":"publisher","unstructured":"Zhao B, Kong L, He W, Zhou G, Zhu H (2024) A fault diagnosis method for manufacturing system based on adaptive brb considering environmental disturbance. International Journal of Fuzzy Systems 1\u201314. https:\/\/doi.org\/10.1007\/s40815-024-01799-9","DOI":"10.1007\/s40815-024-01799-9"},{"issue":"7","key":"7929_CR15","doi-asserted-by":"publisher","first-page":"4903","DOI":"10.1007\/s10994-022-06296-4","volume":"113","author":"D Elreedy","year":"2024","unstructured":"Elreedy D, Atiya AF, Kamalov F (2024) A theoretical distribution analysis of synthetic minority oversampling technique (smote) for imbalanced learning. Machine Learn 113(7):4903\u20134923. https:\/\/doi.org\/10.1007\/s10994-022-06296-4","journal-title":"Machine Learn"},{"issue":"1","key":"7929_CR16","doi-asserted-by":"publisher","first-page":"58","DOI":"10.1186\/s40537-023-00738-z","volume":"10","author":"JL Leevy","year":"2023","unstructured":"Leevy JL, Johnson JM, Hancock J, Khoshgoftaar TM (2023) Threshold optimization and random undersampling for imbalanced credit card data. J Big Data 10(1):58. https:\/\/doi.org\/10.1186\/s40537-023-00738-z","journal-title":"J Big Data"},{"issue":"3","key":"7929_CR17","doi-asserted-by":"publisher","first-page":"1310","DOI":"10.62527\/joiv.8.3.2283","volume":"8","author":"H Hairani","year":"2024","unstructured":"Hairani H, Widiyaningtyas T, Prasetya DD (2024) Addressing class imbalance of health data: A systematic literature review on modified synthetic minority oversampling technique (smote) strategies. JOIV: Int J Inform Visualization 8(3):1310\u20131318. https:\/\/doi.org\/10.62527\/joiv.8.3.2283","journal-title":"JOIV: Int J Inform Visualization"},{"key":"7929_CR18","doi-asserted-by":"publisher","first-page":"111491","DOI":"10.1016\/j.asoc.2024.111491","volume":"156","author":"SA Alex","year":"2024","unstructured":"Alex SA, Nayahi JJV, Kaddoura S (2024) Deep convolutional neural networks with genetic algorithm-based synthetic minority over-sampling technique for improved imbalanced data classification. Appl Soft Comput 156:111491. https:\/\/doi.org\/10.1016\/j.asoc.2024.111491","journal-title":"Appl Soft Comput"},{"issue":"3","key":"7929_CR19","doi-asserted-by":"publisher","first-page":"100064","DOI":"10.1016\/j.dim.2023.100064","volume":"8","author":"Q Zhou","year":"2024","unstructured":"Zhou Q, Sun B (2024) Adaptive k-means clustering based under-sampling methods to solve the class imbalance problem. Data and Inform Manag 8(3):100064. https:\/\/doi.org\/10.1016\/j.dim.2023.100064","journal-title":"Data and Inform Manag"},{"key":"7929_CR20","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1109\/TGRS.2023.3252277","volume":"61","author":"W Huang","year":"2023","unstructured":"Huang W (2023) A genetic algorithm optimized undersampling method for seismic sparse acquisition and reconstruction. IEEE Trans Geosci Remote Sens 61:1\u201310. https:\/\/doi.org\/10.1109\/TGRS.2023.3252277","journal-title":"IEEE Trans Geosci Remote Sens"},{"issue":"4","key":"7929_CR21","doi-asserted-by":"publisher","first-page":"80","DOI":"10.1007\/s10462-023-10652-8","volume":"57","author":"I Araf","year":"2024","unstructured":"Araf I, Idri A, Chairi I (2024) Cost-sensitive learning for imbalanced medical data: a review. Artif Intell Rev 57(4):80. https:\/\/doi.org\/10.1007\/s10462-023-10652-8","journal-title":"Artif Intell Rev"},{"issue":"5","key":"7929_CR22","doi-asserted-by":"publisher","first-page":"5693","DOI":"10.1007\/s40747-023-01013-7","volume":"9","author":"N Thockchom","year":"2023","unstructured":"Thockchom N, Singh MM, Nandi U (2023) A novel ensemble learning-based model for network intrusion detection. Complex & Intell Syst 9(5):5693\u20135714. https:\/\/doi.org\/10.1007\/s40747-023-01013-7","journal-title":"Complex & Intell Syst"},{"issue":"6","key":"7929_CR23","doi-asserted-by":"publisher","first-page":"137","DOI":"10.1007\/s10462-024-10759-6","volume":"57","author":"W Chen","year":"2024","unstructured":"Chen W, Yang K, Yu Z, Shi Y, Chen CLP (2024) A survey on imbalanced learning: latest research, applications and future directions. Artific Intell Rev 57(6):137. https:\/\/doi.org\/10.1007\/s10462-024-10759-6","journal-title":"Artific Intell Rev"},{"key":"7929_CR24","doi-asserted-by":"publisher","first-page":"121288","DOI":"10.1016\/j.ins.2024.121288","volume":"684","author":"B Hou","year":"2024","unstructured":"Hou B, Fu C, Xue M (2024) An extended belief rule-based system with hybrid sampling strategy for imbalanced rule base. Inform Sci 684:121288. https:\/\/doi.org\/10.1016\/j.ins.2024.121288","journal-title":"Inform Sci"},{"key":"7929_CR25","doi-asserted-by":"publisher","first-page":"41201","DOI":"10.1109\/ACCESS.2020.2976708","volume":"8","author":"W Fang","year":"2020","unstructured":"Fang W, Gong X, Liu G, Wu Y, Fu Y (2020) A balance adjusting approach of extended belief-rule-based system for imbalanced classification problem. IEEE Access 8:41201\u201341212. https:\/\/doi.org\/10.1109\/ACCESS.2020.2976708","journal-title":"IEEE Access"},{"issue":"3","key":"7929_CR26","doi-asserted-by":"publisher","first-page":"1555","DOI":"10.3390\/app15031555","volume":"15","author":"F Yang","year":"2025","unstructured":"Yang F, Hu G, Zhu H (2025) A novel ensemble belief rule-based model for online payment fraud detection. Appl Sci 15(3):1555. https:\/\/doi.org\/10.3390\/app15031555","journal-title":"Appl Sci"},{"key":"7929_CR27","doi-asserted-by":"publisher","first-page":"107010","DOI":"10.1016\/j.knosys.2021.107010","volume":"223","author":"Y-G Fu","year":"2021","unstructured":"Fu Y-G, Huang H-Y, Guan Y, Wang Y-M, Liu W, Fang W-J (2021) Ebrb cascade classifier for imbalanced data via rule weight updating. Knowledge-Based Syst 223:107010. https:\/\/doi.org\/10.1016\/j.knosys.2021.107010","journal-title":"Knowledge-Based Syst"},{"key":"7929_CR28","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.artint.2013.09.003","volume":"205","author":"J-B Yang","year":"2013","unstructured":"Yang J-B, Xu D-L (2013) Evidential reasoning rule for evidence combination. Artific Intell 205:1\u201329. https:\/\/doi.org\/10.1016\/j.artint.2013.09.003","journal-title":"Artific Intell"},{"key":"7929_CR29","doi-asserted-by":"publisher","first-page":"77","DOI":"10.1016\/j.isatra.2024.05.019","volume":"150","author":"B Zhao","year":"2024","unstructured":"Zhao B, Zhang Q, He W, Han P, Cao Y, Zhou G (2024) A deep belief rule base-based fault diagnosis method for complex systems. ISA Trans 150:77\u201391. https:\/\/doi.org\/10.1016\/j.isatra.2024.05.019","journal-title":"ISA Trans"},{"issue":"10","key":"7929_CR30","doi-asserted-by":"publisher","first-page":"6043","DOI":"10.1109\/TSMC.2023.3279286","volume":"53","author":"Y Cao","year":"2023","unstructured":"Cao Y, Zhou Z, Tang S, Ning P (2023) On the robustness of belief-rule-based expert systems. IEEE Trans Syst Man and Cybernet Syst 53(10):6043\u20136055. https:\/\/doi.org\/10.1109\/TSMC.2023.3279286","journal-title":"IEEE Trans Syst Man and Cybernet Syst"},{"key":"7929_CR31","doi-asserted-by":"publisher","unstructured":"Gong A, He W, Cao Y, Zhou G, Zhu H (2025) Interpretability metrics and optimization methods for belief rule based expert systems. Expert Systems with Applications 128363. https:\/\/doi.org\/10.1016\/j.eswa.2025.128363","DOI":"10.1016\/j.eswa.2025.128363"},{"issue":"1","key":"7929_CR32","doi-asserted-by":"publisher","first-page":"4038","DOI":"10.1038\/s41598-024-54589-6","volume":"14","author":"K-X Shi","year":"2024","unstructured":"Shi K-X, Li S-M, Sun G-W, Feng Z-C, He W (2024) A fault diagnosis method for wireless sensor network nodes based on a belief rule base with adaptive attribute weights. Sci Reports 14(1):4038. https:\/\/doi.org\/10.1038\/s41598-024-54589-6","journal-title":"Sci Reports"}],"container-title":["The Journal of Supercomputing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11227-025-07929-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11227-025-07929-w\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11227-025-07929-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T16:23:11Z","timestamp":1760286191000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11227-025-07929-w"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,10,12]]},"references-count":32,"journal-issue":{"issue":"15","published-online":{"date-parts":[[2025,10]]}},"alternative-id":["7929"],"URL":"https:\/\/doi.org\/10.1007\/s11227-025-07929-w","relation":{},"ISSN":["1573-0484"],"issn-type":[{"value":"1573-0484","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,10,12]]},"assertion":[{"value":"12 April 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"26 September 2025","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"12 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 no Conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}},{"value":"Not applicable.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethical approval and consent to participate"}},{"value":"The authors have read and approved the final version of the manuscript and consent to its publication.","order":4,"name":"Ethics","group":{"name":"EthicsHeading","label":"Consent for publication"}}],"article-number":"1447"}}