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Existing contribution evaluation mechanisms based on Shapley values uniquely allocate the total utility of a federation based on the marginal contributions of participants. However, in practical engineering applications, participants from different data sources typically exhibit significant differences and uncertainties in terms of their contributions to a federation, thus rendering it difficult to represent their contributions precisely. To evaluate the contribution of each participant to FL more effectively, we propose a novel interval federated Shapley value (IntFedSV) contribution evaluation mechanism. Second, to improve computational efficiency, we utilize a matrix semitensor product\u2010based method to compute the IntFedSV. Finally, extensive experiments on four public datasets (MNIST, CIFAR10, AG_NEWS, and IMDB) demonstrate its potential in engineering applications. Our proposed mechanism can effectively evaluate the contribution levels of participants. Compared with the case of three advanced baseline methods, the minimum and maximum improvement rates of standard deviation for our proposed mechanism are 11.83% and 99.00%, respectively, thus demonstrating its greater stability and fault tolerance. This study contributes positively to promoting engineering applications of FL.<\/jats:p>","DOI":"10.1155\/int\/3466867","type":"journal-article","created":{"date-parts":[[2025,4,22]],"date-time":"2025-04-22T06:41:57Z","timestamp":1745304117000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["IntFedSV: A Novel Participants\u2019 Contribution Evaluation Mechanism for Federated Learning"],"prefix":"10.1155","volume":"2025","author":[{"given":"Tianxu","family":"Cui","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0007-8048-8593","authenticated-orcid":false,"given":"Ying","family":"Shi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wenge","family":"Li","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Rijia","family":"Ding","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qing","family":"Wang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2025,4,22]]},"reference":[{"key":"e_1_2_13_1_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ipm.2018.01.010"},{"key":"e_1_2_13_2_2","doi-asserted-by":"publisher","DOI":"10.1080\/13600834.2019.1573501"},{"key":"e_1_2_13_3_2","doi-asserted-by":"publisher","DOI":"10.1287\/mnsc.2022.4614"},{"key":"e_1_2_13_4_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.eng.2022.12.008"},{"key":"e_1_2_13_5_2","first-page":"1273","article-title":"Communication-Efficient Learning of Deep Networks From Decentralized Data","author":"McMahan B.","year":"2017","journal-title":"Artificial Intelligence and Statistics"},{"key":"e_1_2_13_6_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.future.2017.02.006"},{"key":"e_1_2_13_7_2","doi-asserted-by":"publisher","DOI":"10.1155\/2023\/8017489"},{"key":"e_1_2_13_8_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ipm.2024.103704"},{"key":"e_1_2_13_9_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.future.2023.03.042"},{"key":"e_1_2_13_10_2","doi-asserted-by":"publisher","DOI":"10.1109\/TNNLS.2023.3263594"},{"key":"e_1_2_13_11_2","doi-asserted-by":"crossref","unstructured":"WangG. 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