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In this paper, we consider the training of federated machine models with uncertain participation attitudes and uncertain benefits of each federated participant, and to encourage all participants to train the desired FL models, we design a fuzzy Shapley value incentive mechanism with supervision. In this incentive mechanism, if the supervision of the supervised mechanism detects that the payoffs of a federated participant reach a value that satisfies the Pareto optimality condition, the federated participant receives a distribution of federated payoffs. The results of numerical experiments demonstrate that the mechanism successfully achieves a fair and Pareto optimal distribution of payoffs. The contradiction between fairness and Pareto-efficient optimization is solved by introducing a supervised mechanism.<\/jats:p>","DOI":"10.3390\/axioms13040254","type":"journal-article","created":{"date-parts":[[2024,4,12]],"date-time":"2024-04-12T03:34:37Z","timestamp":1712892877000},"page":"254","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Federated Learning Incentive Mechanism with Supervised Fuzzy Shapley Value"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5335-963X","authenticated-orcid":false,"given":"Xun","family":"Yang","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Guizhou University, Guiyang 550025, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8724-6449","authenticated-orcid":false,"given":"Shuwen","family":"Xiang","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Guizhou University, Guiyang 550025, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8733-4596","authenticated-orcid":false,"given":"Changgen","family":"Peng","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Public Big Data, College of Computer Science and Technology, Guizhou University, Guiyang 550025, China"},{"name":"Guizhou Big Data Academy, Guizhou University, Guiyang 550025, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6590-5757","authenticated-orcid":false,"given":"Weijie","family":"Tan","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Public Big Data, College of Computer Science and Technology, Guizhou University, Guiyang 550025, China"},{"name":"Guizhou Big Data Academy, Guizhou University, Guiyang 550025, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0292-5413","authenticated-orcid":false,"given":"Yue","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Data Science and Information Engineering, Guizhou Minzu University, Guiyang 550025, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8661-6230","authenticated-orcid":false,"given":"Hai","family":"Liu","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Public Big Data, College of Computer Science and Technology, Guizhou University, Guiyang 550025, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4741-8896","authenticated-orcid":false,"given":"Hongfa","family":"Ding","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Public Big Data, College of Computer Science and Technology, Guizhou University, Guiyang 550025, China"},{"name":"Information School, Guizhou University of Finance and Economics, Guiyang 550025, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,4,11]]},"reference":[{"key":"ref_1","unstructured":"Kone\u010dn\u1ef3, J., McMahan, H.B., Ramage, D., and Richt\u00e1rik, P. 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