{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T17:08:03Z","timestamp":1776877683794,"version":"3.51.2"},"reference-count":32,"publisher":"World Scientific Pub Co Pte Ltd","issue":"04","funder":[{"DOI":"10.13039\/501100012456","name":"National Social Science Foundation of China","doi-asserted-by":"crossref","award":["21BGL001"],"award-info":[{"award-number":["21BGL001"]}],"id":[{"id":"10.13039\/501100012456","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["71701115"],"award-info":[{"award-number":["71701115"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100007129","name":"Shandong Natural Science Foundation","doi-asserted-by":"crossref","award":["ZR2020MG003"],"award-info":[{"award-number":["ZR2020MG003"]}],"id":[{"id":"10.13039\/501100007129","id-type":"DOI","asserted-by":"crossref"}]},{"name":"Special Project for Internet Development of Social Science Planning Special Program of Shandong Province","award":["17CHLJ23"],"award-info":[{"award-number":["17CHLJ23"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Unc. Fuzz. Knowl. Based Syst."],"published-print":{"date-parts":[[2025,6]]},"abstract":"<jats:p> The online rumor refutation platform is an important channel for clarifying rumors, and the public obtains relevant debunking information and knows the truth through online rumor refutation platforms. Therefore, it is particularly important to reasonably select and utilize relevant online rumor refutation platforms, which can help the public participate in rumor governance and deepen network ecological governance. However, there are many uncertain factors in the entire process of debunking rumors, such as the promotional debunking abilities of different levels of online rumor refutation platforms, while also considering various practical constraints. In order to consider the influence of uncertain factors during the refutation process to improve the effectiveness of refutation, and explore the applicability of uncertainty theory in practice, this paper studies a new mode of refutation information promotion led by social managers such as the government and collaborated by various online refutation platforms, and proposes an uncertain refutation information propagation (URIP) model by considering multiple realistic constraints. Specifically, we characterize the uncertain factors as uncertain variables in the refutation process, such as the debunking ability of online refutation platforms, and solve for the optimal solution by maximizing the expected value of refutation propagation effectiveness. Subsequently, based on the relevant knowledge of uncertainty theory, we derive an equivalent deterministic model for the URIP model. Finally, in order to enable decision-makers to better apply the URIP model in practice, a numerical example is applied to compare the URIP model proposed in this paper with the URIP model without realistic constraints, which proves the superiority of our model. <\/jats:p>","DOI":"10.1142\/s0218488525500163","type":"journal-article","created":{"date-parts":[[2025,6,25]],"date-time":"2025-06-25T00:55:47Z","timestamp":1750812947000},"page":"381-400","source":"Crossref","is-referenced-by-count":1,"title":["Uncertain Refutation Information Propagation Model by Considering Multiple Realistic Constraints"],"prefix":"10.1142","volume":"33","author":[{"given":"Chunhua","family":"Gao","sequence":"first","affiliation":[{"name":"Business School, Shandong Normal University, Jinan, 250014, P. R. China"}]},{"given":"Yang","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Economics and Management, Beihang University, Beijing, 100191, P. R. China"}]},{"given":"Yufu","family":"Ning","sequence":"additional","affiliation":[{"name":"School of Information Engineering, Shandong Youth University of Political Science, Jinan, 250103, P. R. China"}]},{"given":"Fengming","family":"Liu","sequence":"additional","affiliation":[{"name":"Business School, Shandong Normal University, Jinan, 250014, P. R. 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