{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,16]],"date-time":"2026-03-16T12:02:31Z","timestamp":1773662551311,"version":"3.50.1"},"reference-count":54,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2024,8,20]],"date-time":"2024-08-20T00:00:00Z","timestamp":1724112000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2024,8,20]],"date-time":"2024-08-20T00:00:00Z","timestamp":1724112000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100012456","name":"National Social Science Fund of China","doi-asserted-by":"publisher","award":["21BGL001"],"award-info":[{"award-number":["21BGL001"]}],"id":[{"id":"10.13039\/501100012456","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Soft Comput"],"published-print":{"date-parts":[[2026,3]]},"DOI":"10.1007\/s00500-024-09665-4","type":"journal-article","created":{"date-parts":[[2024,8,20]],"date-time":"2024-08-20T03:03:37Z","timestamp":1724123017000},"page":"1999-2014","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["A dynamic model of social media ad information diffusion in uncertain environment"],"prefix":"10.1007","volume":"30","author":[{"given":"Meiling","family":"Jin","sequence":"first","affiliation":[]},{"given":"Yufu","family":"Ning","sequence":"additional","affiliation":[]},{"given":"Fengming","family":"Liu","sequence":"additional","affiliation":[]},{"given":"Zhen","family":"Li","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7562-0640","authenticated-orcid":false,"given":"Haoran","family":"Zheng","sequence":"additional","affiliation":[]},{"given":"Yichang","family":"Gao","sequence":"additional","affiliation":[]},{"given":"Jian","family":"Zhou","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2024,8,20]]},"reference":[{"issue":"3","key":"9665_CR1","doi-asserted-by":"crossref","first-page":"416","DOI":"10.1108\/RIBS-04-2020-0045","volume":"31","author":"MY Abuhashesh","year":"2021","unstructured":"Abuhashesh MY, Alshurideh MT, Ahmed A et al (2021) The effect of culture on customers? attitudes toward Facebook advertising: the moderating role of gender. Rev Int Bus Strategy 31(3):416\u2013437","journal-title":"Rev Int Bus Strategy"},{"issue":"2","key":"9665_CR2","doi-asserted-by":"crossref","first-page":"369","DOI":"10.1080\/21565503.2019.1637353","volume":"9","author":"C Carpinella","year":"2021","unstructured":"Carpinella C, Bauer NM (2021) A visual analysis of gender stereotypes in campaign advertising. Polit Groups Ident 9(2):369\u2013386","journal-title":"Polit Groups Ident"},{"key":"9665_CR3","doi-asserted-by":"crossref","first-page":"282","DOI":"10.1108\/RAUSP-08-2020-0187","volume":"56","author":"B Casais","year":"2021","unstructured":"Casais B, Pereira AC (2021) The prevalence of emotional and rational tone in social advertising appeals. RAUSP Manag J 56:282\u2013294","journal-title":"RAUSP Manag J"},{"issue":"2","key":"9665_CR4","doi-asserted-by":"crossref","first-page":"321","DOI":"10.21629\/JSEE.2018.02.13","volume":"29","author":"G Chao","year":"2018","unstructured":"Chao G, Shiyou Q, Yingying X et al (2018) Diffusion mechanism simulation of cloud manufacturing complex network based on cooperative game theory. J Syst Eng Electron 29(2):321\u2013335","journal-title":"J Syst Eng Electron"},{"issue":"4","key":"9665_CR5","first-page":"135","volume":"13","author":"PY Chen","year":"2021","unstructured":"Chen PY (2021) A multi-channel assessment model constructed based on transaction cost complexity: newly listed beauty cosmetics case. Int J Org Innov 13(4):135\u2013161","journal-title":"Int J Org Innov"},{"issue":"5","key":"9665_CR6","first-page":"47","volume":"24","author":"Z Chen","year":"2021","unstructured":"Chen Z, Wu Y, S L (2021) Research on the influence of individual information interaction on stock price linkage relationship in stock bars. J Manag Sci 24(5):47\u201369","journal-title":"J Manag Sci"},{"issue":"12","key":"9665_CR7","first-page":"3149","volume":"40","author":"X Ding","year":"2020","unstructured":"Ding X, L L (2020) Research on social media rumor propagation dynamics under the anti-silence spiral effect. Syst Eng Theory Pract 40(12):3149\u20133163","journal-title":"Syst Eng Theory Pract"},{"key":"9665_CR8","doi-asserted-by":"crossref","first-page":"482","DOI":"10.1007\/s12083-020-00984-5","volume":"14","author":"Y Ding","year":"2021","unstructured":"Ding Y, Luo D, Xiang H et al (2021) Design and implementation of blockchain-based digital advertising media promotion system. Peer-to-Peer Netw Appl 14:482\u2013496","journal-title":"Peer-to-Peer Netw Appl"},{"key":"9665_CR9","volume-title":"Network models and information diffusion","author":"EM Fischer","year":"2019","unstructured":"Fischer EM (2019) Network models and information diffusion. Cornell University, New York"},{"key":"9665_CR10","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1016\/j.eswa.2019.05.047","volume":"134","author":"A Foroozani","year":"2019","unstructured":"Foroozani A, Ebrahimi M (2019) Anomalous information diffusion in social networks: Twitter and digg. Expert Syst Appl 134:249\u2013266","journal-title":"Expert Syst Appl"},{"issue":"1","key":"9665_CR11","doi-asserted-by":"crossref","first-page":"283","DOI":"10.1007\/s11424-021-0039-y","volume":"35","author":"R Gao","year":"2022","unstructured":"Gao R, Liu K, Li Z et al (2022a) American barrier option pricing formulas for currency model in uncertain environment. J Syst Sci Complex 35(1):283\u2013312","journal-title":"J Syst Sci Complex"},{"issue":"4","key":"9665_CR12","first-page":"58","volume":"45","author":"Y Gao","year":"2022","unstructured":"Gao Y, Sun Y, Liu F et al (2022b) Research on the echo chamber effect of social network opinion dissemination. Intell Theory Pract 45(4):58\u201366","journal-title":"Intell Theory Pract"},{"key":"9665_CR13","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1023\/A:1011122126881","volume":"12","author":"J Goldenberg","year":"2001","unstructured":"Goldenberg J, Libai B, Muller E (2001a) Talk of the network: a complex systems look at the underlying process of word-of-mouth. Market Lett 12:211\u2013223","journal-title":"Market Lett"},{"issue":"3","key":"9665_CR14","first-page":"1","volume":"9","author":"J Goldenberg","year":"2001","unstructured":"Goldenberg J, Libai B, Muller E (2001b) Using complex systems analysis to advance marketing theory development: modeling heterogeneity effects on new product growth through stochastic cellular automata. Acad Mark Sci Rev 9(3):1\u201318","journal-title":"Acad Mark Sci Rev"},{"issue":"6","key":"9665_CR15","doi-asserted-by":"crossref","first-page":"1420","DOI":"10.1086\/226707","volume":"83","author":"M Granovetter","year":"1978","unstructured":"Granovetter M (1978) Threshold models of collective behavior. Am J Sociol 83(6):1420\u20131443","journal-title":"Am J Sociol"},{"issue":"1","key":"9665_CR16","doi-asserted-by":"crossref","first-page":"16","DOI":"10.1016\/j.intmar.2021.01.001","volume":"55","author":"JL Hayes","year":"2021","unstructured":"Hayes JL, Brinson NH, Bott GJ et al (2021) The influence of consumer-brand relationship on the personalized advertising privacy calculus in social media. J Interact Market 55(1):16\u201330","journal-title":"J Interact Market"},{"issue":"03","key":"9665_CR17","doi-asserted-by":"crossref","first-page":"285","DOI":"10.1142\/S2196888819500155","volume":"6","author":"TKT Ho","year":"2019","unstructured":"Ho TKT, Bui QV, Bui M (2019) Information diffusion on complex networks: a novel approach based on topic modeling and pretopology theory. Vietnam J Comput Sci 6(03):285\u2013309","journal-title":"Vietnam J Comput Sci"},{"issue":"2","key":"9665_CR18","doi-asserted-by":"crossref","first-page":"232","DOI":"10.1080\/10530789.2021.1925046","volume":"31","author":"HT Hsu","year":"2022","unstructured":"Hsu HT, Petering R, Onasch-Vera L (2022) Implications of covid-19 vaccine uptake among young adults experiencing homelessness: a brief report. J Soc Distress Homelessness 31(2):232\u2013237","journal-title":"J Soc Distress Homelessness"},{"key":"9665_CR19","doi-asserted-by":"crossref","first-page":"717","DOI":"10.1007\/s11036-018-1004-4","volume":"23","author":"D Jin","year":"2018","unstructured":"Jin D, Ma X, Zhang Y et al (2018) Information diffusion model based on social big data. Mob Netw Appl 23:717\u2013722","journal-title":"Mob Netw Appl"},{"issue":"4","key":"9665_CR20","first-page":"1","volume":"12","author":"H Li","year":"2023","unstructured":"Li H, Yang X, Ni Y (2023) Uncertain yield-density regression model with application to parsnips. Int J Gen Syst 12(4):1\u201325","journal-title":"Int J Gen Syst"},{"issue":"1","key":"9665_CR21","first-page":"3","volume":"2","author":"B Liu","year":"2008","unstructured":"Liu B (2008) Fuzzy process, hybrid process and uncertain process. J Uncertain Syst 2(1):3\u201316","journal-title":"J Uncertain Syst"},{"key":"9665_CR22","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-540-89484-1","volume-title":"Theory and practice of uncertain programming","author":"B Liu","year":"2009","unstructured":"Liu B (2009) Theory and practice of uncertain programming, 2nd edn. Springer, Berlin","edition":"2"},{"issue":"1","key":"9665_CR23","first-page":"399","volume":"41","author":"Q Liu","year":"2021","unstructured":"Liu Q, Shi G, Sheng Y (2021) An uncertain seir rumor model. J Intell Fuzzy Syst 41(1):399\u2013412","journal-title":"J Intell Fuzzy Syst"},{"issue":"8","key":"9665_CR24","doi-asserted-by":"crossref","first-page":"10403","DOI":"10.1007\/s12652-022-03697-0","volume":"14","author":"Z Liu","year":"2023","unstructured":"Liu Z, Kang R (2023) Michaelis-Menten pharmacokinetics based on uncertain differential equations. J Ambient Intell Human Comput 14(8):10403\u201310415","journal-title":"J Ambient Intell Human Comput"},{"key":"9665_CR25","doi-asserted-by":"crossref","first-page":"1881","DOI":"10.1016\/j.apm.2020.08.061","volume":"89","author":"Z Liu","year":"2021","unstructured":"Liu Z, Yang X (2021a) A linear uncertain pharmacokinetic model driven by Liu process. Appl Math Modell 89:1881\u20131899","journal-title":"Appl Math Modell"},{"key":"9665_CR26","volume":"148","author":"Z Liu","year":"2021","unstructured":"Liu Z, Yang Y (2021b) Selection of uncertain differential equations using cross validation. Chaos Solitons Fractals 148:111049","journal-title":"Chaos Solitons Fractals"},{"key":"9665_CR27","volume":"404","author":"Z Liu","year":"2021","unstructured":"Liu Z, Yang Y (2021c) Uncertain pharmacokinetic model based on uncertain differential equation. Appl Math Comput 404:126118","journal-title":"Appl Math Comput"},{"issue":"4","key":"9665_CR28","doi-asserted-by":"crossref","first-page":"1703","DOI":"10.1007\/s00500-021-06702-4","volume":"26","author":"Z Liu","year":"2022","unstructured":"Liu Z, Yang Y (2022) Swaption pricing problem in uncertain financial market. Soft Comput 26(4):1703\u20131710","journal-title":"Soft Comput"},{"issue":"2","key":"9665_CR29","doi-asserted-by":"crossref","first-page":"287","DOI":"10.17270\/J.LOG.2020.383","volume":"16","author":"A Mahmood","year":"2020","unstructured":"Mahmood A, Haider SZ (2020) Relationship of advertising appeals, corporate reputation and brand advocacy: the mediation role of brand loyalty. LogForum 16(2):287\u2013298","journal-title":"LogForum"},{"issue":"3","key":"9665_CR30","doi-asserted-by":"crossref","first-page":"78","DOI":"10.30525\/2661-5150\/2021-3-11","volume":"2","author":"S Ostrianyn","year":"2021","unstructured":"Ostrianyn S, Yakovenko O (2021) Practical realizations of a generalized advertising cybernetic model. Three Seas Econ J 2(3):78\u201386","journal-title":"Three Seas Econ J"},{"issue":"6","key":"9665_CR31","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1007\/978-3-030-37110-4_14","volume":"32","author":"A Paul","year":"2020","unstructured":"Paul A, Suppakitpaisarn V, Rangan CP (2020) Smart contract-driven mechanism design to mitigate information diffusion in social networks. Springer Proc Bus Econ 32(6):201\u2013216","journal-title":"Springer Proc Bus Econ"},{"issue":"1","key":"9665_CR32","first-page":"11872","volume":"8","author":"J Qi","year":"2018","unstructured":"Qi J, Liang X, Wang Y et al (2018) Discrete time information diffusion in online social networks: micro and macro perspectives. Sci Reports 8(1):11872","journal-title":"Sci Reports"},{"key":"9665_CR33","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s41109-019-0215-3","volume":"4","author":"Z Qiang","year":"2019","unstructured":"Qiang Z, Pasiliao EL, Zheng QP (2019) Model-based learning of information diffusion in social media networks. Appl Netw Sci 4:1\u201316","journal-title":"Appl Netw Sci"},{"issue":"3","key":"9665_CR34","doi-asserted-by":"crossref","first-page":"4304","DOI":"10.3934\/math.2022238","volume":"7","author":"L Rao","year":"2022","unstructured":"Rao L (2022) Portfolio selection based on uncertain fractional differential equation. AIMS Math 7(3):4304\u20134314","journal-title":"AIMS Math"},{"key":"9665_CR35","doi-asserted-by":"crossref","DOI":"10.1016\/j.comnet.2020.107383","volume":"180","author":"M Sasabe","year":"2020","unstructured":"Sasabe M (2020) Mathematical epidemiological analysis of dynamics of delay attacks on pull-based competitive information diffusion. Comput Netw 180:107383","journal-title":"Comput Netw"},{"issue":"9","key":"9665_CR36","first-page":"247","volume":"16","author":"RE Schmidt","year":"2022","unstructured":"Schmidt RE, Petersen T (2022) Lazarsfeld\u2019s legacy| beyond Marienthal: the relationship between Elisabeth Noelle-Neumann and Paul F. Lazarsfeld. Int J Commun 16(9):247\u2013259","journal-title":"Int J Commun"},{"key":"9665_CR37","doi-asserted-by":"crossref","DOI":"10.1016\/j.chb.2021.106919","volume":"124","author":"A Sharma","year":"2021","unstructured":"Sharma A, Dwivedi YK, Arya V et al (2021) Does sms advertising still have relevance to increase consumer purchase intention? a hybrid pls-sem-neural network modelling approach. Comput Hum Behav 124:106919","journal-title":"Comput Hum Behav"},{"issue":"2","key":"9665_CR38","doi-asserted-by":"crossref","first-page":"702","DOI":"10.1017\/S000305542100112X","volume":"116","author":"J Sides","year":"2022","unstructured":"Sides J, Vavreck L, Warshaw C (2022) The effect of television advertising in United States elections. Am Polit Sci Rev 116(2):702\u2013718","journal-title":"Am Polit Sci Rev"},{"issue":"1","key":"9665_CR39","first-page":"216","volume":"31","author":"C Tang","year":"2022","unstructured":"Tang C, Han Y (2022) A study on product information diffusion on online social platforms by integrating two-stage process model and improved bass model. Oper Res Manag 31(1):216\u2013223","journal-title":"Oper Res Manag"},{"issue":"2","key":"9665_CR40","doi-asserted-by":"crossref","first-page":"106","DOI":"10.1080\/16522354.2020.1765669","volume":"18","author":"V Telkmann","year":"2021","unstructured":"Telkmann V (2021) Broadcasters content distribution and programming decisions in multi-channel environments: a literature review. J Media Bus Stud 18(2):106\u2013131","journal-title":"J Media Bus Stud"},{"issue":"1","key":"9665_CR41","doi-asserted-by":"crossref","first-page":"1876545","DOI":"10.1080\/23311975.2021.1876545","volume":"8","author":"A Tresa Sebastian","year":"2021","unstructured":"Tresa Sebastian A, Lal B, Anupama J et al (2021) Exploring the opinions of the Youtube visitors towards advertisements and its influence on purchase intention among viewers. Cogent Bus Manag 8(1):1876545","journal-title":"Cogent Bus Manag"},{"key":"9665_CR42","doi-asserted-by":"crossref","first-page":"604","DOI":"10.1007\/s12083-018-0684-7","volume":"12","author":"M Vitoropoulou","year":"2019","unstructured":"Vitoropoulou M, Karyotis V, Papavassiliou S (2019) Sensing and monitoring of information diffusion in complex online social networks. Peer-to-Peer Netw Appl 12:604\u2013619","journal-title":"Peer-to-Peer Netw Appl"},{"issue":"2","key":"9665_CR43","doi-asserted-by":"crossref","first-page":"60","DOI":"10.3390\/ijgi10020060","volume":"10","author":"K Wakil","year":"2021","unstructured":"Wakil K, Tahir A, Hussnain MQU et al (2021) Mitigating urban visual pollution through a multistakeholder spatial decision support system to optimize locational potential of billboards. ISPRS Int J Geo-Inf 10(2):60\u201382","journal-title":"ISPRS Int J Geo-Inf"},{"issue":"3","key":"9665_CR44","doi-asserted-by":"crossref","first-page":"1275","DOI":"10.1109\/TKDE.2020.2995075","volume":"34","author":"Z Wang","year":"2020","unstructured":"Wang Z, Chen C, Li W (2020) Joint learning of user representation with diffusion sequence and network structure. IEEE Trans Knowl Data Eng 34(3):1275\u20131287","journal-title":"IEEE Trans Knowl Data Eng"},{"issue":"5","key":"9665_CR45","doi-asserted-by":"crossref","first-page":"242","DOI":"10.3390\/info11050242","volume":"11","author":"B Wawrowski","year":"2020","unstructured":"Wawrowski B, Otola I (2020) Social media marketing in creative industries: How to use social media marketing to promote computer games? Information 11(5):242","journal-title":"Information"},{"issue":"2","key":"9665_CR46","first-page":"369","volume":"20","author":"D Yang","year":"2019","unstructured":"Yang D, Liao X, Wei J et al (2019) Modeling information diffusion with the external environment in social networks. J Internet Technol 20(2):369\u2013377","journal-title":"J Internet Technol"},{"issue":"3","key":"9665_CR47","first-page":"825","volume":"25","author":"K Yao","year":"2013","unstructured":"Yao K, Chen X (2013) A numerical method for solving uncertain differential equations. J Intell Fuzzy Syst 25(3):825\u2013832","journal-title":"J Intell Fuzzy Syst"},{"key":"9665_CR48","doi-asserted-by":"crossref","unstructured":"Yi Y, Zhang Z, Gan C (2018) The effect of social tie on information diffusion in complex networks. Physica A 509:783\u2013794","DOI":"10.1016\/j.physa.2018.06.063"},{"key":"9665_CR49","doi-asserted-by":"crossref","unstructured":"Yoon S, Bang H, Choi D et al (2021) Slow versus fast: how speed-induced construal affects perceptions of advertising messages. Int J Advert 40(2):225\u2013245","DOI":"10.1080\/02650487.2020.1766233"},{"key":"9665_CR50","doi-asserted-by":"crossref","first-page":"112","DOI":"10.1016\/j.socnet.2020.06.001","volume":"63","author":"LE Young","year":"2020","unstructured":"Young LE, Mayaud J, Suen SC et al (2020) Modeling the dynamism of hiv information diffusion in multiplex networks of homeless youth. Soc Netw 63:112\u2013121","journal-title":"Soc Netw"},{"key":"9665_CR51","volume":"154","author":"Y Yu","year":"2022","unstructured":"Yu Y, Yang X, Lei Q (2022) Pricing of equity swaps in uncertain financial market. Chaos Solitons Fractals 154:111673","journal-title":"Chaos Solitons Fractals"},{"key":"9665_CR52","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1007\/s10660-018-9316-9","volume":"20","author":"L Zhang","year":"2020","unstructured":"Zhang L, Luo M, Boncella RJ (2020) Product information diffusion in a social network. Electron Commer Res 20:3\u201319","journal-title":"Electron Commer Res"},{"key":"9665_CR53","doi-asserted-by":"crossref","first-page":"28","DOI":"10.1016\/j.comcom.2022.02.024","volume":"189","author":"X Zhang","year":"2022","unstructured":"Zhang X, Wang Y, Zhu W et al (2022) Source node detection in social networks based on trust-gmla algorithm. Comput Commun 189:28\u201335","journal-title":"Comput Commun"},{"issue":"1","key":"9665_CR54","doi-asserted-by":"crossref","first-page":"23","DOI":"10.4149\/cai_2018_1_23","volume":"37","author":"X Zhu","year":"2018","unstructured":"Zhu X, Hao J, Shen Y et al (2018) Diffusion of false information during public crises: analysis based on the cellular automaton method. Comput Inform 37(1):23\u201348","journal-title":"Comput Inform"}],"container-title":["Soft Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00500-024-09665-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00500-024-09665-4","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00500-024-09665-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,3,16]],"date-time":"2026-03-16T11:05:27Z","timestamp":1773659127000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00500-024-09665-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,8,20]]},"references-count":54,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2026,3]]}},"alternative-id":["9665"],"URL":"https:\/\/doi.org\/10.1007\/s00500-024-09665-4","relation":{},"ISSN":["1432-7643","1433-7479"],"issn-type":[{"value":"1432-7643","type":"print"},{"value":"1433-7479","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,8,20]]},"assertion":[{"value":"10 January 2024","order":1,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"20 August 2024","order":2,"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":"This article does not contain any studies with human participants performed by any of the authors.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethics approval"}}]}}