{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,8]],"date-time":"2026-01-08T08:08:59Z","timestamp":1767859739791,"version":"3.49.0"},"reference-count":29,"publisher":"Emerald","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2025,6,3]]},"abstract":"<jats:sec>\n                  <jats:title>Purpose<\/jats:title>\n                  <jats:p>This study aims to address the interaction among influencing factors in real systems and the varying intensity of the impact that independent variables have on dependent variables, a new IDFGM(1,N,ri) model is proposed.<\/jats:p>\n               <\/jats:sec>\n               <jats:sec>\n                  <jats:title>Design\/methodology\/approach<\/jats:title>\n                  <jats:p>Firstly, grey relational analysis is utilized to screen the sequences of influencing factors and identify their interactions. Secondly, particle swarm optimization is employed for differential optimization of the orders and nonlinear parameters of each variable, while the least squares method is used to calculate the structural parameter matrix, constructing time response function of the model. Finally, the model is applied to simulate and predict carbon dioxide emissions in China and is compared with other models.<\/jats:p>\n               <\/jats:sec>\n               <jats:sec>\n                  <jats:title>Findings<\/jats:title>\n                  <jats:p>The results show that the IDFGM(1,N,ri) model has good simulating and predicting performance, verifying its effectiveness. The newly introduced model demonstrates a high degree of compatibility and can be seamlessly integrated with conventional grey models. In the case analysis, the IDFGM(1,N,ri) model shows enhanced predictive performance relative to the benchmark model. This finding suggests that the model articulated in this study successfully captures the nonlinear attributes of each sequence by employing differential optimization of the order, facilitated by the particle swarm optimization algorithm.<\/jats:p>\n               <\/jats:sec>\n               <jats:sec>\n                  <jats:title>Practical implications<\/jats:title>\n                  <jats:p>This article presents a scientifically grounded and effective model for forecasting carbon dioxide emissions. The outcomes of these predictions can serve as a theoretical foundation for the development of policies aimed at carbon reduction and energy transition.<\/jats:p>\n               <\/jats:sec>\n               <jats:sec>\n                  <jats:title>Originality\/value<\/jats:title>\n                  <jats:p>The unique contribution of this article is the incorporation of interactions into multivariable prediction models, along with the optimization of the cumulative sequence of both dependent and independent variables to account for variations. Furthermore, the application of particle swarm optimization has enabled the model to adapt dynamically.<\/jats:p>\n               <\/jats:sec>","DOI":"10.1108\/gs-11-2024-0130","type":"journal-article","created":{"date-parts":[[2025,5,8]],"date-time":"2025-05-08T00:11:07Z","timestamp":1746663067000},"page":"637-658","source":"Crossref","is-referenced-by-count":2,"title":["Interaction-based differential dynamic fractional-order IDFGM(1,N,ri) model and its applications"],"prefix":"10.1108","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0009-0008-3485-510X","authenticated-orcid":false,"given":"Hao","family":"Li","sequence":"first","affiliation":[{"name":"Henan Agricultural University , Zhengzhou,","place":["China"]}]},{"ORCID":"https:\/\/orcid.org\/0009-0007-6613-8538","authenticated-orcid":false,"given":"Qiwen","family":"Wei","sequence":"additional","affiliation":[{"name":"Hainan International College , , Lingshui,","place":["China"]},{"name":"Minzu University of China , , Lingshui,","place":["China"]}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9727-8049","authenticated-orcid":false,"given":"Huimin","family":"Zhou","sequence":"additional","affiliation":[{"name":"Henan Agricultural University , Zhengzhou,","place":["China"]}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8785-6092","authenticated-orcid":false,"given":"Ye","family":"Li","sequence":"additional","affiliation":[{"name":"Henan Agricultural University , Zhengzhou,","place":["China"]}]}],"member":"140","published-online":{"date-parts":[[2025,5,9]]},"reference":[{"key":"2025081310483798900_ref001","doi-asserted-by":"publisher","DOI":"10.1016\/j.asoc.2021.107220","article-title":"Forecasting CO2 emissions from Chinese marine fleets using multivariable trend interaction grey model","volume":"104","author":"Cao","year":"2021","journal-title":"Applied Soft Computing Journal"},{"key":"2025081310483798900_ref002","doi-asserted-by":"publisher","DOI":"10.1016\/j.energy.2021.119952","article-title":"Forecasting seasonal variations in electricity consumption and electricity usage efficiency of industrial sectors using a grey modeling approach","volume":"222","author":"Chen","year":"2021","journal-title":"Energy"},{"key":"2025081310483798900_ref003","doi-asserted-by":"publisher","DOI":"10.1016\/j.eswa.2022.118556","article-title":"A novel multivariate grey model for forecasting periodic oscillation time series","volume":"211","author":"Dang","year":"2023","journal-title":"Expert Systems with Applications"},{"key":"2025081310483798900_ref004","volume-title":"Grey Prediction and Grey Decision","author":"Deng","year":"1993"},{"key":"2025081310483798900_ref005","doi-asserted-by":"publisher","first-page":"7238","DOI":"10.1016\/j.egyr.2021.10.075","article-title":"Forecasting carbon dioxide emissions in BRICS countries by exponential cumulative grey model","volume":"7","author":"Guo","year":"2021","journal-title":"Energy Reports"},{"issue":"3","key":"2025081310483798900_ref006","doi-asserted-by":"publisher","first-page":"612","DOI":"10.1108\/gs-12-2022-0120","article-title":"A novel fractional multivariate GM(1,N) model with interaction effects and its application in forecasting carbon emissions from China's civil aviation","volume":"13","author":"Hu","year":"2023","journal-title":"Grey Systems: Theory and Application"},{"key":"2025081310483798900_ref007","doi-asserted-by":"publisher","DOI":"10.1016\/j.techfore.2022.122203","article-title":"Research and application of multi-variable grey optimization model with interactive effects in marine emerging industries prediction","volume":"187","author":"Li","year":"2023","journal-title":"Technological Forecasting and Social Change"},{"issue":"3","key":"2025081310483798900_ref008","doi-asserted-by":"publisher","first-page":"507","DOI":"10.1108\/gs-09-2023-0095","article-title":"A novel fractional multivariate grey prediction model for forecasting hydroelectricity consumption","volume":"14","author":"Li","year":"2024","journal-title":"Grey Systems: Theory and Application"},{"key":"2025081310483798900_ref009","doi-asserted-by":"publisher","DOI":"10.1016\/j.jclepro.2019.117941","article-title":"Assessing Ghana's carbon dioxide emissions through energy consumption structure towards a sustainable development path","volume":"238","author":"Lin","year":"2019","journal-title":"Journal of Cleaner Production"},{"key":"2025081310483798900_ref010","doi-asserted-by":"publisher","DOI":"10.1016\/j.scitotenv.2024.173351","article-title":"Prediction of carbon emissions in China's construction industry using an improved grey prediction model","volume":"938","author":"Liu","year":"2024","journal-title":"Science of The Total Environment"},{"issue":"4","key":"2025081310483798900_ref011","doi-asserted-by":"publisher","first-page":"671","DOI":"10.1108\/gs-01-2024-0005","article-title":"Forecasting hospital outpatient volume using an optimized medical two-stage hybrid grey model","volume":"14","author":"Ren","year":"2024","journal-title":"Grey Systems: Theory and Application"},{"issue":"3","key":"2025081310483798900_ref012","first-page":"515","article-title":"Multivariate GM(1,N) model with interaction effect","volume":"32","author":"Wang","year":"2017","journal-title":"Control and Decision"},{"key":"2025081310483798900_ref013","doi-asserted-by":"publisher","DOI":"10.1016\/j.energy.2023.130057","article-title":"A novel fractional system grey prediction model with dynamic delay effect for evaluating the state of health of lithium battery","volume":"290","author":"Wang","year":"2024","journal-title":"Energy"},{"key":"2025081310483798900_ref014","doi-asserted-by":"publisher","DOI":"10.1016\/j.scitotenv.2020.137194","article-title":"Forecasting CO2 emissions in Chinas commercial department, through BP neural network based on random forest and PSO","volume":"718","author":"Wen","year":"2020","journal-title":"Science of The Total Environment"},{"key":"2025081310483798900_ref015","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2021.111657","article-title":"A time power-based grey model with conformable fractional derivative and its applications","volume":"155","author":"Wu","year":"2022","journal-title":"Chaos, Solitons and Fractals"},{"key":"2025081310483798900_ref016","doi-asserted-by":"publisher","DOI":"10.1016\/j.energy.2021.121533","article-title":"Forecast of natural gas consumption in the Asia-Pacific region using a fractional-order incomplete gamma grey model","volume":"237","author":"Xiong","year":"2021","journal-title":"Energy"},{"key":"2025081310483798900_ref017","doi-asserted-by":"publisher","DOI":"10.1016\/j.eswa.2022.116691","article-title":"Fractional order time-delay multivariable discrete grey model for short-term online public opinion prediction","volume":"197","author":"Yan","year":"2022","journal-title":"Expert Systems with Applications"},{"issue":"2","key":"2025081310483798900_ref018","doi-asserted-by":"publisher","first-page":"253","DOI":"10.1108\/gs-09-2019-0039","article-title":"Prediction of grain supply and demand structural balance in China based on grey models","volume":"11","author":"Yang","year":"2021","journal-title":"Grey Systems: Theory and Application"},{"key":"2025081310483798900_ref019","doi-asserted-by":"publisher","first-page":"493","DOI":"10.1016\/j.apm.2020.09.045","article-title":"A novel time-delay multivariate grey model for impact analysis of CO2 emissions from China's transportation sectors","volume":"91","author":"Ye","year":"2021","journal-title":"Applied Mathematical Modelling"},{"key":"2025081310483798900_ref020","doi-asserted-by":"publisher","DOI":"10.1016\/j.eswa.2023.121627","article-title":"A novel multivariate time-lag discrete grey model based on action time and intensities for predicting the productions in food industry","volume":"238","author":"Ye","year":"2024","journal-title":"Expert Systems with Applications"},{"key":"2025081310483798900_ref021","doi-asserted-by":"publisher","first-page":"117","DOI":"10.1016\/j.apm.2022.04.031","article-title":"A novel multivariable grey prediction model with different accumulation orders and performance comparison","volume":"109","author":"Yin","year":"2022","journal-title":"Applied Mathematical Modelling"},{"key":"2025081310483798900_ref022","doi-asserted-by":"publisher","DOI":"10.1016\/j.jclepro.2023.136889","article-title":"Prediction of carbon dioxide emissions in China using a novel grey model with multi-parameter combination optimization","volume":"404","author":"Yin","year":"2023","journal-title":"Journal of Cleaner Production"},{"issue":"7","key":"2025081310483798900_ref023","first-page":"2166","article-title":"Research on order difference optimization and structural expansion of multidimensional grey model","volume":"43","author":"Yin","year":"2023","journal-title":"Journal of Systems Engineering Theory and Practice"},{"key":"2025081310483798900_ref024","volume-title":"Grey Prediction Theory and its Application","author":"Zeng","year":"2020"},{"key":"2025081310483798900_ref025","doi-asserted-by":"publisher","DOI":"10.1016\/j.eswa.2023.119943","article-title":"A novel traffic flow prediction model: variable order fractional grey model based on an improved grey evolution algorithm","volume":"224","author":"Zhang","year":"2023","journal-title":"Expert Systems with Applications"},{"key":"2025081310483798900_ref026","doi-asserted-by":"publisher","DOI":"10.1016\/j.apenergy.2024.124232","article-title":"Accurate and efficient daily carbon emission forecasting based on improved ARIMA","volume":"376","author":"Zhong","year":"2024","journal-title":"Applied Energy"},{"key":"2025081310483798900_ref027","doi-asserted-by":"publisher","DOI":"10.1016\/j.envpol.2021.116614","article-title":"Predictions and mitigation strategies of PM2.5 concentration in the Yangtze River Delta of China based on a novel nonlinear seasonal grey model","volume":"276","author":"Zhou","year":"2021","journal-title":"Environmental Pollution"},{"key":"2025081310483798900_ref028","doi-asserted-by":"publisher","DOI":"10.1016\/j.jclepro.2024.142605","article-title":"Innovative approach to daily carbon dioxide emission forecast based on ensemble of quantile regression and attention BILSTM","volume":"460","author":"Zhou","year":"2024","journal-title":"Journal of Cleaner Production"},{"key":"2025081310483798900_ref029","doi-asserted-by":"publisher","DOI":"10.1016\/j.cie.2023.109278","article-title":"A novel conformable fractional nonlinear grey multivariable prediction model with marine predator algorithm for time series prediction","volume":"180","author":"Zhu","year":"2023","journal-title":"Computers and Industrial Engineering"}],"container-title":["Grey Systems: Theory and Application"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.emerald.com\/insight\/content\/doi\/10.1108\/GS-11-2024-0130\/full\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.emerald.com\/gs\/article-pdf\/15\/3\/637\/10069999\/gs-11-2024-0130.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/www.emerald.com\/gs\/article-pdf\/15\/3\/637\/10069999\/gs-11-2024-0130.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,8,13]],"date-time":"2025-08-13T14:48:44Z","timestamp":1755096524000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.emerald.com\/gs\/article\/15\/3\/637\/1274954\/Interaction-based-differential-dynamic-fractional"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,5,9]]},"references-count":29,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2025,6,3]]}},"URL":"https:\/\/doi.org\/10.1108\/gs-11-2024-0130","relation":{},"ISSN":["2043-9377","2043-9385"],"issn-type":[{"value":"2043-9377","type":"print"},{"value":"2043-9385","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,5,9]]}}}