{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,26]],"date-time":"2026-02-26T23:58:00Z","timestamp":1772150280268,"version":"3.50.1"},"reference-count":31,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2019,3,21]],"date-time":"2019-03-21T00:00:00Z","timestamp":1553126400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61802129"],"award-info":[{"award-number":["61802129"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Postdoctoral Science Foundation of China","award":["2015M571931"],"award-info":[{"award-number":["2015M571931"]}]},{"name":"Fundamental Research Funds for 86 the Central Universities","award":["2017MS121"],"award-info":[{"award-number":["2017MS121"]}]},{"name":"Natural Science Foundation Guangdong Province","award":["2018A030310381"],"award-info":[{"award-number":["2018A030310381"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In the classical GM(1,1) model, an accumulated generating operation is made on the original non-negative sequence to obtain a monotone increasing 1-AGO sequence, and the forecasting model is established based on the 1-AGO sequence. A great number of scholars have improved the accuracy of grey model prediction through better developed background value and the equation for the time response. In this work, we reconstruct the background value based on a new developed monotonicity-preserving piecewise cubic interpolations spline, and thereby establish a new GM(1,1) model. Numerical examples show that the new GM(1,1) model has better prediction quality of data than the original GM(1,1) model and improves the precision of prediction in practice.<\/jats:p>","DOI":"10.3390\/sym11030420","type":"journal-article","created":{"date-parts":[[2019,3,21]],"date-time":"2019-03-21T12:28:01Z","timestamp":1553171281000},"page":"420","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["A New GM(1,1) Model Based on Cubic Monotonicity-Preserving Interpolation Spline"],"prefix":"10.3390","volume":"11","author":[{"given":"Yuanpeng","family":"Zhu","sequence":"first","affiliation":[{"name":"School of Mathematics, South China University of Technology, Guangzhou 510640, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zehua","family":"Jian","sequence":"additional","affiliation":[{"name":"School of Business Administration, South China University of Technology, Guangzhou 510640, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yurui","family":"Du","sequence":"additional","affiliation":[{"name":"School of Business Administration, South China University of Technology, Guangzhou 510640, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wenqing","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Business Administration, South China University of Technology, Guangzhou 510640, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jiwei","family":"Fang","sequence":"additional","affiliation":[{"name":"School of Business Administration, South China University of Technology, Guangzhou 510640, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,3,21]]},"reference":[{"key":"ref_1","first-page":"288","article-title":"Control problems of Grey system","volume":"5","author":"Deng","year":"1982","journal-title":"Syst. 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