{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,8,2]],"date-time":"2025-08-02T17:56:40Z","timestamp":1754157400539,"version":"3.41.2"},"reference-count":16,"publisher":"Emerald","issue":"1","license":[{"start":{"date-parts":[[2012,1,27]],"date-time":"2012-01-27T00:00:00Z","timestamp":1327622400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.emerald.com\/insight\/site-policies"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2012,1,27]]},"abstract":"<jats:sec><jats:title content-type=\"abstract-heading\">Purpose<\/jats:title><jats:p>The purpose of this paper is to propose a model for effective data filling and precise prediction, which is used to solve the prediction problem of sequential data with the characteristics of poor information, high growth and containing extraordinary points.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-heading\">Design\/methodology\/approach<\/jats:title><jats:p>After proving that the three principles of smooth sequence are not a sufficient condition for the judgement of sequence smoothness, judgement rules for sequence smoothness based on smoothness efficiency is introduced. Based on the non\u2010homogenous discrete grey model (NDGM) model which fits for high growth sequence, model error caused by equal weight mean value is analyzed, and mean value generation weight efficiency is optimized by the method of differential. Prediction steps that fit sequences with high growth, poor information and containing extraordinary points is established on the basis of equal weight mean value generation efficiency.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-heading\">Findings<\/jats:title><jats:p>The results are convincing: previous judgement rules used for sequence smoothness do not fit for the high growth sequence, new judgement rules introduced are more effective for high growth sequence. Sequence filling algorithm based on differential ration not only improve the filling of high growth sequence, but also enhance the prediction precision of these sequences.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-heading\">Practical implications<\/jats:title><jats:p>The method exposed in the paper can be used to solve the prediction problem of sequences with poor information, high growth and containing extraordinary points, and it was proved in the cases of large and medium company new products income and Ufida Software Company. What is more, the method is also helpful in aspects of corporate financial control and strategy\u2010making process.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-heading\">Originality\/value<\/jats:title><jats:p>The paper succeeds in proposing a new interpolation algorithm that is superior to ordinary mean value generation method in the aspects of generation and prediction and to grey interpolation algorithm in the aspect of information volume by defining sequence smoothness efficiency and introducing smoothness judgement rules that are easy to compute and fits for high growth sequence and not limited to monotonicity sequence.<\/jats:p><\/jats:sec>","DOI":"10.1108\/20439371211197695","type":"journal-article","created":{"date-parts":[[2012,1,28]],"date-time":"2012-01-28T07:09:29Z","timestamp":1327734569000},"page":"70-80","source":"Crossref","is-referenced-by-count":4,"title":["Difference\u2010ratio\u2010based NDGM interpolation forecasting algorithm and its application"],"prefix":"10.1108","volume":"2","author":[{"given":"Chaoyu","family":"Zhu","sequence":"first","affiliation":[]},{"given":"Naiming","family":"Xie","sequence":"additional","affiliation":[]}],"member":"140","reference":[{"doi-asserted-by":"crossref","unstructured":"Altman, E.I. (1968), \u201cFinancial ratios, discriminant analysis and the prediction of corporate bankruptcy\u201d, Journal of Finance, Vol. 23 No. 4, pp. 589\u2010609.","key":"key2022032120035181300_b1","DOI":"10.1111\/j.1540-6261.1968.tb00843.x"},{"doi-asserted-by":"crossref","unstructured":"He, W.S., Hu, G.M. and Xiang, H.M. (2008), \u201cApply anomaly grey forecasting algorithm to cyberspace situation prediction\u201d, Proc. of IEEE Int. Conf. on Cybernetics and Intelligent Systems, IEEE Press, New York, NY, pp. 503\u20105.","key":"key2022032120035181300_b6","DOI":"10.1109\/ICCIS.2008.4670842"},{"doi-asserted-by":"crossref","unstructured":"Huang, C.C. and Lee, H.M. (2004), \u201cA grey\u2010based nearest neighbor approach for missing attribute value prediction\u201d, Applied Intelligence, Vol. 20 No. 3, pp. 239\u201052.","key":"key2022032120035181300_b7","DOI":"10.1023\/B:APIN.0000021416.41043.0f"},{"unstructured":"Jin, Y.F., Zhu, Q.S. and Xing, Y.K. (2006), \u201cGrey interpolation reasoning approach for missing value in series data\u201d, Control and Decision, Vol. 21 No. 2, pp. 236\u201040.","key":"key2022032120035181300_b8"},{"unstructured":"Li, J.F. and Dai, W.Z. (2004), \u201cA new approach of background value\u2010building and its application based on data interpolation and Newton\u2010Cores formula\u201d, Systems Engineering\u2010Theory & Practice, Vol. 24 No. 10, pp. 122\u20106.","key":"key2022032120035181300_b5"},{"unstructured":"Liu, S.F. and Lin, Y. (2006), Grey Information Theory and Practical Applications, Springer, London.","key":"key2022032120035181300_b2"},{"doi-asserted-by":"crossref","unstructured":"Qin, Y., Zhang, S., Zhu, X., Zhang, J. and Zhang, C. (2009), \u201cPOP algorithm: kernel\u2010based imputation to treat missing values in knowledge discovery from databases\u201d, Expert Systems with Applications, Vol. 36 No. 2, pp. 2794\u2010804.","key":"key2022032120035181300_b3","DOI":"10.1016\/j.eswa.2008.01.059"},{"unstructured":"Wei, Y. and Zhang, Y. (2007a), \u201cA criterion of comparing the function transformations to raise the smooth degree of grey modeling data\u201d, The Journal of Grey System, Vol. 19 No. 1, pp. 91\u20108.","key":"key2022032120035181300_b9"},{"unstructured":"Wei, Y. and Zhang, Y. (2007b), \u201cAn essential characteristic of the discrete function transformation to increase the smooth degree of data\u201d, The Journal of Grey System, Vol. 19 No. 3, pp. 293\u2010300.","key":"key2022032120035181300_b10"},{"unstructured":"Xie, N.M. and Liu, S.F. (2005), \u201cDiscrete GM(1,1) and mechanism of grey forecasting model\u201d, Systems Engineering\u2010Theory & Practice, Vol. 25 No. 1, pp. 93\u20108.","key":"key2022032120035181300_b14"},{"doi-asserted-by":"crossref","unstructured":"Xie, N.M. and Liu, S.F. (2009), \u201cDiscrete grey forecasting model and its optimization\u201d, Applied Mathematical Modeling, Vol. 33 No. 2 pp. 1173\u20101186. Science, Vol. 18 No. 2 pp. 184\u2010192.","key":"key2022032120035181300_b15","DOI":"10.1016\/j.apm.2008.01.011"},{"unstructured":"Zeng, B., Liu, S.F., Fang, Z.G. and Xie, N.M. (2009), \u201cGrey combined forecast models and its application\u201d, Chinese Journal of Management Science, Vol. 17 No. 5, pp. 150\u20105.","key":"key2022032120035181300_b11"},{"doi-asserted-by":"crossref","unstructured":"Zeng, J.S. and Gao, C.H. (2009), \u201cImprovement of identification of blast furnace iron making process by outlier detection and missing value imputation\u201d, Journal of Process Control, Vol. 19 No. 9, pp. 1519\u201028.","key":"key2022032120035181300_b4","DOI":"10.1016\/j.jprocont.2009.07.006"},{"unstructured":"Zhang, Q.S. (2007), \u201cImproving the precision of GM(1,1) model by using particle swarm optimization\u201d, Chinese Journal of Management Science, Vol. 15 No. 5, pp. 126\u20109.","key":"key2022032120035181300_b12"},{"unstructured":"Zeng, X. and Xiao, X. (2009), \u201cImprovement of GM(1,1) model and its applicable region\u201d, Systems Engineering, Vol. 27 No. 1, pp. 103\u20107.","key":"key2022032120035181300_b13"},{"doi-asserted-by":"crossref","unstructured":"Xinping, X. and Kunkun, P. (2011), \u201cResearch on generalized non\u2010equidistance GM(1,1) model based on matrix analysis\u201d, Grey Systems: Theory and Application, Vol. 1 No. 1, pp. 87\u201096.","key":"key2022032120035181300_frd1","DOI":"10.1108\/20439371111106759"}],"container-title":["Grey Systems: Theory and Application"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.emeraldinsight.com\/doi\/full-xml\/10.1108\/20439371211197695","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.emerald.com\/insight\/content\/doi\/10.1108\/20439371211197695\/full\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.emerald.com\/insight\/content\/doi\/10.1108\/20439371211197695\/full\/html","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,7,24]],"date-time":"2025-07-24T23:52:37Z","timestamp":1753401157000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.emerald.com\/gs\/article\/2\/1\/70-80\/101411"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,1,27]]},"references-count":16,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2012,1,27]]}},"alternative-id":["10.1108\/20439371211197695"],"URL":"https:\/\/doi.org\/10.1108\/20439371211197695","relation":{},"ISSN":["2043-9377"],"issn-type":[{"type":"print","value":"2043-9377"}],"subject":[],"published":{"date-parts":[[2012,1,27]]}}}