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In order to ensure the stability and efficiency of grey forecasting control model, the data transformation for a raw series is an important and useful method for enhancing accuracy and improving ill\u2010condition of the non\u2010equigap GM(1,1) model.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-heading\">Findings<\/jats:title><jats:p>This paper discusses the quantitative relations between the multiple transformation and the parameters of the non\u2010equigap GM(1,1) model in detail, and studies the effect of the multiple transformation on the condition number of the non\u2010equigap GM(1,1) model.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-heading\">Research limitations\/implications<\/jats:title><jats:p>Accessibility and availability of data are the main limitations based on which model will be applied.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-heading\">Practical implications<\/jats:title><jats:p>Choosing an appropriate multiple of transformation cannot only eliminate dimension, lessen computation and maintain high accuracy, but also largely reduce the condition number of the model and improve the ill\u2010condition of non\u2010equigap GM(1,1) model effectively.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-heading\">Originality\/value<\/jats:title><jats:p>This paper seems to be the first to discuss the stability problems for the non\u2010equigap GM(1,1) model.<\/jats:p><\/jats:sec>","DOI":"10.1108\/03684920910994060","type":"journal-article","created":{"date-parts":[[2009,11,14]],"date-time":"2009-11-14T07:00:38Z","timestamp":1258182038000},"page":"1701-1708","source":"Crossref","is-referenced-by-count":8,"title":["Research on the stability of non\u2010equigap grey control model under multiple transformations"],"prefix":"10.1108","volume":"38","author":[{"given":"Xinping","family":"Xiao","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fuqin","family":"Li","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"140","reference":[{"key":"key2022012520313083200_b12","unstructured":"Deng, J.L. 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(1988), \u201cThe concept of stabilities of general systems\u201d, International Journal of General Systems, Vol. 14 No. 3, pp. 239\u201049.","DOI":"10.1080\/03081078808935006"},{"key":"key2022012520313083200_b19","unstructured":"Lin, Y. (1991), \u201cStabilities and controllabilities of hierarchies of general systems\u201d, Cybernetica: Journal of International Association for Cybernetics, Vol. 34 No. 1, pp. 46\u201061."},{"key":"key2022012520313083200_b22","doi-asserted-by":"crossref","unstructured":"Lin, Y. (1998), \u201cDiscontinuity: a weakness of calculus and beginning of a new era\u201d, Kybernetes: The International Journal of Systems & Cybernetics, Vol. 27 Nos 6\/7, pp. 614\u201018.","DOI":"10.1108\/03684929810223021"},{"key":"key2022012520313083200_b24","doi-asserted-by":"crossref","unstructured":"Lin, Y. 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(1996), \u201cApplication of non\u2010equigap GM(1,1) model in fatigue experiment data processing online inspecting\u201d, Machine Intensity, Vol. 18 No. 3, pp. 60\u20103."},{"key":"key2022012520313083200_b23","doi-asserted-by":"crossref","unstructured":"OuYang, S.C., Miao, J.H., Wu, Y., Lin, Y., Peng, T.Y. and Xiao, T.G. (2000), \u201cSecond stir and incompleteness of quantitative analysis\u201d, Kybernetes: The International Journal of Systems & Cybernetics, Vol. 29, pp. 53\u201070.","DOI":"10.1108\/03684920010308853"},{"key":"key2022012520313083200_b10","unstructured":"Shi, B.Z. (1993), \u201cModelling of non\u2010equigap GM(1,1)\u201d, The Journal of Grey System, Vol. 5 No. 2, pp. 105\u201014."},{"key":"key2022012520313083200_b13","unstructured":"Tan, G.J. 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