{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,8,2]],"date-time":"2025-08-02T19:03:26Z","timestamp":1754161406219,"version":"3.41.2"},"reference-count":23,"publisher":"Emerald","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2013,10,28]]},"abstract":"<jats:sec>\n                  <jats:title>Purpose<\/jats:title>\n                  <jats:p>\u2013 This paper aims to find an effective and standardized function transformation method to apply in both high-growth original data sequences and low-growth original data sequences, which can improve the accuracy of model prediction in GM(1, 1) forecast.<\/jats:p>\n               <\/jats:sec>\n               <jats:sec>\n                  <jats:title>Design\/methodology\/approach<\/jats:title>\n                  <jats:p>\u2013 In GM(1, 1) forecast, many original data sequences need to meet the quasi-exponential characteristic by methods of function transformation. However, many methods of function transformation have complex transformation processes or narrow application range. On the basis of the research results of Ye and Li, the paper presents a standardized approach based on to original data sequences and designs four situations of the standardized approach. By using high-growth and low-growth original data sequences as the objects, respectively, the paper verifies the effectiveness of the proposed method and compares the forecasting effects of GM(1, 1) based on function transformation with the original GM(1, 1).<\/jats:p>\n               <\/jats:sec>\n               <jats:sec>\n                  <jats:title>Findings<\/jats:title>\n                  <jats:p>\u2013 Most of the results show that function transformations can improve the accuracy of the conventional GM(1, 1) forecast, and transform is a powerful tool to effectively process original data sequence of GM(1, 1) modeling.<\/jats:p>\n               <\/jats:sec>\n               <jats:sec>\n                  <jats:title>Practical implications<\/jats:title>\n                  <jats:p>\u2013 GM(1, 1) forecast have been widely used in many fields such as agriculture, economy, meteorology, and geology. The proposed method in this paper can effectively apply to prediction of high-growth original data sequences and low-growth original data sequences, to some extent, enrich and deepen application of GM(1, 1) forecast.<\/jats:p>\n               <\/jats:sec>\n               <jats:sec>\n                  <jats:title>Originality\/value<\/jats:title>\n                  <jats:p>\u2013 The paper succeeds in providing a standardized approach based on and designs four intensity levels for different data sequences based on the standardized approach.<\/jats:p>\n               <\/jats:sec>","DOI":"10.1108\/gs-08-2013-0019","type":"journal-article","created":{"date-parts":[[2013,10,31]],"date-time":"2013-10-31T09:18:04Z","timestamp":1383211084000},"page":"236-249","source":"Crossref","is-referenced-by-count":3,"title":["GM(1, 1) forecast under function cot\u2009<i>x<\/i> transformation"],"prefix":"10.1108","volume":"3","author":[{"given":"Jing","family":"Ye","sequence":"first","affiliation":[{"name":"College of Information and Management Science, Henan Agricultural University, Zhengzhou, People's Republic of China and Research Center for Innovation Management, Henan Agricultural University, Zhengzhou, People's Republic of China"}]},{"given":"Bingjun","family":"Li","sequence":"additional","affiliation":[{"name":"College of Information and Management Science, Henan Agricultural University, Zhengzhou, People's Republic of China and Research Center for Innovation Management, Henan Agricultural University, Zhengzhou, People's Republic of China"}]},{"given":"Fang","family":"Liu","sequence":"additional","affiliation":[{"name":"College of Information and Management Science, Henan Agricultural University, Zhengzhou, People's Republic of China and Research Center for Innovation Management, Henan Agricultural University, Zhengzhou, People's Republic of China"}]}],"member":"140","reference":[{"issue":"3","key":"2025072817563645400_b1","first-page":"262","article-title":"An improvement of grey forecasting model","volume":"28","author":"","year":"2005","journal-title":"Journal of Liaoning Normal University (Natural Science Edition)"},{"issue":"7","key":"2025072817563645400_b2","first-page":"50","article-title":"A new development of grey forecasting model","volume":"8","author":"","year":"1990","journal-title":"System Engineering"},{"issue":"1","key":"2025072817563645400_b3","doi-asserted-by":"crossref","first-page":"24","DOI":"10.1108\/20439371211197640","article-title":"Study on parameters characteristics of NGM(1, 1, k) prediction model with multiplication transformation","volume":"2","author":"","year":"2012","journal-title":"Grey Systems: Theory and Application"},{"key":"2025072817563645400_b5","unstructured":"Cui, L.Z.\n           and Liu, S.F. (2010a), \u201cData transformation technique for grey forecasting model based on trigonometic function\u201d, 19th China's Grey System Conference Symposium (Beijing), pp. 225-229."},{"issue":"5","key":"2025072817563645400_b4","first-page":"104","article-title":"Grey forecasting model based on data transformation technology","volume":"28","author":"","year":"2010","journal-title":"Systems Engineering"},{"issue":"1","key":"2025072817563645400_b6","first-page":"132","article-title":"The GM models that x(1) (n) be taken as initial value","volume":"13","author":"","year":"2005","journal-title":"Chinese Journal of Management Science"},{"key":"2025072817563645400_b7","unstructured":"Deng, J.L.\n           (2002), Elements on Grey Theory, Huazhong University of Science and Technology Press, Wuhan."},{"issue":"9","key":"2025072817563645400_b8","first-page":"89","article-title":"An approach to grey modeling based on cot(x                   \u03b1) transformation","volume":"26","author":"","year":"2008","journal-title":"Systems Engineering"},{"key":"2025072817563645400_b9","unstructured":"He, B.\n           and Meng, Q. (2002), \u201cStudy on generalization for grey forecasting model\u201d, Systems Engineering Theory & Practice, Vol. 9, pp. 138-141."},{"issue":"1","key":"2025072817563645400_b10","first-page":"69","article-title":"On a gens arithmetic for parameters estimating of model GM(1, 1)","volume":"25","author":"","year":"2005","journal-title":"Systems Engineering Theory & Practice"},{"issue":"6","key":"2025072817563645400_b11","first-page":"35","article-title":"Method of transformation for modelling in grey systems","volume":"14","author":"","year":"1996","journal-title":"Systems Engineering"},{"issue":"3","key":"2025072817563645400_b12","first-page":"110","article-title":"An approach of the grey modeling based on cot\u2009x transformation","volume":"23","author":"","year":"2005","journal-title":"Systems Engineering"},{"issue":"10","key":"2025072817563645400_b13","first-page":"122","article-title":"A new approach of background value-building and its application based on data interpolation and Newton-Cores formula","volume":"24","author":"","year":"2004","journal-title":"Systems Engineering Theory & Practice"},{"issue":"1","key":"2025072817563645400_b14","first-page":"64","article-title":"The further generalization for grey forecasting model","volume":"13","author":"","year":"1993","journal-title":"Systems Engineering Theory & Practice"},{"issue":"8","key":"2025072817563645400_b15","first-page":"82","article-title":"Grey cluster of flying support mission","volume":"17","author":"","year":"1997","journal-title":"Systems Engineering"},{"key":"2025072817563645400_b16","unstructured":"Liu, S.F.\n           and Xie, N.M. (2008), Grey System Theory and Its Application, 4th ed., Science Press, Beijing, pp. 96-98."},{"key":"2025072817563645400_b17","unstructured":"National Bureau of Statistics of China\n           (2011), China Statistical Yearbook, China Statistics Press, Beijing."},{"issue":"12","key":"2025072817563645400_b18","first-page":"2879","article-title":"New type of data transformation and its application in GM (1, 1) model","volume":"31","author":"","year":"2009","journal-title":"Systems Engineering and Electronics"},{"issue":"1","key":"2025072817563645400_b19","first-page":"98","article-title":"The structure method and application of background value in grey system GM (1, 1) model","volume":"25","author":"","year":"2005","journal-title":"Systems Engineering Theory & Practice"},{"key":"2025072817563645400_b20","unstructured":"(The) Bureau of Statistics of Henan Province\n           (2011), Henan Statistical Yearbook, China Statistics Press, Beijing."},{"issue":"4","key":"2025072817563645400_b21","first-page":"14","article-title":"A note on the theory of gray system forecasting model","volume":"14","author":"","year":"1996","journal-title":"Systems Engineering"},{"issue":"4","key":"2025072817563645400_b22","first-page":"73","article-title":"On parameters in grey models","volume":"11","author":"","year":"2000","journal-title":"The Journal of Grey System"},{"issue":"4","key":"2025072817563645400_b23","first-page":"110","article-title":"Analysis of boundary condition for GM(1, 1) mode","volume":"10","author":"","year":"2001","journal-title":"Journal of Huazhong University of Science & Technology"}],"container-title":["Grey Systems: Theory and Application"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.emeraldinsight.com\/doi\/full-xml\/10.1108\/GS-08-2013-0019","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.emerald.com\/insight\/content\/doi\/10.1108\/GS-08-2013-0019\/full\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.emerald.com\/gs\/article-pdf\/3\/3\/236\/638543\/gs-08-2013-0019.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/www.emerald.com\/gs\/article-pdf\/3\/3\/236\/638543\/gs-08-2013-0019.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,7,28]],"date-time":"2025-07-28T21:56:46Z","timestamp":1753739806000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.emerald.com\/gs\/article\/3\/3\/236\/97922\/GM-1-1-forecast-under-function-cot-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,10,28]]},"references-count":23,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2013,10,28]]}},"URL":"https:\/\/doi.org\/10.1108\/gs-08-2013-0019","relation":{},"ISSN":["2043-9377","2043-9385"],"issn-type":[{"type":"print","value":"2043-9377"},{"type":"electronic","value":"2043-9385"}],"subject":[],"published":{"date-parts":[[2013,10,28]]}}}