{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,8]],"date-time":"2025-10-08T16:21:46Z","timestamp":1759940506924,"version":"3.41.2"},"reference-count":17,"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 expand discrete GM (1,1) model and solve the problem of non\u2010equidistance grey prediction problem with integral interval or digital interval.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-heading\">Design\/methodology\/approach<\/jats:title><jats:p>Discrete GM (1,1) model can be utilized to simulate exponential sequence without errors, but it can't be utilized to simulate non\u2010equidistance data sequence. This paper applied optimization theories to establish generalized discrete GM (1,1) model. First, this paper established the time response of simulation sequence directly. Second, this paper established the steps of non\u2010equidistance data sequence. Finally, this paper utilized examples to test the method put forward.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-heading\">Findings<\/jats:title><jats:p>The results indicate the generalized discrete GM (1,1) (GDGM) model can perfectly simulate non\u2010equidistance exponential series. Discrete GM (1,1) model is only the special form of GDGM model.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-heading\">Practical implications<\/jats:title><jats:p>Though grey forecasting models are widely used, most of the forecasting models are based on the equal distance sequence. Due to many reasons, the raw data available usually is incomplete. There are mainly four reasons which caused non\u2010equidistance sequence. So generalized discrete GM (1,1) model can be utilized to simulate non\u2010equidistance sequence and has great application values.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-heading\">Originality\/value<\/jats:title><jats:p>The paper succeeds in establishing a generalized discrete GM (1,1) model which can be utilized to solve non\u2010equidistance data sequence forecasting. The GDGM model can be solved by MATLAB or other corresponding software.<\/jats:p><\/jats:sec>","DOI":"10.1108\/20439371211197622","type":"journal-article","created":{"date-parts":[[2012,1,28]],"date-time":"2012-01-28T07:09:22Z","timestamp":1327734562000},"page":"4-12","source":"Crossref","is-referenced-by-count":20,"title":["Generalized discrete GM (1,1) model"],"prefix":"10.1108","volume":"2","author":[{"given":"Tianxiang","family":"Yao","sequence":"first","affiliation":[]},{"given":"Jeffery","family":"Forrest","sequence":"additional","affiliation":[]},{"given":"Zaiwu","family":"Gong","sequence":"additional","affiliation":[]}],"member":"140","reference":[{"key":"key2022031520265132900_b1","unstructured":"Dai, W.Z. and Li, J.F. 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