{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,6]],"date-time":"2026-03-06T21:28:56Z","timestamp":1772832536001,"version":"3.50.1"},"reference-count":33,"publisher":"Springer Science and Business Media LLC","issue":"23","license":[{"start":{"date-parts":[[2019,2,20]],"date-time":"2019-02-20T00:00:00Z","timestamp":1550620800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["71401051"],"award-info":[{"award-number":["71401051"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["71871084"],"award-info":[{"award-number":["71871084"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Soft Comput"],"published-print":{"date-parts":[[2019,12]]},"DOI":"10.1007\/s00500-019-03845-3","type":"journal-article","created":{"date-parts":[[2019,2,20]],"date-time":"2019-02-20T16:50:16Z","timestamp":1550681416000},"page":"12873-12881","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":45,"title":["Discrete grey model with the weighted accumulation"],"prefix":"10.1007","volume":"23","author":[{"given":"Lifeng","family":"Wu","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hongying","family":"Zhao","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2019,2,20]]},"reference":[{"issue":"12","key":"3845_CR1","doi-asserted-by":"publisher","first-page":"7557","DOI":"10.1016\/j.eswa.2010.04.088","volume":"37","author":"CI Chen","year":"2010","unstructured":"Chen CI, Hsin PH, Wu CS (2010) Forecasting Taiwan\u2019s major stock indices by the Nash nonlinear grey Bernoulli model. Expert Syst Appl 37(12):7557\u20137562","journal-title":"Expert Syst Appl"},{"issue":"1","key":"3845_CR2","first-page":"133","volume":"13","author":"YG Dang","year":"2005","unstructured":"Dang YG, Liu SF, Liu B (2005) The GM models that x(1)(n) be taken as initial value. Chin J Manag Sci 13(1):133\u2013136","journal-title":"Chin J Manag Sci"},{"key":"3845_CR3","doi-asserted-by":"publisher","first-page":"1527","DOI":"10.1016\/j.jclepro.2017.06.167","volume":"162","author":"S Ding","year":"2017","unstructured":"Ding S, Dang YG, Li XM, Wang JJ, Zhao K (2017) Forecasting Chinese CO2 emissions from fuel combustion using a novel grey multivariable model. J Clean Prod 162:1527\u20131538","journal-title":"J Clean Prod"},{"issue":"1","key":"3845_CR4","first-page":"52","volume":"8","author":"Z Han","year":"1995","unstructured":"Han Z (1995) Application of exponential cumulative generation method and logarithmic cumulative generation method to grey prediction. China J Highw Transp 8(1):52\u201357","journal-title":"China J Highw Transp"},{"issue":"17","key":"3845_CR5","first-page":"218","volume":"46","author":"P Hu","year":"2016","unstructured":"Hu P (2016) The DGM(1,1) models that x(1)(n) be taken as initial value. Math Pract Theory 46(17):218\u2013222","journal-title":"Math Pract Theory"},{"key":"3845_CR6","volume-title":"Matrix perturbation analysis","author":"Sun Jiguang","year":"1987","unstructured":"Jiguang Sun (1987) Matrix perturbation analysis. Science Press, Beijing"},{"issue":"12","key":"3845_CR7","first-page":"3227","volume":"37","author":"C Li","year":"2017","unstructured":"Li C, Xie XP (2017) The DGM(1,1)atan arc-tangent function and its application. Syst Eng Theory Pract 37(12):3227\u20133234","journal-title":"Syst Eng Theory Pract"},{"issue":"8","key":"3845_CR8","doi-asserted-by":"publisher","first-page":"1465","DOI":"10.1016\/j.techfore.2006.07.010","volume":"74","author":"GD Li","year":"2007","unstructured":"Li GD, Yamaguchi D, Nagai M (2007) A GM(1,1)\u2013Markov chain combined model with an application to predict the number of Chinese international airlines. Technol Forecast Soc Chang 74(8):1465\u20131481","journal-title":"Technol Forecast Soc Chang"},{"key":"3845_CR9","doi-asserted-by":"publisher","first-page":"2475","DOI":"10.3390\/en11092475","volume":"11","author":"ML Li","year":"2018","unstructured":"Li ML, Wang W, De G, Ji XH, Tan ZF (2018) Forecasting\u00a0carbon\u00a0emissions\u00a0related\u00a0to\u00a0energy consumption\u00a0in\u00a0Beijing-Tianjin-Hebei\u00a0region\u00a0based on\u00a0grey\u00a0prediction\u00a0theory\u00a0and\u00a0extreme\u00a0learning machine\u00a0optimized\u00a0by\u00a0support\u00a0vector machine\u00a0algorithm. Energies 11:2475\u20132489","journal-title":"Energies"},{"key":"3845_CR10","doi-asserted-by":"publisher","first-page":"390","DOI":"10.1016\/j.apm.2018.08.017","volume":"65","author":"C Li","year":"2019","unstructured":"Li C, Yang YJ, Liu SF (2019a) A new method to mitigate data fluctuations for time series prediction. Appl Math Model 65:390\u2013407","journal-title":"Appl Math Model"},{"key":"3845_CR11","doi-asserted-by":"publisher","first-page":"257","DOI":"10.1016\/j.cnsns.2018.06.029","volume":"68","author":"C Li","year":"2019","unstructured":"Li C, Yang YJ, Liu SF (2019b) Comparative analysis of properties of weakening buffer operators in time series prediction models. Commun Nonlinear Sci Numer Simul 68:257\u2013285","journal-title":"Commun Nonlinear Sci Numer Simul"},{"key":"3845_CR12","doi-asserted-by":"publisher","first-page":"695","DOI":"10.3390\/su11030695","volume":"11","author":"SY Li","year":"2019","unstructured":"Li SY, Yang X, Li RR (2019c) Forecasting\u00a0coal\u00a0consumption\u00a0in\u00a0India\u00a0by\u00a02030:using linear modified linear\u00a0(MGM-ARIMA)\u00a0and linear\u00a0modified\u00a0nonlinear\u00a0(BP-ARIMA) combined\u00a0models. Sustaina bility 11:695\u2013713","journal-title":"Sustaina bility"},{"issue":"4","key":"3845_CR13","doi-asserted-by":"publisher","first-page":"734","DOI":"10.1016\/j.engappai.2012.01.001","volume":"25","author":"YH Lin","year":"2012","unstructured":"Lin YH, Chiu CC, Lee PC, Lin YJ (2012) Applying fuzzy grey modification model on inflow forecasting. Eng Appl Artif Intell 25(4):734\u2013743","journal-title":"Eng Appl Artif Intell"},{"issue":"8","key":"3845_CR14","first-page":"172","volume":"24","author":"JF Liu","year":"2016","unstructured":"Liu JF, Liu SF, Fang ZG (2016) A class of new weakening buffer operators whose adjustable intensity can be changed and their applications. Chin J Manag Sci 24(8):172\u2013176","journal-title":"Chin J Manag Sci"},{"key":"3845_CR15","doi-asserted-by":"publisher","first-page":"206","DOI":"10.1016\/j.neucom.2015.11.032","volume":"177","author":"JS Lu","year":"2016","unstructured":"Lu JS, Xie WD, Zhou HB, Zhang AJ (2016) An optimized nonlinear grey Bernoulli model and its applications. Neurocomputing 177:206\u2013214","journal-title":"Neurocomputing"},{"issue":"2","key":"3845_CR16","first-page":"113","volume":"9","author":"YS Ma","year":"1993","unstructured":"Ma YS, Dai YZ (1993) Improvement of data generation method in grey system. Syst Sci Compr Stud Agric 9(2):113\u2013116","journal-title":"Syst Sci Compr Stud Agric"},{"key":"3845_CR17","doi-asserted-by":"publisher","first-page":"33","DOI":"10.1016\/j.compag.2012.03.007","volume":"85","author":"SL Ou","year":"2012","unstructured":"Ou SL (2012) Forecasting agricultural output with an improved grey forecasting model based on the genetic algorithm. Comput Electron Agric 85:33\u201339","journal-title":"Comput Electron Agric"},{"issue":"15","key":"3845_CR18","first-page":"47","volume":"39","author":"WY Qian","year":"2009","unstructured":"Qian WY, Dang YG, Wang YM (2009) GM(1, 1) model based on weighting accumulated generating operation and its application. Math Pract Theory 39(15):47\u201351","journal-title":"Math Pract Theory"},{"issue":"1","key":"3845_CR19","first-page":"88","volume":"19","author":"T Song","year":"2004","unstructured":"Song T (2004) The accumulated generating space. J Shandong Inst Archit Eng 19(1):88\u201390","journal-title":"J Shandong Inst Archit Eng"},{"issue":"1","key":"3845_CR20","first-page":"66","volume":"19","author":"ZM Song","year":"2001","unstructured":"Song ZM, Deng JL (2001) The accumulated generating operation in opposite direction and its use in grey model GOM(1,1). Syst Eng 19(1):66\u201369","journal-title":"Syst Eng"},{"issue":"5","key":"3845_CR21","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/S1006-706X(10)60001-5","volume":"16","author":"Q Song","year":"2009","unstructured":"Song Q, Wang AM (2009) Simulation and prediction of alkalinity in sintering process based on grey least squares support vector machine. J Iron Steel Res 16(5):1\u20136","journal-title":"J Iron Steel Res"},{"issue":"4","key":"3845_CR22","first-page":"634","volume":"19","author":"GW Stewart","year":"1977","unstructured":"Stewart GW (1977) On the perturbation of pseudo-inverses, projections and linear least squares problems. Slam Rev 19(4):634\u2013662","journal-title":"Slam Rev"},{"key":"3845_CR23","doi-asserted-by":"publisher","first-page":"369","DOI":"10.1016\/j.tourman.2015.07.005","volume":"52","author":"X Sun","year":"2016","unstructured":"Sun X, Sun WS, Wang JZ, Zhang YX, Gao YN (2016) Using a grey-Markov model optimized by Cuckoo search algorithm to forecast the annual foreign tourist arrivals to China. Tour Manag 52:369\u2013379","journal-title":"Tour Manag"},{"issue":"8","key":"3845_CR24","doi-asserted-by":"publisher","first-page":"5640","DOI":"10.1016\/j.eswa.2010.02.048","volume":"37","author":"YH Wang","year":"2010","unstructured":"Wang YH, Dang YG, Li YQ, Liu SF (2010) An approach to increase prediction precision of GM(1,1) model based on optimization of the initial condition. Expert Syst Appl 37(8):5640\u20135644","journal-title":"Expert Syst Appl"},{"key":"3845_CR25","doi-asserted-by":"publisher","first-page":"482","DOI":"10.1016\/j.asoc.2017.04.022","volume":"57","author":"QR Wang","year":"2017","unstructured":"Wang QR, Liu L, Wang S, Wang JZ, Liu M (2017) Predicting Beijing\u2019s tertiary industry with an improved grey model. Appl Soft Comput 57:482\u2013494","journal-title":"Appl Soft Comput"},{"issue":"5","key":"3845_CR26","doi-asserted-by":"publisher","first-page":"1215","DOI":"10.1007\/s00521-014-1605-1","volume":"25","author":"LF Wu","year":"2014","unstructured":"Wu LF, Liu SF, Cui W, Liu DL, Yao TX (2014) Non-homogenous discrete grey model with fractional-order accumulation. Neural Comput Appl 25(5):1215\u20131221","journal-title":"Neural Comput Appl"},{"key":"3845_CR27","doi-asserted-by":"publisher","first-page":"327","DOI":"10.1016\/j.energy.2018.05.147","volume":"157","author":"LF Wu","year":"2018","unstructured":"Wu LF, Gao XH, Xiao YL, Yang YJ, Chen XN (2018) Using a novel multi-variable grey model to forecast the electricity consumption of Shandong province in China. Energy 157:327\u2013335","journal-title":"Energy"},{"issue":"1","key":"3845_CR28","first-page":"187","volume":"38","author":"N Xu","year":"2018","unstructured":"Xu N, Dang YG (2018) Characteristic adaptive GM(1,1) model and forecasting of Chinese traffic pollution emission. Syst Eng Theory Pract 38(1):187\u2013196","journal-title":"Syst Eng Theory Pract"},{"issue":"10","key":"3845_CR29","first-page":"21","volume":"33","author":"BH Yang","year":"2003","unstructured":"Yang BH, Zhang ZQ (2003) The grey model has been accumulated generating operation in reciprocal number and its application. Math Pract Theory 33(10):21\u201326","journal-title":"Math Pract Theory"},{"issue":"1","key":"3845_CR30","doi-asserted-by":"publisher","first-page":"141","DOI":"10.3233\/JIFS-151249","volume":"32","author":"Bo Zeng","year":"2017","unstructured":"Zeng Bo (2017) Forecasting the relation of supply and demand of natural gas in China during 2015\u20132020 using a novel grey model. J Intell Fuzzy Syst 32(1):141\u2013155","journal-title":"J Intell Fuzzy Syst"},{"key":"3845_CR31","doi-asserted-by":"publisher","first-page":"810","DOI":"10.1016\/j.energy.2016.06.090","volume":"112","author":"B Zeng","year":"2016","unstructured":"Zeng B, Li C (2016) Forecasting the natural gas demand in China using a self-adapting intelligent grey model. Energy 112:810\u2013825","journal-title":"Energy"},{"key":"3845_CR32","doi-asserted-by":"publisher","first-page":"272","DOI":"10.1016\/j.energy.2016.04.009","volume":"107","author":"HR Zhao","year":"2016","unstructured":"Zhao HR, Guo S (2016) An optimized grey model for annual power load forecasting. Energy 107:272\u2013286","journal-title":"Energy"},{"issue":"8","key":"3845_CR33","first-page":"140","volume":"25","author":"WJ Zhou","year":"2017","unstructured":"Zhou WJ, Zhang HR, Dang YG, Wang ZX (2017) New information priority accumulated grey discrete model and its application. Chin J Manag Sci 25(8):140\u2013148","journal-title":"Chin J Manag Sci"}],"container-title":["Soft Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00500-019-03845-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00500-019-03845-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00500-019-03845-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,2,19]],"date-time":"2020-02-19T19:15:05Z","timestamp":1582139705000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00500-019-03845-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,2,20]]},"references-count":33,"journal-issue":{"issue":"23","published-print":{"date-parts":[[2019,12]]}},"alternative-id":["3845"],"URL":"https:\/\/doi.org\/10.1007\/s00500-019-03845-3","relation":{},"ISSN":["1432-7643","1433-7479"],"issn-type":[{"value":"1432-7643","type":"print"},{"value":"1433-7479","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,2,20]]},"assertion":[{"value":"20 February 2019","order":1,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Compliance with ethical standards"}},{"value":"The authors declare that they have no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}},{"value":"This article does not contain any studies with human participants or animals.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethical approval"}}]}}