A gray model for increasing sequences with nonhomogeneous index trends based on fractional‐order accumulation. (12th March 2018)

• Record Type: Journal Article
• Authors: Zeng, Liang
• Is Part Of: Mathematical methods in the applied sciences. Volume 41:Number 10(2018)
• Page Start: 3750
• Page End: 3763
• Publication Date: 2018-03-12
• Subjects: 3/8 Simpson formula -- background value -- fractional‐order accumulation -- gray system -- sequence with a nonhomogeneous index trend; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.4862
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : By comparing the class ratio deviation and restoring error of first‐order accumulation with that of fractional‐order accumulation, a gray model for monotonically increasing sequences can obtain optimal simulation accuracy via selecting a proper cumulative order. In this study, a gray model for increasing sequences with nonhomogeneous index trends based on fractional‐order accumulation is proposed. To reduce the modeling error caused by the background value and to improve the prediction accuracy of the model, an optimized model using the 3/8 Simpson formula is constructed. Finally, the 2 proposed models are used to predict the total energy consumption in China and the monthly sales of new products in an enterprise. Compared with the GM(1, 1) model based on fractional‐order accumulation, the proposed model exhibits better simulation and prediction accuracy.