An Improved Nonhomogeneous Grey Model with Fractional-Order Accumulation and Its Application

Abstract

The nonhomogeneous grey model has been seen as an effective method for forecasting time series with approximate nonhomogeneous index law, which has been widely used in diverse disciplines on account of its high prediction precision. However, there remains room for improvements. For this, this study presents an improved nonhomogeneous grey model by incorporating the dynamic integral mean value theorem and fractional accumulation simultaneously. In order to promote the efficacy of the optimised model, we apply the whale optimization algorithm (WOA) to ascertain its optimal parameter. In particular, two examples are conducted to validate the superiority of the proposed model in contrast with other benchmarks, and the experimental results show that the mean absolute percentage error of the proposed approach is 808692% and 6.0706%, respectively, indicating the proposed approach performs better than other competing models.

Ishikawa Diagram, Gray Numbers and Pareto Principle for the Analysis of the Causes of WEEE Production in Cameroon: Case of SMEs Implementing ISO 14001:2015

“…GST has been applied as a method to predict waste emissions. Liu et al [50] proposed and applied the fractional-order reverse accumulative grey forecasting model (FRAG-GM(l,l)) to predict the sulfur-dioxide emissions in waste gas in Beijing. Duman et al [51] presented a grey multivariate model for WEEE prediction.…”

Investigating economic replacement policy under uncertainty for managerial application based on grey-reliability approach using QCC

“…Memon et al (2015) merged grey system theory and uncertainty theory to develop a novel tool for evaluating supplier selection problem. Liu et al (2015a) presented a fractional reverse accumulative grey Verhulst model to improve the stability and the prediction accuracy of the system characteristics. Chu et al (1998) decided the system maintenance policy based on predictive maintenance by developing a global approach to determine the optimal policy for maintenance.…”

“…production management, forecasting, transportation management, system control and decision making (Cui et al, 2016;Li et al, 2016;Guo et al, 2016). Some basic definitions for representing grey system, grey set and grey number in grey theory are as follows (Khuman et al, 2016;Liu et al, 2015a;Datta et al, 2013): Definition 1. Grey set theory is an estimation methodology, which assists in projecting and revealing the state of a system by representing it in terms of grey number and grey variables to embrace uncertain information.…”

“…(2015) merged grey system theory and uncertainty theory to develop a novel tool for evaluating supplier selection problem. Liu et al (2015a) presented a fractional reverse accumulative grey Verhulst model to improve the stability and the prediction accuracy of the system characteristics. Chu et al .…”

A New Grey Prediction IANGM (1,1, k, k2) Model

“…Due to the existence of different characteristics of data in real life, most of the models constructed by such methods cannot achieve better modeling results. Therefore, scholars have studied the optimization methods of the model from different angles and integrated the research methods: First, the improvement of the model, such as optimizing the grey derivative [9,10], the grey action [11][12][13], etc; the second is the improvement of the sequence generation method, such as reverse accumulation [14][15][16][17][18][19]and one-time accumulation [20,21]. These new optimization methods have achieved certain practical application results and further broadened the application scope of the grey model.…”