| Summary: | The recent increase in the road transportation necessitates scheduling to reduce the adverse impacts of the road transportation and evaluate the effectiveness of previous actions taken in this context. However, it is impossible to undertake the scheduling and evaluation tasks unless previous information are available to predict the future. The grey model requires a limited volume of data for estimating the behavior of an unknown system. It provides high-accuracy predictions based on few data points. Various grey prediction models have been proposed so far, in which three different approaches are followed to increase the accuracy: (1) data preprocessing, (2) improved equation models, and (3) error improvement or error balancing. In this paper, firstly, a theorem is proposed and proved to recognize the parameters affecting two grey models, namely GM(1, 1) and FGM(1, 1). Then, the effective parameters are adjusted through particle swarm optimization (PSO) to formulate two adjusted models, namely IGM(1, 1) and IFGM(1, 1). According to the simulation results of the proposed models, accuracy of the modeling improved by a minimum of 14.24% and a maximum of 82.39%. Finally, the number of users of a public road transportation system was predicted using the proposed models. The results showed enhanced accuracy (by 7.7%) of the proposed models for predicting the number of users of the public road transportation system.
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