Grey relational analysis model with cross-sequences and its application in evaluating air quality index

It is important to detect the internal operating regularity in system developing with poor information. To identify the real relationship among multi factors, we propose a grey relational analysis (GRA) method inspired by the characteristics of sequences variation. The proposed model considers the changes of fluctuating sequences like cross-sequences both in domain time and between time intervals. To obtain the quantitative change about sequences, relative angle change is employed to determine the variation in each interval, and the relative angle oscillation change is utilized for measuring variations between intervals. To find the optimal time lag or time intervals, the corresponding cycles are extracted by time-delay models. The reliability of the proposed models will be verified through cases in identifying crucial factors for air quality, and the final detection will then be made. To compare with existing representative GRA models clearly, the relation between two fluctuating sequences shaped in cross-sequences is examined by the proposed model. The empirical results show that the relation degree between pollutants and air quality is reasonable. The compared experiment shows that the GRA for cross-sequences can effectively identify the relationship among fluctuating sequences and the impact of time-delay is small for the proposed model with similar shapes.