# Robust Grey Relational Analysis-Based Accuracy Evaluation Method
###### Abstract
And due to the dependence of grey relational analysis on the geometric similarity between data to determine the degree of correlation, there are limitations in the processing of data with highly nonlinear features; moreover, grey relational analysis may be affected by data distribution and sample size when determining weights, which may lead to inaccurate weight allocation in some cases, difficulty in accurately reflecting the true correlation between factors in situations with small data volume or low data quality, and may affect the predictive ability of the model [14; 15; 16]. This leads to poorer robustness of the grey relational analysis method against noise and disturbances. Simply adjusting parameters such as the relational coefficient and resolution coefficient in hopes of achieving an approximation between simulation results and actual test results may adversely affect the reliability assessment and applicability of the model; in addition, traditional GRA models are mostly constructed based on sample matrices, and changes in the way the sample matrices are constructed will affect the stability of the results, and most of the models only describe the features from the perspectives of local distances and slopes, which makes it difficult to reflect the overall trend when the data are dispersed [17; 18; 19; 20]. This can result in predictive deviations and limitations in subsequent model evaluations and practical applications [21; 22]. Among the accuracy assessment methods of gray system theory, there are limitations in each method. For example, the gray correlation analysis model mentioned in reference [19] can effectively deal with \"weak information\" and \"gray nature\" data; however, it has certain requirements on the statistical characteristics of the data and the sample size, and the reliability of the results is affected when the non-statistical pattern of the data is obvious or the sample size is insufficient. Reference [23] highlighted that the standardization method in the calculation of grey relative occurrence has a great impact on the test results, and the original standardization method is prone to increasing the weight of the initial data and reducing the accuracy of the results. Although the multivariate gray prediction model in reference [24] has been improved in various ways, traditional models such as GM(1,1) are underperforming in multivariate interaction scenarios, and the MGM(1,n) model has an inherent error mechanism that affects the accuracy of simulated predictions. Overall, the existing accuracy assessment methods need to be improved in model construction, data processing, and result validation, and they need to be flexibly selected and improved according to specific problems and data characteristics in order to improve the reliability of the assessment results. Compared to the previous methods, the proposed method has lower computational complexity and less difficulty in model construction. Unlike previous methods, the pro posed method incorporates both an enhanced interpolation mechanism and bias tolerance control to improve robustness to noise and perturbation and incorporates the effect of relative distance between sequences on accuracy assessment taking into account the sequence geometry instead of relying solely on metrics such as mean deviation, percentage error, and geometric variation for accuracy assessment. For instance, the Mean Absolute Percentage Error (MAPE) is very sensitive to cases where the actual value is close to zero because it is calculated based on a percentage of the actual value, which can result in an infinitely magnified error. In addition, MAPE may have computational problems or lose its meaning when dealing with zero or negative data. Mean Absolute Error (MAE) fails to reflect the direction of the prediction error, i.e., it cannot distinguish whether the error is due to overestimation or underestimation.