Evaluation and Comparison of Data Pre-Processing Transformer for Grey Relational Analysis

Chao-Lieh Pan ； Ying-Fang Huang ； Grier Lin

《Journal of Grey System》 7卷2期 (2004/12) Pp. 65-74

https://doi.org/10.30016/JGS.200412.0001

並列摘要

In multiple criteria decision-making, the difference between the units for each selection targets will affects a decision results, or even let to an incorrect one. Standard processing or pre-processing must be applied to all selection targets to standardize the units; that is, the units of all targets in the decision matrix are transformed into standard value without quantity and difference. In the Grey relational analysis, this is called data pre-processing or Grey relational generating. It aims to transform incomparable serials in a complete set of serials into comparable data for pre-processing to ensure that important factors are not neglected and no incorrect decision is made.
This study applies Grey relational analysis as a theoretical basis for conventional data pre-processing and linear data pre-processing, It calculates the Grey relation grade between two transformers and compares consistency between the best serial positions for these two data pre-processing transformers, the Spearman classic correlation coefficient among serial positions the Spearman rank order correlation coefficient of transformers and transformers' MSEs. A smaller MSE indicates that the bias and variance of the data are smaller, thus implying a better estimator.
Using EXCEL's random number generator, this study generates 24000 data (x(subscript ij)) to execute 50 times in the Grey under the conditions of n=30, n=20 and n=10 separately in the Grey relational analysis. The results indicate high replacement in the conventional data pre-processing transformer and the linear data pre-processing transformer. Additionally, for data structure, the MSE of the conventional data pre-processing transformer is smaller and with high accuracy in the serial ranking of transformer. Therefore, conventional data pre-processing should be adopted in the evaluation and selection of the best decision alternative through Grey relational analysis.

並列關鍵字

Grey relational analysis ； Multiple criteria decision making (MCDM) ； Mean squared error (MSE) ； Spearman classic correlation coefficient