Journal of Grey System, VoL?, No.2, 65-74
Evaluation and Comparison of Data Pre-Processing
Transformer for Grey Relational Analysis
Chao-lieh Pan, Ying-Fang Huang and Grier lin
ABSTRACT
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, Itcalculates 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
Corresponding Author: Chao-Lieh Pan is with University of SouthAustralia
Tel:+886-7-582414lExt.2163 E-mail address:229385@cpc.com.tw
( ) 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.
Keywords: Grey relational analysis, Multiple criteria decision making (MCDM), Mean squared error (MSE), Spearman classic correlation coefficient
1. Introduction
Multiple criteria decision making (MCDM) ranks feasible alternatives in order of preference according to the characteristics of each attribute of every alternative, and evaluate and select one alternative that conforms the decision maker's ideal [1]. In multiple criteria decision-making, the hierarchical additive weighting method, the simple additive weighting method, ELECTRE and TOPSIS have been commonly applied. the last ten years, Grey relational analysis of grey system theory, proposed by Ju-Long Deng has been used to handle uncertain information related to management. Grey relational analysis involves simple calculations, and so is widely applied in the
of management.
December 2004, Vol. 7 No.2I 65
