Effects of the entropy weight on TOPSIS

Abstract

The Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) is a classical multi-attribute decision-making method, which is widely used in various fields for decision-making or evaluation. The entropy method (EM) is frequently used in determining attribute weights for TOPSIS, and the weight determined by the EM is always called entropy weight (EW). In this paper, based on a large number of data and theoretical analysis, the effects of the EW on TOPSIS are analyzed. It is found that the EW can enhance the function of the attribute with the highest diversity of attribute data (DAD) as well as weaken the function of the attributes with a low DAD in decision-making or evaluation. Sometimes the EW even causes the decision-making or evaluation result to be seriously affected by the attribute with the highest DAD (called primacy attribute, abbreviated as PA). Since the EW can enhance the function of the PA in decision-making or evaluation, it is conducive to increase the dipartite degree of the relative closeness (RC), but reduces the comprehensiveness of the RC, and may even lead to unreasonable decision-making or evaluation result. In order to adjust the effects of the EW on TOPSIS, the entropy-based TOPSIS with adjustable weight coefficient is proposed in this paper. Some discussions on the application of the proposed method are also given.