Effects of normalization on the entropy-based TOPSIS method

By Pengyu Chen. Expert systems with applications, 2019

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Abstract In this paper, the frequently used normalization methods for the entropy method (EM) and the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) when these two methods are used in combination with each other are summarized. Taking information entropy (IE) as an indicator to measure the diversity of attribute data (DAD), the effects of normalization on the entropy-based TOPSIS method are analyzed. It is found that normalization can affect the decision result by affecting the DAD, while the DAD affects the contribution of attributes to the distance of each alternative from the ideal solution and the negative ideal solution, manifested in that the higher the DAD is, the bigger the contribution of the attribute will be. It is proved that vector normalization (VN) and sum normalization (SN) will not change the DAD, whereas min-max normalization (MMN) not only will change the DAD, but also may cause the appearance of numerous zero values, finally resulting in the fact that the calculated results of IE cannot represent the diversity of raw data. Therefore, normalization is not suggested for the EM, and VN is suggested for TOPSIS method. Some discussions on the combinability between the EM and TOPSIS method are also given as well as the applicability of different normalization methods in TOPSIS method.

Subfields: Artificial Intelligence, Computational Theory and Mathematics, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/520fa16c3a5ff76595b24e9516bf435668a4d84f