Can Entropy Weight Method Correctly Reflect the Distinction of Water Quality Indices?
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Can Entropy Weight Method Correctly Reflect the Distinction of Water Quality Indices? Qian Bao 1 & Zhu Yuxin 2 & Wang Yuxiao 3 & Yan Feng 4 Received: 13 November 2019 / Accepted: 28 July 2020/ # Springer Nature B.V. 2020
Abstract
Entropy weight method (EWM) is a widely used weighting approach in water quality evaluation that assigns weights according to the discriminating degree of indicators. A higher discrete degree corresponds to a larger weight requirement, and vice versa. By using two water quality evaluation examples, this study proves that the weighting result of EWM cannot accurately reflect the information content and discriminability of indices in many conditions. For the EWM that uses the directly generating quotient (DGQ) in standardization, when the concentration dataset contains many zero values, the EWM results become prone to distortion. Similarly, for the EWM that utilizes the generating quotient after range pretreatment (GQARP) in standardization, when similar maximum values are present in the concentration dataset, the EWM results become prone to distortion. From the distortion weighting results of EWM, those indicators with high pollution degrees can be easily neglected, thereby leading to overoptimistic comprehensive water quality evaluation results. Although the source of distortion in the EWM results can be traced to the standardization and ranging processes, a solution to this problem is not yet available. In sum, the conventional EWM cannot correctly reflect the distinction of water quality indices; and it cannot be directly applied in water quality evaluation. Keywords Entropy weight method (EWM) . Water quality evaluation . Weight distortion
* Yan Feng [email protected]
1
Bureau of Hydrology, Changjiang Water Resources Commission, Wuhan 430010, China
2
School of Hydropower and Information Engineering, Huazhong University of Science and Technology, Wuhan 430074, China
3
School Hydrology and Water Resources, Hohai University, Nanjing 210098, China
4
School of Civil Engineering and Architecture, Nanchang University, Nanchang 330031, China
Bao Q. et al.
1 Introduction The entropy weight method (EWM) represents an important application of information entropy theory in multi-index decision-making problems (Chang et al. 2016; Yang et al. 2017). EWM was first applied in the field of social sciences and was introduced in water quality evaluation by Zou in 2005 (Zou et al. 2006). As its major advantage over subjective weighting models, EWM avoids the interference of human factors during the weighting process, thereby enhancing the objectivity of the comprehensive evaluation results (Taheriyoun et al. 2010; Li et al. 2012; Ding et al. 2017). Therefore, EWM has been widely used in water quality evaluation in recent years (Wang et al. 2007; Wang et al. 2016). For example, Wang et al. (2014) used EWM in a comprehensive water quality assessment of Taihu Lake to provide valuable information about the present aquatic environment for decision making. Li et al. (2016) performed an entropy-based
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