Abstract
Entropy weight method (EWM) is a commonly used weighting method that measures value dispersion in decision-making. The greater the degree of dispersion, the greater the degree of differentiation, and more information can be derived. Meanwhile, higher weight should be given to the index, and vice versa. This study shows that the rationality of the EWM in decision-making is questionable. One example is water source site selection, which is generated by Monte Carlo Simulation. First, too many zero values result in the standardization result of the EWM being prone to distortion. Subsequently, this outcome will lead to immense index weight with low actual differentiation degree. Second, in multi-index decision-making involving classification, the classification degree can accurately reflect the information amount of the index. However, the EWM only considers the numerical discrimination degree of the index and ignores rank discrimination. These two shortcomings indicate that the EWM cannot correctly reflect the importance of the index weight, thus resulting in distorted decision-making results.
Highlights
Higher weight should be given to the index. erefore, in the Entropy weight method (EWM), the calculation method of weight wi is [1, 19]
Of the five participating water sources, only Water 1 was rated excellent in all three criteria
The weight of NH3, the smallest among all the indicators, had the highest degree of discrimination and grade discrimination, which was only 0.119. e weights in Table 3 were opposite of the reasonable weight ranking discussed above
Summary
In this method, m indicators and n samples are set in the evaluation, and the measured value of the ith indicator in the jth sample is recorded as xij. E standardized value of the ith index in the jth sample is denoted as pij, and its calculation method is as follows: pij. Given that CODMn, NH3, and sulfide are the indicators with smaller and better values than other indicators, their water quality index can be calculated as follows: WQIij. li1 ≤ xij ≤ ri[1], li2 < xij ≤ ri[2], li3 < xij ≤ ri[3], li4 < xij ≤ ri[4], li5 < xij ≤ ri[5].
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