Unlock Objective Decision-Making with the Entropy Weight Method (EWM)

1 Entropy Weight Method

Entropy Weight Method is an effective way to accurately measure the relative importance of identified criteria. Originating from thermodynamics, it later developed for information systems. The concept of information entropy includes uncertainty of signals in communication. The basis of EWM is calculating the information amount of indicator weights, similar to other methods, aiming to determine weights objectively.

EWM is an important information weight model that has been widely researched and applied. Compared with various subjective weighting models, EWM's biggest advantage is avoiding human interference on indicator weights, thus enhancing objectivity of comprehensive evaluation results; consequently, EWM has been widely used in decision making in recent years.

For example, Wu et al. evaluated the water quality of Shahu Lake, providing valuable information for decision making. Based on EWM, Zhang and Wang assessed pressure factors and efficiency of water resource management measures in Chongqing.

EWM evaluates value by measuring the degree of differentiation. The higher the dispersion of measurement values, the higher the differentiation of the indicator, and the more information can be obtained, so the indicator should be assigned a higher weight, and vice versa.

According to previous literature, EWM results are relatively reliable and effective.

2 Evaluation Process

The method sets m indicators and n samples; the measurement value of the i‑th indicator of the j‑th sample is denoted as x ij .

- Step 1: Standardization

The first step is to standardize the measurement values. The standardized value of the i‑th indicator for the j‑th sample is denoted as z ij , calculated as follows:

- Step 2: Calculate the entropy of each indicator

...

- Step 3: Calculate weights

The entropy value ranges from [0,1]. The larger it is, the greater the differentiation of the indicator and the more information obtained, thus the weight should be increased. In EWM, the weight w i is calculated as:

...

Thus we obtain the indicator weights through EWM. Because the process is entirely based on data information and does not rely on subjective assignment, the resulting weights are relatively objective.

3 Summary

This article briefly introduced the concept and basic process of the Entropy Weight Method.

References

Dehdasht, Gholamreza, et al. "A hybrid approach using entropy and TOPSIS to select key drivers for a successful and sustainable lean construction implementation." PLoS ONE 15.2 (2020): e0228746.

Zhu, Yuxin, Dazuo Tian, and Feng Yan. "Effectiveness of entropy weight method in decision-making." Mathematical Problems in Engineering 2020 (2020).