Unlock Objective Decision-Making with the Entropy Weight Method

1 Entropy Weight Method

Entropy Weight Method (EWM) is an effective technique for accurately measuring the relative importance of identified criteria. Originating from thermodynamics, it was later adapted for information systems, where information entropy reflects uncertainty in communication signals. EWM calculates indicator weights based on information content, aiming to determine objective weights.

EWM is a widely researched information weight model. Compared with subjective weighting models, its main advantage is avoiding human bias in indicator weights, thereby enhancing the objectivity of comprehensive evaluation results. Consequently, EWM has been extensively applied in decision‑making.

For example, Wu et al. used EWM to evaluate the water quality of Lake Shahu, providing valuable information for decision‑making. Zhang and Wang applied EWM to assess pressure factors and efficiency of water resource management measures in Chongqing.

EWM evaluates value by measuring the degree of differentiation. The greater the dispersion of an indicator, the more information it provides, and thus the higher its weight, and vice versa.

Literature indicates that EWM results are reliable and effective.

2 Evaluation Process

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

Step 1: Standardization

The first step normalizes 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: Compute the entropy of each indicator

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Step 3: Compute weights

The entropy value ranges from 0 to 1. A larger entropy indicates greater differentiation of the indicator and more information, thus a higher weight. In EWM, the weight w_i is calculated as:

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Thus, the indicator weights obtained by EWM are based entirely on data information without subjective assignment, making them relatively objective.

3 Summary

This article briefly introduced the concept and basic procedure 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).