ArticleEntropy (Basel, Switzerland)2024
Impact of Normalization on Entropy-Based Weights in Hellwig's Method: A Case Study on Evaluating Sustainable Development in the Education Area.
Article in Entropy (Basel, Switzerland), 2024. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 5 papers.
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5 citing papers in PubMed.
- An integrated framework for evaluating sustainable outcomes of vocational college graduates under ethnic heterogeneity and unequal college level resource allocation.Scientific reports · 2026Article
- Entropy and Normalization in MCDA: A Data-Driven Perspective on Ranking Stability.Entropy (Basel, Switzerland) · 2026Article
- Article
- Dynamic Evolution and Convergence of the Coupled and Coordinated Development of Urban-Rural Basic Education in China.Entropy (Basel, Switzerland) · 2025Article
- Evaluating and enhancing the service capacity of secondary public hospitals in urban China: a multi-method empirical analysis based on Guangzhou (2019-2023).Frontiers in health services · 2025Article
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Abstract
Determining criteria weights plays a crucial role in multi-criteria decision analyses. Entropy is a significant measure in information science, and several multi-criteria decision-making methods utilize the entropy weight method (EWM). In the literature, two approaches for determining the entropy weight method can be found. One involves normalization before calculating the entropy values, while the second does not. This paper investigates the normalization effect for entropy-based weights and Hellwig's method. To compare the influence of various normalization methods in both the EWM and Hellwig's method, a study evaluating the sustainable development of EU countries in the education area in the year 2021 was analyzed. The study used data from Eurostat related to European countries' realization of the SDG 4 goal. It is observed that vector normalization and sum normalization did not change the entropy-based weights. In the case study, the max-min normalization influenced EWM weights. At the same time, these weights had only a very weak impact on the final rankings of countries with respect to achieving the SDG 4 goal, as determined by Hellwig's method. The results are compared with the outcome obtained by Hellwig's method with equal weights. The simulation study was conducted by modifying Eurostat data to investigate how the different normalization relationships discovered among the criteria affect entropy-based weights and Hellwig's method results.
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