Calculating Criteria Weights Using the Rank Order Centroid Method when the Ranks are Guided by the Entropy Method
Received: 30 July 2025 | Revised: 19 August 2025 and 10 September 2025 | Accepted: 11 September 2025 | Online: 9 November 2025
Corresponding author: Hoang Xuan Thinh
Abstract
This study proposes a novel weighting approach for solving multi-objective optimization problems, called Entropy and Rank Order Centroid (ER) weighting, that integrates data-driven and preference-based weighting principles. The method consists of two sequential stages. In the first stage, the Entropy method is applied to the decision matrix to establish the priority ranking of the criteria based on their information content. In the second stage, this ranking is used to compute the final criteria weights through the Rank Order Centroid (ROC) method. To assess its effectiveness, the ER method was evaluated using a representative multi-objective optimization case: the selection of polishing machines. The results show that ER provides clear advantages over the conventional Entropy method, particularly in ensuring the stability of alternative rankings within multi-objective optimization problems.
Keywords:
multi-objective optimization, weighting method, entropy method, Rank Order Centroid (ROC) method, Entropy and ROC (ER) methodDownloads
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Copyright (c) 2025 Nguyen Trong Mai, Nguyen Chi Bao, Duong Van Duc, Tran Van Trung, Hoang Xuan Thinh
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