Adaptive Balanced Entropy Weighting for Mitigating Criterion Weight Imbalance in Multi-Criteria Decision Making
Multi-Criteria Decision Making (MCDM) relies on criterion weights to represent the relative importance of evaluation criteria in ranking alternatives. However, conventional Entropy Weighting may generate highly imbalanced weights when criteria exhibit substantially different levels of information variation, potentially causing excessive dominance of particular criteria. This study proposes Adaptive Balanced Entropy (A-Entropy), an objective weighting method that integrates the information-based principle of Entropy Weighting with an adaptive balancing mechanism. The method derives entropy-based weights, measures weight imbalance using a Weight Imbalance Index, and adaptively adjusts the weights according to the identified imbalance level. The effectiveness of A-Entropy is evaluated through two MCDM case studies involving lecturer selection and leasing customer selection. The resulting weights are compared with conventional Entropy Weighting, while their effects on alternative rankings are evaluated using MOORA and PIV, respectively. The results show that A-Entropy substantially reduces weight concentration in the lecturer selection case, where the highest weight decreases from 0.4368 to 0.3333 and the lowest weight increases from 0.0042 to 0.0665. In the leasing customer selection case, the adjustment is more moderate due to its comparatively lower initial imbalance. Furthermore, A-Entropy produces higher Spearman correlations with the original rankings than Entropy, increasing from 0.8303 to 0.9030 for lecturer selection and from 0.9758 to 0.9879 for leasing customer selection. These findings indicate that A-Entropy reduces excessive criterion weight imbalance while preserving meaningful differences in criterion importance and maintaining high ranking consistency. Therefore, A-Entropy provides an adaptive objective weighting approach for MCDM-based Decision Support Systems.
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