An Improved Vague Similarity Measure via Dynamic Weighting and Kernel Divergence

Similarity measures play a crucial role in handling uncertain and indeterminate information in Vague sets. To overcome the limitations of traditional Vague-set similarity models, such as insufficient consideration of indeterminacy and the use of fixed parameter weights, this paper proposes a novel Vague similarity measure that incorporates indeterminacy, adopts a dynamic weight allocation strategy based on Vague entropy, and introduces a kernel divergence term. The proposed measure adaptively adjusts the weights assigned to the truth-membership, falsity-membership, and indeterminacy components, while using kernel divergence to characterize the overall deviation between the truth-membership and falsity-membership degrees. From a theoretical perspective, we rigorously prove that the proposed measure satisfies boundedness, symmetry, and normalization. Experiments are conducted on both small-sample comparative tests and ternary tuples constructed from NASA software defect datasets. Combined with KNN classification and a discrimination index, the proposed method is compared with eight existing similarity measures. The experimental results show that the proposed method generally outperforms traditional approaches in software defect identification metrics such as F1-score, precision, and recall, demonstrating its effectiveness and stability in handling class imbalance and uncertain information in software defect data.