A multi-granularity decision tree algorithm based on variable precision rough sets and Zentropy

The existing decision tree algorithms often use a single-layer measure to process data, which cannot fully consider the complex interactions and dependencies between different granularity levels. In addition, decision tree algorithms inevitably face the issue of multi-value preference, which may lead to the selection of unreasonable attributes in the process of partition, thereby affecting the performance of the algorithms. Therefore, this paper proposes an improved decision tree algorithm, called Ze-VNDT, which combines variable precision rough sets with Zentropy. First, to avoid the information loss caused by data discretization, this paper introduces variable precision neighborhood rough sets for data processing. Second, by analyzing the granularity level structure within the variable precision neighborhood rough set model, knowledge uncertainty is analyzed from three granularity levels: decision classes, approximate relations, and similarity classes. We describe the uncertain knowledge from the overall to the internal using the idea of going from coarse to fine, and design a Zentropy to measure uncertainty. To address the issue of multi-value preference, an adaptive weighted Zentropy uncertainty measure is designed based on the definition of uncertainty measure based on Zentropy. Third, when constructing the improved decision tree algorithm, the optimal attributes are selected based on the designed uncertainty measure. Finally, numerical experiments on 18 UCI datasets validated the effectiveness and rationality of the proposed algorithm. The experimental results showed that, compared to traditional algorithms and the latest improved algorithms, the proposed algorithm achieved an average accuracy of 94.79%, an average precision of 85.77%, an average recall rate of 84.68%, and an F1-score of 84.97% across the 18 datasets. It ranked first in all five evaluation metrics, demonstrating higher stability and accuracy.