An artificial bee colony-based framework for multi-objective optimization of three-way decisions with probabilistic rough sets

The cogent area, Probabilistic rough sets, offers methods that are used to trisect the data into positive, negative and boundary regions for optimum (alpha, beta) pairs. These basic methods generate three regions based on a single quality, including cost, entropy, impurity, correlation and variance, thereby the best (alpha, beta) pair is generated. The optimization of multiple qualities has significance in real-life applications; however, experiments rarely discussed the optimization of different criteria together in probabilistic rough sets. This probe conducts multi-objective optimization of uncertainty, impurity and correlation, to determine a trisection at optimal (alpha, beta) pairs. For that, this work proposes a hybrid method that involves Weighted Sum and Artificial Bee Colony Algorithm to optimize the thresholds. The results are compared with the Information-theoretic rough sets and Game-theoretic rough sets. The proposed method outperforms regarding optimal qualities, multiple optimum thresholds, minimal size of boundary regions, and better evaluation results. By attesting the study on experimental data sets, optimal (alpha, beta) pairs are obtained at which the uncertainty and impurity are minima. Moreover, the correlation at this threshold is reasonable. From the application viewpoint, it reduces the cost of further analysis by generating the minimum delayed decision and maximizes the benefit with optimal decisions by considering multiple optimized qualities simultaneously.

Automated summary

This study proposes a hybrid method that involves Weighted Sum and Artificial Bee Colony Algorithm to optimize thresholds. The method conducts multi-objective optimization of uncertainty, impurity, and correlation and generates optimal (alpha, beta) pairs for data trisecting. The results show that the proposed method outperforms in terms of optimal qualities, multiple optimum thresholds, minimal size of boundary regions, and better evaluation results compared to Information-theoretic rough sets and Game-theoretic rough sets.