A novel approach for shortest optimal reduct computation

Rough set theory has emerged as a robust soft computing paradigm for feature selection, commonly known as reduct computation. A decision system may contain multiple reducts of varying sizes, all offering equivalent classification capabilities. However, when model performance is a critical factor, the shortest reduct is generally preferred due to its simplicity and interpretability. The discernibility matrix method is a widely used technique for computing such reducts. Despite its effectiveness, this method is computationally intensive and classified as NP-hard, limiting its scalability for datasets where discernibility matrix computation becomes infeasible. This study addresses the limitations of traditional discernibility matrix-based approaches by introducing a novel method that combines a Breadth-First Search control strategy with an incremental approach to compute the absorbed discernibility matrix. The Breadth First Search strategy enables efficient exploration of the search space to identify the shortest optimal reduct early, while the incremental absorbed discernibility matrix enhances the computational scalability of the algorithm. To validate the proposed method, an experimental evaluation was conducted against two state-of-the-art algorithms: Breadth-First Search, representing the discernibility matrix-based strategy, and MinReduct, a benchmark for absorbed discernibility matrix-based approaches. Results demonstrate superior computational performance and earlier discovery of shortest reducts without compromising correctness or optimality.